The simulation of a quantum search algorithm in an Ising spin chain is equivalent to solving a system of 2^*L* coupled first order differential equations with *L* being the number of qubits. The near-resonant approximation can be used to simplify the evolution of the states in the database. In this work, we compare the simulation of a quantum search algorithm using the exact evolution according to Schr{\"o}dinger equation and using the near-resonant approximation. Our results show that the error of the near-resonant approximation is comparable to that of the exact evolution in terms of the fidelity measure. The advantage gained in having this small error at the near-resonant approximation is its faster execution time relative to the exact case.

},
author = {Neris D Ilano and Ronald Banzon and Cristine Villagonzalo}
}
@article {baldo2016a,
title = {Spin inverter and polarizer curved nanowire driven by Rashba and Dresselhaus spin-orbit interactions},
journal = {Physica E},
volume = {83},
year = {2016},
note = {cited By 0; Article in Press},
pages = {498-504},
abstract = {We propose in theory a curved nanowire structure that can both serve as a spin inverter and a spin polarizer driven by a periodic Rashba spin{\textendash}orbit coupling (SOC) and a uniform Dresselhaus SOC. The curved section of the U-shaped quasi-one dimensional nanowire with an arc of radius R and circumferential length πR is divided into segments of equal length initially having only its inherent homogeneous Dresselhaus SOC. Then a Rashba-type SOC is applied at every alternating segment. By tuning the Rashba SOC strength and the incident electron energy, this device can flip the spin at the output of an incoming spin-polarized electron. On the other hand, this same device acts as a spin filter for an unpolarized input for which an outgoing electron with a non-zero polarization can be achieved without the application of an external magnetic field. Moreover, the potential modulation caused by the periodic Rashba SOC enables this device to function as an attenuator for a certain range of incident electron energies that can make the probability current density drop to 10^(-4) of its otherwise magnitude in other regimes.

},
doi = {10.1016/j.physe.2015.11.024},
author = {Carlos F Baldo III and Cristine Villagonzalo}
}
@inproceedings {320,
title = {A critically damped quantum search may not necessarily be optimal},
booktitle = {Proceedings of the AQIS Conference 2015},
year = {2015},
month = {24{\textendash}30 Aug 2015},
pages = {147-148},
address = {Korea Institute for Advanced Study, Seoul},
abstract = {We explore the rate at which the target state is obtained in a damped quantum search of an Ising system. As the number of target states is reduced, the damped quantum search gives a higher probability of success than that of the classical search. For any system in general, a new damping parameter was obtained from an optimization of the damped quantum search. Application of the optimum damping parameter per iteration on the damped quantum search shows a significant improvement of the probability of success over the critically damped quantum search.},
url = {http://aqis-conf.org/2015/program/},
author = {Neris D Ilano and Ronald Banzon and Cristine Villagonzalo}
}
@conference {350,
title = {Effect of varying the position of the ancilla qubit and the coupling constants in the simulation of Grover{\textquoteright}s quantum search algorithm},
year = {2015},
month = {7{\textendash}11 Jan 2015},
pages = {P-62},
publisher = {9th International Conference on Computational Physics},
address = {National University of Singapore},
abstract = {We simulate Grover{\textquoteright}s algorithm in an Ising spin chain quantum computer with spatially-dependent coupling constant. The interaction to the nearest and second-nearest neighbor of the spins is considered. The behavior of the fidelity as a function of the number of Grover iteration during the algorithm is determined. For a fixed location of the ancilla qubit, the overall fidelity decreases as we increase the size of the database. Also, as we vary the coupling constant per neighbor, we obtain a high fidelity for a given number of iteration. The simulation of the algorithm using a classical computer system restricts the size of the database that gives a high fidelity result.},
url = {http://www.physics.nus.edu.sg/iccp9/},
author = {Neris D Ilano and Cristine Villagonzalo and Ronald Banzon}
}
@inproceedings {cortez-spp-2015,
title = {Electric field and spin precession effects on spin injection to semiconductors in three-terminal ferromagnet-insulator-nonmagnetic junctions},
booktitle = {Proceedings of the 33rd Samahang Pisika ng Pilipinas Physics Congress},
year = {2015},
month = {3{\textendash}6 Jun 2015},
pages = {SPP-2015-PA-44},
address = {University of Northern Philippines, Vigan City},
abstract = {The application of an electric field and the ensuing spin precession due to internal magnetic fields in the semiconductor of a three-terminal (3T) device is investigated using the standard diffusion theory. Because the externally applied current is confined in one direction in such a device, the effective electric field is assumed to be significant. The dominant precession direction that dictates the spin dynamics is perpendicular to both the injected spins and the electric field. At large effective electric fields, the polarization in the semiconductor is completely drawn from the polarization of the ferromagnet and becomes well-distributed in the semiconductor.

},
author = {April Cortez and Cristine Villagonzalo}
}
@inproceedings {baldo-spp-2015,
title = {Electron spin polarization along a one-dimensional wire with periodic Rashba and uniform Dresselhaus spin-orbit couplings},
booktitle = {Proceedings of the 33rd Samahang Pisika ng Pilipinas Physics Congress},
year = {2015},
month = {3{\textendash}6 Jun 2015},
pages = {SPP-2015-3B-05},
address = {University of Northern Philippines, Vigan City},
abstract = {We investigate the transmission of an electron spin on a one-dimensional wire with a periodic Rashba spin-orbit couplings (SOC) and a constant contribution from a Dresselhaus SOC. The straight wire is divided into initially uniform segments and the Rashba SOC is turned on every alternating segment. Eigenvalues and eigenfunctions for both without and with Rashba SOC segments are analytically derived. From these obtained values, we numerically calculate the net polarization at the output. We find in our result that regardless of the initial spin orientation, the output polarization turns out to be spin-up polarized. The modulation effect of the segment length of the wire via a periodic Rashba SOC is manifested by the appearance of an energy gap whose width increases with larger Rashba coupling strength. On the other hand, the position of the gap can be tuned by setting the strength of the Dresselhaus SOC. We find that for electrons with Fermi energies falling within this gap, the output spin current is unpolarized.

},
author = {Carlos F Baldo III and Cristine Villagonzalo}
}
@inproceedings {itable-spp-2015,
title = {Non-equilibrium collective transport in an Ising chain with Kawasaki dynamics},
booktitle = {Proceedings of the 33rd Samahang Pisika ng Pilipinas Physics Congress},
year = {2015},
month = {3{\textendash}6 Jun 2015},
pages = {SPP-2015-5C-03},
address = {University of Northern Philippines, Vigan City},
abstract = {An Ising chain with Kawasaki spin-exchange dynamics in contact with a heat bath with temporal periodic variation between two temperatures is considered. This environment prohibits the system from attaining thermal equilibrium. We demonstrate here via Monte Carlo simulations that such a case exhibits a Brownian motor type collective transport. This confirms our hypothesis that a cycle of cluster and dispersion of domains with fine tuned parameters, in effect, results into spin transport.

},
author = {Gene Moses M Itable and Cristine Villagonzalo}
}
@conference {349,
title = {Optimal curvilinear transport of a spin-polarized electron with Rashba and Dresselhaus spin-orbit coupling in a uniform magnetic field},
year = {2015},
month = {7{\textendash}11 Jan 2015},
pages = {C3-13},
publisher = {9th International Conference on Computational Physics},
address = {National University of Singapore},
abstract = {The spin-polarized transport of an electron along a curved-one dimensional wire with Rashba and Dresselhaus spin-orbit couplings (SOCs) and a uniform perpendicular magnetic field is considered in this study. Here we analytically derived the appropriate eigenenergies and eigenvalues of the system and numerically determine the output transmission coefficients. Spin polarization, probability current density and conductance are then obtained using transfer matrix approach to examine the dependence of spin transport on the radius, R, of curved wire, on the external magnetic field, B, and on the SOCs strengths.From our results, we find the condition, B ≈ R^(1/3), at which there would be no spin switching regardless of the SOC strengths. A value of R beyond this condition will no longer have a spin reversal. Moreover, for a material with sufficiently strong SOCs, regardless of its type, the effect of the external magnetic field is reduced. The effective SOC strength follows the standard form equation of a circle in which the Rashba SOC and the Dresselhaus SOC are the component coordinates. From here, we optimize the probability current density by properly tuning the Rashba coupling strength for a given value of B, R and Dresselhaus SOC.}, url = {http://www.physics.nus.edu.sg/iccp9/}, author = {Carlos F Baldo III and Cristine Villagonzalo} } @inproceedings {ilano-spp-2015, title = {Simulation of Grover{\textquoteright}s algorithm with position-variation of the ancilla qubit}, booktitle = {Proceedings of the 33rd Samahang Pisika ng Pilipinas Physics Congress}, year = {2015}, month = {3{\textendash}6 Jun 2015}, pages = {SPP-2015-2B-06}, address = {University of Northern Philippines, Vigan City}, abstract = {

We simulate Grover{\textquoteright}s quantum search algorithm in an Ising spin chain quantum computer with nearest and second-nearest neighbor interactions. We determine the optimum Rabi frequency that satisfies the 2πk method by selecting a high fidelity value in the frequency scan for each database size. Also, we vary the position of the ancilla qubit and investigate the effect on the fidelity for different sizes of the database. The behavior of the fidelity as a function of the number of Grover iterations during the algorithm is considered. For a fixed location of the ancilla qubit, the overall fidelity decreases as we increase the size of the database.

},
author = {Neris D Ilano and Ronald S. Banzon and Cristine Villagonzalo}
}
@conference {villagonzalo-qpcmp-2015,
title = {Spectral and thermodynamic properties of two-dimensional electron systems in the quantum Hall regime},
year = {2015},
month = {22{\textendash}23 Apr 2015},
publisher = {Workshop on Theories in Quantum Phenomena and Condensed Matter Physics},
address = {University of the Philippines Los Ba{\~n}os, Laguna},
url = {https://imsp.uplb.edu.ph/index.php/component/content/article/17-imsp-news/research/370-workshop-on-theories-in-quantum-phenomena-and-condensed-matter-physics},
author = {Cristine Villagonzalo}
}
@conference {355,
title = {Fundamental studies and simulation of nanostructured materials},
year = {2014},
month = {13{\textendash}15 Feb 2014},
publisher = {6th Asian Computational Materials Design Workshop},
address = {De La Salle University, Manila},
url = {http://cmdasiaphilippines.wixsite.com/cmd-asia/6th-cmd-programme-day-1},
author = {Cristine Villagonzalo}
}
@inproceedings {baldo-spp-2014,
title = {Magnetoconductance of a spin polarized electron along a curved one-dimensional wire},
booktitle = {Proceedings of the 32nd Samahang Pisika ng Pilipinas Physics Congress},
year = {2014},
month = {17{\textendash}20 Oct 2014},
pages = {SPP2014-1A-6},
address = {University of the Philippines Diliman, Quezon City},
abstract = {In this paper, we revisit our transport studies on the motion of a spin-polarized electron along a curved quantum wire under the presence of a uniform perpendicular magnetic field **B** and both the Rashba and Dresselhaus spin-orbit couplings (SOCs). Then from the previously derived output transmission coefficients, we numerically determine the magnetoconductance of the electron motion along the curved wire. Our results agree with our earlier reports that for large effective SOCs, the effects of **B** on spin switching is reduced. Moreover, we found that for a given energy\ *E*, the desired high MC ratio can be achieved by tuning **B**. Finally, with large *R* the MC reduces significantly due to adiabatic transport.

},
author = {Carlos F Baldo III and Cristine Villagonzalo}
}
@conference {354,
title = {Simulation of Grover{\textquoteright}s algorithm with spatially-dependent coupling constant},
year = {2014},
month = {16{\textendash}25 Sep 2014},
pages = {19},
publisher = {Okinawa School in Physics: Coherent Quantum Dynamics},
address = {Okinawa Institute of Science and Technology, Japan},
abstract = {We simulate Grover{\textquoteright}s algorithm in an Ising spin chain quantum computer with spatially-dependent coupling constant. The simulation shows that the tendency of two distinct states to transition from the same initial state is reduced. The fidelity with the ideal result and the probability of finding the target state are also investigated.},
url = {https://groups.oist.jp/cqd/participants-0},
author = {Neris D Ilano and Cristine Villagonzalo and Ronald Banzon}
}
@article {Baldo201493,
title = {Spin-orbit coupled transport in a curved quantum wire},
journal = {Physica E},
volume = {63},
year = {2014},
note = {cited By 0},
pages = {93-98},
abstract = {We study the interplay of both Rashba and Dresselhaus spin{\textendash}orbit couplings (SOCs) and a uniform perpendicular magnetic field **B** on the transport of a spin-polarized electron along a curved quantum wire. Eigenenergies and eigenfunctions of the system were analytically solved in the presence of both SOCs for a confinement radius R. From the transmission coefficients, the spin transport properties such as spin polarization, probability current density and spin conductance were computed numerically to determine their dependence on the SOCs, **B** and R. We find the condition for **B** that if it is beyond R^{1/3}, no spin reversal will occur. Our results show that for a sufficiently large SOC strength, regardless of its inversion asymmetry origin, the effect of the external magnetic field is reduced. Finding the optimal effective SOC strength is essential in achieving suitable magneto-transport properties for possible spintronic device applications.

},
doi = {10.1016/j.physe.2014.05.013},
author = {Carlos F Baldo III and Cristine Villagonzalo}
}
@inproceedings {ilano-spp-2014,
title = {Working precision in a simulation of Grover{\textquoteright}s algorithm in an Ising spin system},
booktitle = {Proceedings of the 32nd Samahang Pisika ng Pilipinas Physics Congress},
year = {2014},
month = {17{\textendash}20 Oct 2014},
pages = {SPP2014-5A-2},
address = {University of the Philippines Diliman, Quezon City},
abstract = {We consider the simulation of Grover{\textquoteright}s algorithm in an Ising nuclear spin chain computer with first- and second-nearest neighbor interaction. We calculate the fidelity, a measure of the accuracy of the state, as a function of π/2- and π-pulses and investigate the precision of the success probability of the target state. The fidelity is constrained by the set working precision of the computer system, hence we simulate the algorithm using different working precisions. A reduction of precision is also observed as you increase the number of iterations that restricts the size of the database to effectively simulate the algorithm. The amount of decrease is dependent on the decomposition of pulses.

},
author = {Neris D Ilano and Cristine Villagonzalo and Ronald S. Banzon}
}
@inproceedings {suico-spp-2013,
title = {Characteristics of non-spanning clusters in a percolating two-dimensional square lattice},
booktitle = {Proceedings of the 31st Samahang Pisika ng Pilipinas Physics Congress},
year = {2013},
month = {23{\textendash}25 Oct 2013},
pages = {SPP2013-PB-10},
address = {University of San Carlos, Cebu City},
abstract = {A study of interest in site percolation is to determine the characteristics of other clusters formed that do not span a given space. In this work we simulate on a square lattice of size *L* x *L*\ and show the behavior of the mean cluster size and its associated parameters near the percolation threshold. We find that at the percolation threshold the mean cluster size is proportional to *L*^1.656.

},
author = {Joachim Suico and Ronald S. Banzon and Cristine Villagonzalo}
}
@inproceedings {capili-spp-2013,
title = {Determination of the percolation critical exponent as measure of dimension},
booktitle = {Proceedings of the 31st Samahang Pisika ng Pilipinas Physics Congress},
year = {2013},
month = {23{\textendash}25 Oct 2013},
pages = {SPP2013-4C-6},
address = {University of San Carlos, Cebu City},
abstract = {The critical exponent\ β\ related to the percolation probability describes the dimensionality of a specific lattice topology. The\ accurate determination of\ β\ will aid in distinguishing different universality classes. This work describes the fine tuning of the\ Sigma method developed previously by the authors in obtaining\ β. The approach uses the log-log plot of the percolation\ probability versus the difference of the occupation probability and the percolation threshold. Considering a symmetric distribution of points about the midpoint of this plot yields the\ β\ with (1) the lowest standard deviation and (2) the\ appropriate asymptotic behavior for both one and two-dimensional lattices.

},
author = {Micielle N Capili and Ronald S. Banzon and Cristine Villagonzalo}
}
@inproceedings {ilano-spp-2013,
title = {The effect of the Hadamard gate decomposition in the simulation of Grover{\textquoteright}s algorithm},
booktitle = {Proceedings of the 31st Samahang Pisika ng Pilipinas Physics Congress},
year = {2013},
month = {23{\textendash}25 Oct 2013},
pages = {SPP2013-5B-2},
address = {University of San Carlos, Cebu City},
abstract = {Simulation of Grover{\textquoteright}s algorithm in an Ising nuclear spin chain computer with first- and second-nearest neighbor interaction is considered. The most frequently used quantum gate in the algorithm is the Hadamard gate. We investigate the effect of its decomposition into several rotation matrices and numerically calculate the fidelity and probability of success of finding the target state. Using an appropriate decomposition, we obtain a high fidelity for different numbers of iterations. The probability of finding the target state also increased and is much closer to the ideal result.

},
author = {Neris D Ilano and Cristine Villagonzalo and Ronald S. Banzon}
}
@conference {356,
title = {Signatures of Landau level crossings in a two-dimensional electron gas},
year = {2013},
month = {1{\textendash}5 Jul 2013},
pages = {MoP110},
publisher = {20th International Conference on Electronic Properties of Two-Dimensional Systems},
address = {Wroc{\l}aw University of Technology, Poland},
url = {http://www.ep2dsmss.org/},
author = {Rayda Gammag and Cristine Villagonzalo}
}
@inproceedings {baldo-spp-2013,
title = {Spin switching on a quantum wire with spin orbit coupling in a uniform magnetic field},
booktitle = {Proceedings of the 31st Samahang Pisika ng Pilipinas Physics Congress},
year = {2013},
month = {23{\textendash}25 Oct 2013},
pages = {SPP2013-5B-4},
address = {University of San Carlos, Cebu City},
abstract = {In this paper, the interplay of a uniform perpendicular magnetic field and the radius of curvature on the spin transport along a curved quantum wire with Rashba and Dresselhaus spin-orbit interactions is investigated. From the analytic calculations of the system{\textquoteright}s eigenenergies and eigenfunctions, transmission coefficients were numerically determined using transfer-matrix approach and were used to calculate the probability current densities and output polarization. Our results show that the spin orientation of the initially spin-polarized electron can be switched for smaller values of radius of curvature of the curved quantum wire. However, the range of spin switching is largely dependent on the threading magnetic field and on the strength of the spin-orbit interactions.

},
author = {Carlos F Baldo III and Cristine Villagonzalo}
}
@article {Gammag201316,
title = {Two-dimensional electron gas tilt-induced Landau level crossings},
journal = {Solid State Commun.},
volume = {156},
year = {2013},
note = {cited By 1},
pages = {16-20},
abstract = {This work elucidates the novel behavior found in a two-dimensional electron gas (2DEG) under a tilted magnetic field in which the field{\textquoteright}s angle becomes the dominant factor in tuning the spin-splitting rather than the strength of the spin-orbit interaction. The 2DEG eigenvalues are derived with Rashba and Zeeman interactions for various tilt angles and they show crossing-free levels except at very high tilt. Moreover, concomitant with the crossings is the appearance of beats in the 2DEG density of states. The crossings from different levels occur consecutively at around 87{\textdegree}. Similar new observations in Shubnikov{\textendash}de Haas experimental measurements by Hatke et al. (2012) [6] attributed such phenomena to an in-plane-magnetic-field-induced increase in the effective mass. We show here that this behavior is inherent to a 2DEG where spin{\textendash}orbit interaction and the in-plane magnetic field contribution are taken into account.

},
doi = {10.1016/j.ssc.2012.12.006},
author = {Rayda Gammag and Cristine Villagonzalo}
}
@inproceedings {242,
title = {The effect of RF distribution on the implementation of quantum CN gate in an Ising spin chain},
booktitle = {Proceedings of the 30th Samahang Pisika ng Pilipinas Physics Congress},
year = {2012},
month = {22{\textendash}24 Oct 2012},
pages = {SPP-2012-056},
address = {De La Salle Health Sciences Institute, Dasmari{\~n}as, Cavite},
abstract = {We consider the dynamics of an Ising spin quantum computer with a radio frequency (RF) pulse distribution. The effect of the frequency spread decreases the resonant transition probability and increases thenear-resonant transition probability. Also, we apply the 2πk method to suppress the near-resonant transition. However, it has an unwanted effect on the probability of the resonant transition. It turns out that the desirable result can be obtained if we use the lowest possible value of k.

},
author = {Neris D Ilano and Cristine Villagonzalo and Ronald S. Banzon}
}
@article {Gammag2012,
title = {The interplay of Rashba spin-orbit interaction and Landau level broadening on a two-dimensional electron gas under a tilted magnetic field},
journal = {J. Phys. Conf. Ser.},
volume = {400},
number = {PART 4},
year = {2012},
note = {cited By 0},
pages = {042009},
abstract = {A two-dimensional electron gas in a tilted magnetic field with Rashba spin-orbit interaction (RSOI) was studied. The RSOI is accredited to the asymmetry of the heterostructure where the two-dimensional electron gas is found. The effects of the disorder-attributed Landau level broadening and the RSOI on the spin splitting were identified by simulating the density of states which was assumed to take a Gaussian shape. Increased Landau level broadening obscures the spin splitting and increases the overlap between spin states resulting to stout Gaussian peaks. On the other hand, stronger RSOI amplifies the splitting and lessens the overlap between spin states of the Landau levels. The splitting, however, results to stouter peaks. The similarity in the RSOI and Landau level broadening effects can be explained by recognizing that the asymmetry of the heterostructure is in itself a form of structural disorder.

},
doi = {10.1088/1742-6596/400/4/042009},
author = {Rayda Gammag and Cristine Villagonzalo}
}
@article {BaldoIII2012,
title = {Low-lying spin excitations due to next-nearest neighbour interactions in a ferromagnetic lattice with a body-centred cubic (bcc) crystal structure},
journal = {J. Phys. Conf. Ser.},
volume = {400},
number = {PART 3},
year = {2012},
note = {cited By 0},
pages = {032007},
abstract = {Spin excitations due to the next-nearest-neighbour interactions are investigated for a ferromagnetic lattice with a body-centred cubic (bcc) crystal structure. Using the three-dimensional Heisenberg spin model in a uniform external magnetic field, both the nearest-neighbour (NN) and next-nearest-neighbour (NNN) exchange interactions are considered. The spin wave energies at low temperatures are calculated for which the system is close to its ground state. From the dispersion plots, the additional exchange interactions by the NNN cause an increase in the spin excitation energies. Furthermore, there is a critical NNN/NN exchange ratio for which the effect of the NNN interactions becomes evident as characterized by the presence of two maximum energy peaks in the energy spectra.

},
doi = {10.1088/1742-6596/400/3/032007},
author = {Carlos F Baldo III and Cristine Villagonzalo}
}
@inproceedings {245,
title = {Percolation critical exponent of a constrained lattice},
booktitle = {Proceedings of the 30th Samahang Pisika ng Pilipinas Physics Congress},
year = {2012},
month = {22{\textendash}24 Oct 2012},
pages = {SPP-2012-004},
address = {De La Salle Health Sciences Institute, Dasmari{\~n}as, Cavite},
abstract = {We implement the Average Occupation Probability method to treat site percolation on a square lattice with banned sites. It was found that the introduction of banned sites increases the value of the percolation probability while reducing the value of the critical exponent\ β. The deviation of\ β\ in site percolation of a constrained lattice from that of a regular system suggests that these\ lattice\ topologies belong to two different universality classes.

},
author = {Micielle N Capili and Cristine Villagonzalo and Ronald S. Banzon}
}
@article {Gammag2012,
title = {Persistent spin splitting of a two-dimensional electron gas in tilted magnetic fields},
journal = {Eur. Phys. J. B},
volume = {85},
number = {1},
year = {2012},
note = {cited By 1},
pages = {22},
abstract = {By varying the orientation of the applied magnetic field with respect to the normal of a two-dimensional electron gas, the chemical potential and the specific heat reveal persistent spin splitting in all field ranges. The corresponding shape of the thermodynamic quantities distinguishes whether the Rashba spin-orbit interaction (RSOI), the Zeeman term or both dominate the splitting. The interplay of the tilting of the magnetic field and RSOI resulted to an amplified splitting even in weak fields. The effects of changing the RSOI strength and the Landau level broadening are also investigated.

},
doi = {10.1140/epjb/e2011-20615-x},
author = {Rayda Gammag and Cristine Villagonzalo}
}
@article {Gammag2012757,
title = {Quenching of the DOS beats in a two-dimensional electron gas in tilted magnetic fields},
journal = {Solid State Commun.},
volume = {152},
number = {9},
year = {2012},
note = {cited By 2},
pages = {757-761},
abstract = {A two-dimensional electron gas exposed to a tilted magnetic field is considered with the Rashba spin{\textendash}orbit interaction and the Zeeman effect. An exact solution for the eigenvalues was obtained assuming that two opposite spin states of adjacent Landau levels have equal probability. No crossings between adjacent eigenenergies were observed, for the tilt angles studied here (θ<=80{\textdegree}), unlike in the perpendicular-magnetic-field case. The absence of crossings leads to quenched beating structures in the oscillations of the density of states (DOS). Persistent spin-splittings were observed at the weak magnetic field region. The splittings, however, can be effectively screened by an increased Landau level broadening. The results shed light on how spins can be controlled through the Rashba interaction strength, the disorder-related broadening and the magnetic field tilt angle.

},
doi = {10.1016/j.ssc.2012.01.047},
author = {Rayda Gammag and Cristine Villagonzalo}
}
@inproceedings {244,
title = {Rashba and Dresselhaus spin-orbit interactions in a curvilinear motion of a spin-polarized electron},
booktitle = {Proceedings of the 30th Samahang Pisika ng Pilipinas Physics Congress},
year = {2012},
month = {22{\textendash}24 Oct 2012},
pages = {SPP-2012-054},
address = {De La Salle Health Sciences Institute, Dasmari{\~n}as, Cavite},
abstract = {To see the effects of both Rashba and Dresselhaus spin-orbit interactions on a spin-polarized electron along a curved path, we obtain the system{\textquoteright}s exact energy spectrum taking into account the Zeeman effect. This approximates the motion of an electron in a one-dimensional wire. Our results show that the lifted degeneracy between spins of opposite polarization does not only depend on both Rashba and Dresselhaus coupling constants, but also on the radius of curvature.

},
author = {Carlos F Baldo III and Cristine Villagonzalo}
}
@inproceedings {248,
title = {Determination of the critical exponent β in site percolation using average occupation probability on a square lattice},
booktitle = {Proceedings of the 29th Samahang Pisika ng Pilipinas National Physics Congress},
year = {2011},
month = {24{\textendash}26 Oct 2011},
pages = {SPP2011-5A-3},
address = {University of the Philippines Diliman, Quezon City},
abstract = {Using the Average Occupation Probability in site percolation, the critical exponent\ β\ for a lattice (L {\texttimes} L) is determined. The results for different lattice\ sizes show that as the lattice becomes larger, the calculated\ β\ agrees better with that obtained from 2D scaling theory. There appears a common\ range of p-pc which can be used for any L to compute for\ β. We estimate that a minimum lattice size of 200 {\texttimes} 200 is necessary for the\ procedure to yield an acceptable value of the critical exponent.

},
url = {https://paperview.spp-online.org/proceedings/article/view/3139},
author = {Micielle N Capili and Cristine Villagonzalo and Ronald S. Banzon}
}
@article {Villagonzalo201143,
title = {The intrinsic features of the specific heat at half-filled Landau levels of two-dimensional electron systems},
journal = {J. Low Temp. Phys.},
volume = {163},
number = {1-2},
year = {2011},
note = {cited By 2},
pages = {43-52},
abstract = {The specific heat capacity of a two-dimensional electron gas is derived for two types of the density of states, namely, the Dirac delta function spectrum and that based on a Gaussian function. For the first time, a closed form expression of the specific heat for each case is obtained at half-filling. When the chemical potential is temperature-independent, the temperature is calculated at which the specific heat is a maximum. Here the effects of the broadening of the Landau levels are distinguished from those of the different filling factors. In general, the results derived herein hold for any thermodynamic system having similar resonant states.

},
doi = {10.1007/s10909-010-0259-3},
author = {Cristine Villagonzalo and Rayda Gammag}
}
@inproceedings {ilano-spp-2011,
title = {Optimizing the damped quantum search algorithm},
booktitle = {Proceedings of the 29th Samahang Pisika ng Pilipinas National Physics Congress},
year = {2011},
month = {24{\textendash}26 Oct 2011},
pages = {SPP2011-4A-4},
address = {University of the Philippines Diliman, Quezon City},
abstract = {An optimization of the damped quantum search is introduced by calculating the damping parameter that gives the minimum probability of failure per iteration. The resulting damping parameter is compared with the critical damping. The result shows that the optimized damping is generally not equal to the critical damping if the degeneracy of the target state is not comparable to the size of the database. The probability of failure for the optimized damping and critical damping does not differ significantly for the first two iterations. This difference is relatively large for the third iteration. This suggests that for greater number of iterations, the critically damped search is not optimized.

},
url = {https://paperview.spp-online.org/proceedings/article/view/3135},
author = {Neris D Ilano and Ronald S. Banzon and Cristine Villagonzalo}
}
@inproceedings {249,
title = {Persistence in the zero temperature dynamics of the 1D Ising model with long range interactions},
booktitle = {Proceedings of the 29th Samahang Pisika ng Pilipinas National Physics Congress},
year = {2011},
month = {24{\textendash}26 Oct 2011},
pages = {SPP2011-PB-33},
address = {University of the Philippines Diliman, Quezon City},
abstract = {We study the zero-temperature dynamics of the 1D Ising Model with long range interactions. In particular, we focus on the persistence behavior as the strength of the long range interaction is varied. Persistence pertains to those spins that did not flip after some time. We observe that whatever the strength of the long range interaction, the system exhibits blocking where some spins do not flip at all. The system size is also varied to see its effect on these properties.

},
url = {https://paperview.spp-online.org/proceedings/article/view/3240},
author = {Hilton Lazo and Ronald Banzon and Cristine Villagonzalo}
}
@conference {358,
title = {Long range disorder effects on the heat capacity of two-dimensional electron systems},
year = {2010},
month = {12{\textendash}15 Dec 2010},
pages = {66-67},
publisher = {9th Asia-Pacific Workshop on Materials Physics},
address = {Hanoi University of Science, Vietnam},
abstract = {Broadening of Landau levels of two dimensional electron systems at low temperature and at high perpendicular magnetic fields causes perceptible variations in their interlevel and intralevel excitations as seen in their heat capacity. At a characteristic temperature, the interlevel excitations become negligible and the effect of a small broadening on the energy spectrum vanishes. In this work, a long-range disorder is considered. This can be modeled for the two-dimensional electron gas via a Lorentzian density of states or a Gaussian density of states whose broadening is much larger than kT. The temperature dependence of the heat capacity is derived at half-filled Landau levels or when the chemical potential is a constant. The heat capacity behavior of a system with a long-range disorder is compared to the case of impurity-free quantum Hall systems.},
url = {http://www.iop.vast.ac.vn/theor/conferences/apwmp/files/Detailed\%20Program.pdf},
author = {Cristine Villagonzalo and Rayda P Gammag}
}
@inproceedings {baldospp2010,
title = {Spin waves in a simple ferromagnetic cubic lattice using the Heisenberg model with nearest and next-nearest neighbor interactions},
booktitle = {Proceedings of the 28th Samahang Pisika ng Pilipinas Physics Congress},
year = {2010},
month = {25{\textendash}27 Oct 2010},
pages = {SPP-2010-006},
address = {Meralco Management and Leadership Development Center, Antipolo City},
abstract = {We study the combined effect of the nearest and the next-nearest neighbor interactions on the spin wave dispersion of an isotropic cubic ferromagnet in a uniform magnetic field using the Heisenberg model. Near the groundstate, the components of the spin angular momentum perpendicular to the applied field are negligible as compared to the parallel spin component. Hence, the dispersion relation and the ground state energy estimate of the system are obtained by considering the spin fluctuations along the plane normal to the magnetic field. The results herein are compared to the case where only the effect of the nearest neighbors are present.

},
author = {Carlos F Baldo III and Cristine Villagonzalo}
}
@inproceedings {257,
title = {Uncertainty relation of the momentum components of a two-dimensional electron system under a tilted magnetic field},
booktitle = {Proceedings of the 28th Samahang Pisika ng Pilipinas Physics Congress},
year = {2010},
month = {25{\textendash}27 Oct 2010},
pages = {SPP-2010-005},
address = {Meralco Management and Leadership Development Center, Antipolo City},
abstract = {A two-dimensional electron gas along the *xy*-plane is considered. When an applied perpendicular magnetic field, directed along the *z*-axis, is turned on, the electrons move in cyclotron orbits and the components of the momentum along the *x*- and *y*-axes do not commute. This work shows that if the applied magnetic field is tilted at an angle\ θ\ with respect to the *z*-axis, the uncertainty in simultaneous measurements of the momentum components becomes dependent on\ θ.

},
author = {Rayda P Gammag and Cristine Villagonzalo}
}
@article {gammag2009a,
title = {Crossover of the specific heat from the quantum Hall to the classical regime},
journal = {AIP Conf. Proc.},
volume = {1119},
year = {2009},
pages = {213},
abstract = {The specific heat, *C _{V}*, of a two-dimensional electron system in the quantum Hall effect (QHE) regime was calculated numerically. A peak was observed at temperature

We seek on 8 and a 12 spins Ising systems at least one of their eigenstates of a certain eigenvalue by applying the damped quantum search. In particular, without the knowledge of the number of degeneracy, it requires 150 queries to find at least one of the characteristic states having an eigenvalue of -11ε in a database of 4096 items with a probability of 99.1\%. The average number of queries are compared with that of the undamped quantum search. It is found that for a small number of target states, the damped quantum search still preserves the quantum results, while for a large number of target states the classical limit is approached. Moreover, the damped quantum search is shown to increase monotonically as the number of iteration is increased.

},
author = {Neris D Ilano and Ronald S. Banzon and Cristine Villagonzalo}
}
@article {jacosalem2009a,
title = {Numerical investigations of symmetric embedded quantum well systems using the shooting method and transfer matrix technique},
journal = {AIP Conf. Proc.},
volume = {1119},
year = {2009},
pages = {219},
abstract = {Embedded quantum well systems are constructed via a superposition of modified P{\"o}schl-Teller (MPT) potentials. To illustrate the advantages and/or disadvantages of each system, a comparison is made on their energy spectra and scattering properties. The bound states of each system are obtained using the numerical shooting method. The accuracy of this method depends on the step length δz, which can be completely controlled, allowing an improved comparison with analytical solutions to be achieved. A systematic approach of finding the eigenenergies En (n = 0, 1, 2, 3, {\textellipsis}) is also developed in this work. The approach utilizes the established bisection method{\textemdash}a root-finding algorithm that repeatedly divides an interval in half then selects the subinterval in which a root exists. Here selective bisection is implemented for computational efficiency. This entire procedure in finding the solutions of the Schr{\"o}dinger equation is tested for a single MPT well where the solution is analytically known. The result shows a perfect agreement between the numerical and the analytical method. The transfer matrix approach is used to obtain the transmission probability of a particle passing through the embedded quantum well systems. This technique also shows a perfect agreement with the analytical solution.

},
doi = {http://dx.doi.org/10.1063/1.3137825},
author = {Naomi Jane Jacosalem and Cristine Villagonzalo}
}
@inproceedings {johnson-spp-2009,
title = {One dimensional migration of DNA in the presence of point particle traps},
booktitle = {Proceedings of the 27th Samahang Pisika ng Pilipinas Physics Congress},
year = {2009},
month = {28{\textendash}30 Oct 2009},
pages = {SPP-2009-071},
address = {Development Academy of the Philippines Convention Center, Tagaytay City},
abstract = {This paper studies the one-dimensional motion of a DNA molecule through a microchannel with a series of point particle electric traps. The three particle molecule model uses three beads connected via harmonic springs in the presence of a Weeks Chandler-Andersen repulsive potential and a Brownian force. Using the stochastic fourth order Runge-Kutta method, the trajectory of the center of mass is observed as the field strengths were varied. System parameters are identified that can impede the flow of a DNA molecule.

},
author = {Sarah Johnson and Cristine Villagonzalo}
}
@inproceedings {gammag-spp-2009,
title = {Sensitivity of the specific heat to the electronic density of states},
booktitle = {Proceedings of the 27th Samahang Pisika ng Pilipinas Physics Congress},
year = {2009},
month = {28{\textendash}30 Oct 2009},
pages = {SPP-2009-062},
address = {Development Academy of the Philippines Convention Center, Tagaytay City},
abstract = {The effect of an anomalous shape of the electronic density of states near the Fermi energy on the specific heat for bulk solids is investigated in this work. The density of states was simulated using a superposition of the usual square-root-energy-dependent function, and an additional Gaussian function centered in the region about the Fermi energy. The results show an enhanced specific heat when the anomalous density of states{\textquoteright} peak is located after but near the Fermi energy. If this peak is narrow, the specific heat displays an extra maximum with temperature. A large specific heat is suitable for applications wherein it is preferred to keep a system at constant temperature despite a large thermal energy exchange with its environment.

},
author = {Rayda P Gammag and Cristine Villagonzalo}
}
@inproceedings {lazo-spp-2009,
title = {Site percolation of a fixed lattice size with growing regions of disallowed occupancy},
booktitle = {Proceedings of the 27th Samahang Pisika ng Pilipinas Physics Congress},
year = {2009},
month = {28{\textendash}30 Oct 2009},
pages = {SPP-2009-036},
address = {Development Academy of the Philippines Convention Center, Tagaytay City},
abstract = {We study site percolation in a rectangular lattice with increasing size of two clumped groups of banned sites. The percolation threshold was found to increase as the size of the banned sites is increased. The results were compared to the previously studied lattice with a system with a single group of clumped banned sites with the same number of available sites for occupation. It was observed that the percolation threshold for the dual case is greater than that of the single case. However, the thresholds follow the same trend as the number of available sites is increased.

},
author = {Hilton Lazo and Cristine Villagonzalo and Ronald S. Banzon}
}
@inproceedings {panganiban-spp-2009,
title = {Thresholds of percolating systems with two symmetric forbidden zones having a constant separation},
booktitle = {Proceedings of the 27th Samahang Pisika ng Pilipinas Physics Congress},
year = {2009},
month = {28{\textendash}30 Oct 2009},
pages = {SPP-2009-034},
address = {Development Academy of the Philippines Convention Center, Tagaytay City},
abstract = {In this paper, we investigate the percolation thresholds for a two-dimensional system with two square banned sites, its topological equivalence with another system with a single square banned site, and the scaling property between their thresholds. An eight-corner check algorithm was implemented to evaluate the percolation of this dual banned sites system. We found that percolation threshold for the dual case follows the same trend as the single case, where the threshold increases as the banned site dimension (*X*) is increased. Our results suggest that the thresholds for the single and dual case are related by some finite scaling laws.

},
author = {Earl Angelo Panganiban and Cristine Villagonzalo and Ronald S. Banzon}
}
@article {villagonzalo2009a,
title = {Women in physics in the Philippines: Quantized yet taking steps toward a mature science culture},
journal = {AIP Conf. Proc.},
volume = {1119},
year = {2009},
pages = {155-156},
abstract = {Scientific culture in the Philippines is young and physics is no exception. There are only four physics PhD-granting universities with research laboratories. More than 10 universities offer a bachelor{\textquoteright}s degree or master{\textquoteright}s degree in Physics. Like the world trend, these physics institutions are male dominated. However, four of the leading universities already have female PhD faculty members in physics occupying positions of an assistant professor or better. On a positive note, female physicists are no longer limited to work in the national capital region but have carved out their careers in other parts of the country. Also, female physicists have spread into other non-physics-degree-granting universities or found work in the industrial sector. The number of female graduates in physics in the undergraduate and graduate level have slowly but steadily increased since 2002. With the observed increase in number, a working group for women in physics in the Philippines was created this year. In order to provide recommendations to regulators and policy makers, the group{\textquoteright}s first step is to monitor the number of female students and physicists, their study and work environments, and the scholarships and opportunities for development that are available to them.

},
doi = {http://dx.doi.org/10.1063/1.3137751},
author = {Cristine Villagonzalo and Jinky Bornales and Jelly Grace Betoya-Nonesa}
}
@inproceedings {gammag-spp-2008,
title = {The 2DES chemical potential: Revealing the link from the classical to the quantum Hall regime},
booktitle = {Proceedings of the 26th Samahang Pisika ng Pilipinas Physics Congress},
year = {2008},
month = {22{\textendash}24 Oct 2008},
pages = {SPP-2008-026},
address = {University of the Phlippines Baguio, Baguio City},
abstract = {A two-dimensional electron system under a magnetic field was studied numerically particularly, the temperature dependence of its chemical potential. For all fillings ν the chemical potential μ saturated to a common value at high temperature T - the classical Hall region. Approaching low T, the quantum Hall regime, μ followed varying paths depending on ν. For the complete fillings, μ showed a knee temperature Tν pointing to the juncture between the two regimes. This crossover, characterized by Tν being constant, indicates the balance between the localization and delocalization effects of the magnetic field and temperature, respectively.

},
author = {Rayda P Gammag and Cristine Villagonzalo}
}
@article {Gammag2008487,
title = {The interplay of Landau level broadening and temperature on two-dimensional electron systems},
journal = {Solid State Commun.},
volume = {146},
number = {11-12},
year = {2008},
note = {cited By 5},
pages = {487-490},
abstract = {This work investigates the influence of low temperature and broadened Landau levels on the thermodynamic properties of two-dimensional electron systems. The interplay between these two physical parameters on the magnetic field dependence of the chemical potential, the specific heat and the magnetization is calculated. In the absence of a complete theory that explains the Landau level broadening, experimental and theoretical studies in literature perform different model calculations of this parameter. Here it is presented that different broadening parameters of Gaussian-shaped Landau levels cause width variations in their contributions to interlevel and intralevel excitations. Below a characteristic temperature, the interlevel excitations become negligible. Likewise, at this temperature range, the effect of the Landau level broadening vanishes.

},
doi = {10.1016/j.ssc.2008.03.042},
author = {Rayda P Gammag and Cristine Villagonzalo}
}
@inproceedings {jacosalem-spp-2008,
title = {Realignment of energy spectra of modified P{\"o}schl-Teller potentials in a composite quantum well-in-a-well system},
booktitle = {Proceedings of the 26th Samahang Pisika ng Pilipinas Physics Congress},
year = {2008},
month = {22{\textendash}24 Oct 2008},
pages = {SPP-2008-021},
address = {University of the Phlippines Baguio, Baguio City},
abstract = {Quantum well-in-a-well (QWW) systems are constructed via a superposition of modified Poschl-Teller potential wells. The systems are constructed such that the bound states of the component side wells correspond exactly to the excited states of the constituent center well. The energy spectra of these systems are obtained using the shooting method. The contribution of each component well on the total number of bound states of the constructed composite system is presented. Results show that the middle component well is the dominant contributor to the total number of bound states of the QWW system. All contributions are accounted for, however, they are shifted relative to the initial energy level.

},
author = {Naomi Jane Jacosalem and Cristine Villagonzalo}
}
@inproceedings {johnson-spp-2008,
title = {Simulation of DNA mobility in one-dimension using the bead-spring model},
booktitle = {Proceedings of the 26th Samahang Pisika ng Pilipinas Physics Congress},
year = {2008},
month = {22{\textendash}24 Oct 2008},
pages = {SPP-2008-138},
address = {University of the Phlippines Baguio, Baguio City},
abstract = {This paper studies the one-dimensional motion of a DNA molecule through a microchannel with a single electric trap. The three particle molecule model uses three beads connected via harmonic springs in the presence of a Weeks-Chandler-Andersen repulsive potential and a Brownian force. Using the stochastic fourth order Runge-Kutta method, the spring constant is sought that allows motion through the microchannel without overlap between the three beads.

},
author = {Sarah Johnson and Cristine Villagonzalo}
}
@inproceedings {amarra-spp-2008,
title = {Simulation of Grover{\textquoteright}s algorithm on a one-dimensional two-level Ising spin system},
booktitle = {Proceedings of the 26th Samahang Pisika ng Pilipinas Physics Congress},
year = {2008},
month = {22{\textendash}24 Oct 2008},
pages = {SPP-2008-004},
address = {University of the Phlippines Baguio, Baguio City},
abstract = {We present an application of Grover{\textquoteright}s search algorithm for quantum computers to the one-dimensional Ising model. In particular, a linear, open ferromagnetic system of four spins is considered, and the algorithm is used to find the six states having energy -ε. By using the Hamiltonian operator, the action of a phase-flipping oracle is defined. An 84\% probability of success is obtained after one iteration.

},
author = {Anthony Amarra and Cristine Villagonzalo and Ronald S. Banzon}
}
@inproceedings {hernal-spp-2008,
title = {Spanning a space in a quasi-one dimensional lattice vs. two-dimensional lattice with square banned sites},
booktitle = {Proceedings of the 26th Samahang Pisika ng Pilipinas Physics Congress},
year = {2008},
month = {22{\textendash}24 Oct 2008},
pages = {SPP-2008-163},
address = {University of the Phlippines Baguio, Baguio City},
abstract = {Percolation thresholds in quasi- one and two dimensional systems were compared. In the former, one-way spanning is employed with a spanning cluster defined as an array that extends horizontally from one end of the lattice to the other. A four-corner checking procedure is introduced in this study to measure the percolation threshold in the corresponding two-dimensional systems with square banned sites (2DSBS). The results indicate that the threshold values from the two methods converge suggesting that the quasi-1D system and the 2DSBS are equivalent topologically.

},
author = {Mary Joyce Hernal and Cristine Villagonzalo and Ronald S. Banzon}
}
@inproceedings {castro-spp-2007,
title = {Analysis of symmetric solutions to the Ginzburg-Landau equations for superconducting films},
booktitle = {Proceedings of the 25th Samahang Pisika ng Pilipinas Physics Congress},
year = {2007},
month = {24{\textendash}26 Oct 2007},
pages = {SPP-2007-177},
address = {University of the Phlippines Los Ba{\~n}os, Laguna},
abstract = {Superconductivity in films in a tangential external magnetic field is simulated using a one-dimensional Ginzburg-Landau (GL) model. A symmetric solution to the GL equations is sought using a central difference approximation. This work will illustrate the behavior of superconducting electrons across thick and thin films for various magnetic field strengths. The Meissner effect for type-1 and type II superconductors is verified.

},
author = {Criswelynn D Castro and Cristine Villagonzalo}
}
@inproceedings {cortez-spp-2007,
title = {Analysis of transient heat conduction on aluminum and iron contacts},
booktitle = {Proceedings of the 25th Samahang Pisika ng Pilipinas Physics Congress},
year = {2007},
month = {24{\textendash}26 Oct 2007},
pages = {SPP-2007-115},
address = {University of the Phlippines Los Ba{\~n}os, Laguna},
abstract = {In this paper, transient temperature profiles for material configurations involving Al-Fe layers in contact with continuous and single pulse heat sources are obtained. A stable and convergent solution is achieved by imposing a suitable Courant-Friedrichs-Lewy (CFL) condition. The magnitude of the effective thermal conductivity of composite materials as compared to their homogeneous counterparts is demonstrated to rise as the number of contacts increases.

},
author = {April D Cortez and Cristine Villagonzalo}
}
@inproceedings {capili-spp-2007,
title = {Calculation of the average occupation probability for spanning cluster formation in site percolation},
booktitle = {Proceedings of the 25th Samahang Pisika ng Pilipinas Physics Congress},
year = {2007},
month = {24{\textendash}26 Oct 2007},
pages = {SPP-2007-192},
address = {University of the Phlippines Los Ba{\~n}os, Laguna},
abstract = {The average occupation probability for spanning cluster formation in square lattice using site percolation was calculated. Starting with an empty lattice, sites were generated using a pseudo-random number generator. A cluster labeling procedure was implemented for the detection of a spanning cluster. Our results show that the average occupation probability decreases linearly with inverse lattice edge length. The average occupation probability{\textquoteright}s extrapolated value of 0.608 as the lattice size approaches infinity is found to be a good estimate of the accepted value for the site percolation threshold in two dimensions equal to 0.598.

},
author = {Micielle N Capili and Cristine Villagonzalo and Ronald S. Banzon}
}
@inproceedings {gammag-spp-2007,
title = {The influence of the level broadening on the chemical potential and the heat capacity of two-dimensional electron system},
booktitle = {Proceedings of the 25th Samahang Pisika ng Pilipinas Physics Congress},
year = {2007},
month = {24{\textendash}26 Oct 2007},
pages = {SPP-2007-179},
address = {University of the Phlippines Los Ba{\~n}os, Laguna},
abstract = {Experiments on two dimensional electron systems (2DES) in a magnetic field show a broadening of an otherwise delta-like density of states. This broadening has been attributed as an effect of impurity scattering, electron-electron interactions, electron transfers into a reservoir of electronic states, or disorder, among others. As this broadening is usually present in 2DES, this work incorporates the Landau level broadening to have a more realistic electron system. Its effect on the chemical potential and the heat capacity is simulated. Under strong magnetic fields *B* and fixed electron concentration, both the chemical potential and the heat capacity are found to oscillate with *B* at constant temperature.

},
author = {Rayda P Gammag and Cristine Villagonzalo}
}
@inproceedings {villagonzalo-spp-2007,
title = {Reduction of the thermal conductivity in a 1D superlattice},
booktitle = {Proceedings of the 25th Samahang Pisika ng Pilipinas Physics Congress},
year = {2007},
month = {24{\textendash}26 Oct 2007},
pages = {SPP-2007-022},
address = {University of the Phlippines Los Ba{\~n}os, Laguna},
abstract = {Many technological applications require solids having very low thermal conductivity. This work demonstrates that this can be achieved for specific layer parameters in a superlattice. The phonon dispersion for thick or uneven layered superlattices is modeled using the harmonic approximation in one dimension (1D). The dispersion curves for superlattices with uneven thickness in layers are characterized by the disappearance of forbidden regions. These gaps are usually found in superlattices having uniform thickness. From these results and assuming a constant phonon mean free path, a marked decrease in the lattice contribution to the thermal conductivity is obtained as a function of layer thickness, mass ratio between the layers or asymmetry in its structure.

},
author = {Cristine Villagonzalo and Jane Dizon}
}
@inproceedings {villagonzalo-spp-2006,
title = {A finite temperature magnetic phase transition in a one-dimensional lattice},
booktitle = {Proceedings of the 24th Samahang Pisika ng Pilipinas Physics Congress},
year = {2006},
month = {25{\textendash}27 Oct 2006},
pages = {SPP-2006-155},
address = {Ateneo de Davao University, Davao City},
abstract = {The effects of a long-range interaction on the magnetization and the heat capacity of a one-dimensional (1D) magnetic ring is studied. In this work, the Monte Carlo method is employed to obtain the equilibrium state of a modified 1D Ising model in a ring geometry having a dipolar interaction of strength *G* between spins. For a ring consisting of ten spins, the critical temperature at which an ordered state is achieved increases with the absolute value of the dipolar strength. A peak in the heat capacity is observed at finite temperatures. Depending on the magnitude of *G*, a phase transition at finite temperature may occur.

},
author = {Cristine Villagonzalo and Gina Rose Tongco}
}
@inproceedings {villagonzalo-spp-2006,
title = {Heat capacity of logistic maps with bidirectional coupling},
booktitle = {Proceedings of the 24th Samahang Pisika ng Pilipinas Physics Congress},
year = {2006},
month = {25{\textendash}27 Oct 2006},
pages = {SPP-2006-22},
address = {Ateneo de Davao University, Davao City},
abstract = {The energy spectra and the heat capacity of two bidirectionally coupled logistics maps obtained from direct numerical simulations are presented. Varying the coupling strength changes the onset of chaos in both maps. In some cases, synchronization in the orbits and heat capacity oscillations of coupled maps are also observed. It is found that the logarithmic-periodic oscillations in the heat capacity of uncoupled logistic maps are no longer observed upon introduction of dissipative coupling.

},
author = {Cristine Villagonzalo and Razel Flores}
}
@inproceedings {gammag-spp-2006,
title = {Thermodynamic properties of a two-dimensional electron gas in the fractional quantum Hall regime},
booktitle = {Proceedings of the 24th Samahang Pisika ng Pilipinas Physics Congress},
year = {2006},
month = {25{\textendash}27 Oct 2006},
pages = {SPP-2006-69},
address = {Ateneo de Davao University, Davao City},
abstract = {We investigate the chemical potential μ and specific heat *CV* of a two-dimensional electron gas at temperatures *T*\<1 K subject to high magnetic fields *B* that correspond to filling factors *ν*\<1. We found out that at *ν*=1/2, the chemical potential is pinned at ℏω_c/2 which is equal to the energy of the first Landau level. The μ(*T*) increases when *ν*\>1/2 and decreases when *ν*\<1/2. This behavior is dictated by the change in the number of states available to the electrons. We also found out that μ(*B*) converged at ℏω_c/2 and this trend has a negligible *T*-dependence. When this behavior of the chemical potential was used in calculating the specific heat at the fractional quantum Hall filling factors, *CV*(*T*) exhibited a humpy behavior as compared to its smoothly increasing trend at the integral quantum Hall regime. This trend is a direct consequence of the discontinuities in the chemical potential.

},
author = {Rayda P Gammag and Cristine Villagonzalo}
}
@inproceedings {vasquez-spp-2005,
title = {Constant perturbation in the tight-binding bands of a single-walled carbon nanotube},
booktitle = {Proceedings of the 23rd Samahang Pisika ng Pilipinas Physics Congress},
year = {2005},
month = {26{\textendash}28 Oct 2005},
pages = {SPP-2005-019},
address = {Central Philippine University, Iloilo City},
abstract = {Using a tight-binding calculation, we explain the origin of a large thermopower *S* in ropes of single-walled carbon nanotubes. We have shown that, by breaking the symmetric energy bands and increasing the overlap energy γ0, a larger *S* can be obtained. We have also found that a 10\% increase in γ0 resulted to a thermopower that is four times as large.

},
author = {Louella Judy Vasquez and Cristine Villagonzalo}
}
@inproceedings {jaramillo-spp-2005,
title = {Constrained percolation in two dimensions},
booktitle = {Proceedings of the 23rd Samahang Pisika ng Pilipinas Physics Congress},
year = {2005},
month = {26{\textendash}28 Oct 2005},
pages = {SPP-2005-130},
address = {Central Philippine University, Iloilo City},
abstract = {The effect of implanting square lattice sites of zero occupation probability at the center of a finite but large square lattice for site percolation was investigated. The introduction of symmetrical forbidden site lattices of different sizes inside 40x40 and 60x60 lattices yield percolation threshold values increasing with the size of the forbidden lattice. It was shown that topology in two dimensions dictates the value of the percolation threshold.

},
author = {Christian Oliver Jaramillo and Cristine Villagonzalo and Ronald Banzon}
}
@inproceedings {delatorre-spp-2005,
title = {Finite difference scheme for hyperbolic heat conduction with continuous and pulsed heat sources},
booktitle = {Proceedings of the 23rd Samahang Pisika ng Pilipinas Physics Congress},
year = {2005},
month = {26{\textendash}28 Oct 2005},
pages = {SPP-2005-015},
address = {Central Philippine University, Iloilo City},
abstract = {The temperature distribution in a region of a one dimensional (1D) semi-infinite slab as defined by the hyperbolic heat equation, is modelled by utilizing the finite-difference approximation for partial-differential equations. The distribution is observed for both pulsed and continuous heat sources for a homogenous medium. The stability of the numerical scheme is determined via the Von-Neumann stability criteria.

},
author = {de la Torre, Agatha and Cristine Villagonzalo}
}
@inproceedings {gammag-spp-2005,
title = {Magnetic field effects on the chemical potential and specific heat of a 2DEG},
booktitle = {Proceedings of the 23rd Samahang Pisika ng Pilipinas Physics Congress},
year = {2005},
month = {26{\textendash}28 Oct 2005},
pages = {SPP-2005-040},
address = {Central Philippine University, Iloilo City},
abstract = {We investigate the effect of the filling factors on the chemical potential and the specific heat of a two-dimensional electron gas in an external magnetic field. At integer and half-integer filling factors *ν* the chemical potential is found to jump with an increment of ℏω_c from one Landau level to the next as the magnetic field is increased. In between these special *ν*{\textquoteright}s the chemical potential tends to infinitesimally increase or decrease in a stepwise manner. This behavior of the chemical potential, in turn, caused the specific heat to vary its behavior with temperature.

},
author = {Rayda P Gammag and Cristine Villagonzalo}
}
@inproceedings {vasquez-spp-2004,
title = {Diffusive thermoelectric transport in carbon nanotubes},
booktitle = {Proceedings of the 22nd Samahang Pisika ng Pilipinas Physics Congress},
year = {2004},
month = {25{\textendash}27 Oct 2004},
pages = {119},
address = {Bohol Tropics Resort, Tagbilaran City},
abstract = {This paper aims to study the diffusion thermoelectric power of singe-walled carbon nanotubes (SWNTs). This was obtained using a linear response method and a semiclassical treatment of metallic-like systems. The energy and the density of states were generated using the tight binding model for both electrons and holes. The SWNT, exhibiting a diffusive transport, is shown to have a negative thermoelectric power for an energy-dependent relaxation time. This indicates that electrons are dominant and demonstrates a metallic-like behavior.},
author = {Louella Judy Vasquez and Cristine Villagonzalo}
}
@inproceedings {tongco-spp-2004,
title = {Dipolar interaction in a 1-D Ising ring},
booktitle = {Proceedings of the 22nd Samahang Pisika ng Pilipinas Physics Congress},
year = {2004},
month = {25{\textendash}27 Oct 2004},
pages = {31},
address = {Bohol Tropics Resort, Tagbilaran City},
abstract = {The effects of a long-range interaction in a one-dimensional (1D) magnetic ring is studied. In this work, the Monte Carlo method is employed to obtain the equilibrium state of a modified quasi-1D Ising model having a dipolar interaction in a ring geometry. At low temperatures (*T*), the behavior of the magnetization (*M*) as a function of *T* is shown to depend on the strength of the dipolar interaction *(G)*. For a ring consisting of 10 spins, ferromagnetic states occur in the ground state (*T*=0) for a small value of *G*. Antiferromagnetic states are favored when *G* is large even at a finite temperature. The magnetization saturates at high *T*. Also, an effective lowering of the total energy is achieved when smaller values of *G* approach zero and when large value of *G* is increased further. Similar effects are observed for rings having a larger number of spins.

},
author = {Gina Rose Tongco and Cristine Villagonzalo}
}
@article {Tongco2004,
title = {Dipolar interaction in a one-dimensional Ising ring},
journal = {Science Diliman},
volume = {16},
year = {2004},
pages = {8-9},
abstract = {As synthesis of low-dimensional magnetic systems become possible, the need for theoretical understanding of their behavior arises. In this work, the authors explore a one-dimensional magnetic structure with the spins having dipolar interaction.

},
url = {http://journals.upd.edu.ph/index.php/sciencediliman/article/view/85},
author = {Gina Rose Tongco and Cristine Villagonzalo}
}
@inproceedings {marco-spp-2004,
title = {Effect of the hopping parameter on the current through a two-atom molecular wire},
booktitle = {Proceedings of the 22nd Samahang Pisika ng Pilipinas Physics Congress},
year = {2004},
month = {25{\textendash}27 Oct 2004},
pages = {27},
address = {Bohol Tropics Resort, Tagbilaran City},
abstract = {We utilize the Hubbard model approach in analyzing the effect of the hopping parameter in the transport properties of a two-atom molecular device. A root finding method was utilized to implement self-consistent calculations to obtain the transport properties and our results agree with that in the literature. Variation of the hopping parameter shows that its value is proportional to the threshold voltage in the presence of an on-site Coulomb interaction *U*.

},
author = {Ronaldo Marco Jr and Ronald S. Banzon and Cristine Villagonzalo}
}
@article {Morales2004,
title = {Enhancement of Fe magnetic moments in Fe/Co (001) multilayers},
journal = {Science Diliman},
volume = {16},
year = {2004},
pages = {6-7},
abstract = {In order to investigate the electronic and magnetic properties of a bcc Fe/Co (001) multilayer, we have performed electronic structure calculations employing the total energy full-potential linear muffin tin orbital method. The magnetic moments of the layers are calculated. Based on these results, the magnetization profiles and the microscopic origin of the enhancement of Fe moments in the multilayers of the same Co content but with different interface qualities are reported. Large enhancement of magnetic moment is observed in the Fe monolayer located at the interface, and an even greater increase is obtained for the multilayer with one monolayer of intermixing between Fe and Co layers. The Co atoms were found to have similar magnetic moments in the bulk and at the interface.

},
url = {http://journals.upd.edu.ph/index.php/sciencediliman/article/view/84},
author = {Marienette B Morales and Cristine Villagonzalo}
}
@inproceedings {morales-spp-2004,
title = {Enhancement of Fe magnetic moments in Fe/Co(001) multilayer},
booktitle = {Proceedings of the 22nd Samahang Pisika ng Pilipinas Physics Congress},
year = {2004},
month = {25{\textendash}27 Oct 2004},
pages = {72},
address = {Bohol Tropics Resort, Tagbilaran City},
abstract = {In order to investigate the electronic and magnetic properties of a bcc Fe/Co (001) multilayer, we have performed electronic structure calculations employing the total energy full-potential linear muffin tin orbital method (FP-LMTO). The magnetic moments of the layers are calculated. Based on these results, the magnetization profiles and the microscopic origin of the enhancement of Fe moments in the multilayers of the same Co content but with different interface quality are reported. Large enhancement of magnetic moment is observed in Fe monolayer located at the interface, and even greater increase is obtained for the multilayer with one monolayer of intermixing between Fe and Co layers. The Co atoms were found to have similar magnetic moments in the bulk and at the interface.

},
author = {Marienette Morales and Cristine Villagonzalo}
}
@article {Marco2004,
title = {Hopping in a molecular wire},
journal = {Science Diliman},
volume = {16},
year = {2004},
pages = {10-11},
abstract = {We utilize the Hubbard model approach in analyzing the effect of the hopping parameter in the transport properties of a two-atom molecular device.

},
url = {http://journals.upd.edu.ph/index.php/sciencediliman/article/view/86},
author = {Ronaldo Marco Jr and Ronald Banzon and Cristine Villagonzalo}
}
@inproceedings {pari{\~n}as-spp-2004,
title = {Pre-collision dynamics of short 1D anharmonic chains},
booktitle = {Proceedings of the 22nd Samahang Pisika ng Pilipinas Physics Congress},
year = {2004},
month = {25{\textendash}27 Oct 2004},
pages = {118},
address = {Bohol Tropics Resort, Tagbilaran City},
abstract = {This paper investigates the dynamics of short one-dimensional lattices having a temperature gradient. An anharmonic potential using the Fermi-Pasta-Ulam (FPU) model was assumed. Three different systems were studied: a uniform chain, a chain with a single impurity, and a diatomic chain. Numerical simulations using the fourth order Runge-Kutta algorithm was used to solve the equations of motion. An impurity in the chain serves as a {\textquotedblleft}thermal barrier{\textquotedblright}. In the diatomic lattice, an energy excitation is formed even before any particle collision occurs. Here the energy distribution at different times will be shown.

},
author = {Ricelle Pari{\~n}as and Cristine Villagonzalo}
}
@inproceedings {gammag-spp-2004,
title = {The specific heat of a 2DEG in a magnetic field},
booktitle = {Proceedings of the 22nd Samahang Pisika ng Pilipinas Physics Congress},
year = {2004},
month = {25{\textendash}27 Oct 2004},
pages = {154},
address = {Bohol Tropics Resort, Tagbilaran City},
abstract = {We investigate the specific heat of a two-dimensional electron gas (2DEG) and how it varies with the system{\textquoteright}s temperature and chemical potential in the presence of an external magnetic field. In this work, we take into account the dependence of the chemical potential with temperature. We show that the specific heat of the system exhibits a two-peak behavior at low T regardless of the field{\textquoteright}s magnitude if μ~T^2 and that this is consistent with results in the literature where the broadening of Landau levels was considered. The underlying processes may be different but the effect on CV is similar.

},
author = {Rayda P Gammag and Cristine Villagonzalo}
}
@inproceedings {dizon-spp-2004,
title = {Thermal conductivity in a one-dimensional superlattice},
booktitle = {Proceedings of the 22nd Samahang Pisika ng Pilipinas Physics Congress},
year = {2004},
month = {25{\textendash}27 Oct 2004},
pages = {155},
address = {Bohol Tropics Resort, Tagbilaran City},
abstract = {We investigate the phonon thermal conductivity in a one-dimensional superlattice for transport perpendicular to the layers by utilizing analytic methods. A reduction on the thermal conductivity was observed when the layer thickness of the superlattice was increased. Difference in the mass ratio of the atoms in the chain and force constant ratio on alternating layers produced variations in the thermal conductivity. Higher difference of either of these two parameters results in the decrease of the thermal conductivity.

},
author = {Jane Dizon and Cristine Villagonzalo}
}
@inproceedings {muldera-spp-2004,
title = {Thermal efficiency of a quasi-one-dimensional conductor},
booktitle = {Proceedings of the 22nd Samahang Pisika ng Pilipinas Physics Congress},
year = {2004},
month = {25{\textendash}27 Oct 2004},
pages = {113},
address = {Bohol Tropics Resort, Tagbilaran City},
abstract = {How does a system{\textquoteright}s dimension affect its thermal efficiency? In this work, we will show that if conduction is constrained in a single direction in a three dimensional conductor, it will become more efficient in conducting thermal energy as its width is reduced. Herein, we investigate the electric and thermal properties of a quasi-one-dimensional conductor using the free electron gas model in the relaxation time approximation scheme. This is demonstrated in the wire width dependence of the electric conductivity, thermal conductivity and figure of merit. We will also show the dependence of these transport properties to the system{\textquoteright}s chemical potential.

},
author = {Joselito Muldera and Cristine Villagonzalo}
}
@inproceedings {sandagon-spp-2004,
title = {Variational Monte Carlo of a 2D quantum well system},
booktitle = {Proceedings of the 22nd Samahang Pisika ng Pilipinas Physics Congress},
year = {2004},
month = {25{\textendash}27 Oct 2004},
pages = {153},
address = {Bohol Tropics Resort, Tagbilaran City},
abstract = {The convergence of a Variational Monte Carlo method with Gaussian importance sampling (VMC-GIS), as applied to a two-dimensional time-independent quantum well, was improved by optimizing the standard deviation σ of the Gaussian probability distribution. The fastest convergence in attaining the ground state is obtained by using VMC-GIS with σ=0.6 .

},
author = {Ryan Sandagon and Ronald S. Banzon and Cristine Villagonzalo}
}
@inproceedings {labora-spp-2003,
title = {Ab-initio structural investigation of Fe/V (001) multilayers},
booktitle = {Proceedings of the 21st Samahang Pisika ng Pilipinas Physics Congress},
year = {2003},
month = {22{\textendash}25 Oct 2003},
pages = {5-8},
address = {University of San Carlos, Cebu City},
abstract = {The structural properties of Fe/V multilayers are studied using electronic structure calculations. A first principle numerical calculation is implemented using the Full Potential Linear Muffin-Tin (FPLMTO) method based on the Density Functional Theory (DFT). The number of Fe and V in a Fe/V supercell is varied while the total atoms is kept constant. The energetically equilibrium structure of this multilayer is presented. Two types of multilayer structures, the Fe-on-V and the V-on-Fe, are investigated and compared to bulk values and reported experimental results. Results show that the total energy for Fe-on-V multilayer gives a lower value compared to V-on-Fe multilayer signifying that the V-on-Fe is a more stable structure than Fe-on-V, a result which is consistent with experimental observations. The simple case of the effect of intermixing is presented and its total energy and spin moment is compared to the bulk value.},
author = {Marites Labora and Cristine Villagonzalo}
}
@inproceedings {morales-spp-2003,
title = {Magnetization and magnetic anisotropy of Fe/Co multilayers: A first-principles calculation},
booktitle = {Proceedings of the 21st Samahang Pisika ng Pilipinas Physics Congress},
year = {2003},
month = {22{\textendash}25 Oct 2003},
pages = {446-449},
address = {University of San Carlos, Cebu City},
abstract = {The magnetic properties of bcc Fe/Co (001) multilayers are calculated from first-principles by means of the full potential linear muffin tin orbital method (FLMTO). A significant enhancement in the magnetic moments of each atom in the multilayer is observed. The magnetization and magnetic anisotropy energy MAE are described as a function of Fe/Co layer thickness ratio. For comparison with the obtained multilayer values, the magnetization and MAE of constituent atoms, bcc Co bulk are also verified. The results for the magnetization and MAE agree well with experimental results.},
author = {Marienette B Morales and Cristine Villagonzalo}
}
@inproceedings {villagonzalo-spp-2003,
title = {Numerical investigations on the growth textures of Co/Cu multilayers},
booktitle = {Proceedings of the 21st Samahang Pisika ng Pilipinas Physics Congress},
year = {2003},
month = {22{\textendash}25 Oct 2003},
pages = {262-265},
address = {University of San Carlos, Cebu City},
abstract = {A first-principles investigation on the growth textures of cobalt/copper multilayers is presented. Through an ab-initio local-density approximation in a full-potenatial linear muffin-tin orbital (FPLMTO) electronic structure method, the different growth textures of Co/Cu multilayers are compared. Through total energy minimization, the face-centered cubic (111) configuration is determined to be the preferred textural orientation as compared to the (110) and (001) directions. Physically, this suggests that (111) configuration is more favorable to grow. Included in this report are results of intermixing Co/Cu interfaces which verifies that Co and Cu are immiscible in the bulk. This work provides a benchmark for thermal transport studies in multilayers.},
author = {Cristine Villagonzalo and Arun K Setty and Bernard R Cooper}
}
@article {R{\"o}mer2003167,
title = {Thermoelectric properties of disordered systems},
journal = {J. Phys. Soc. Jpn. Suppl. A},
volume = {72},
number = {SUPPL. A},
year = {2003},
note = {cited By 5},
pages = {167-168},
abstract = {The electronic properties of disordered systems have been the subject of intense study for several decades. Thermoelectric properties, such as thermopower and thermal conductivity, have been relatively neglected. A long standing problem is represented by the sign of the thermoelectric power. In crystalline semiconductors this is related to the sign of the majority carriers, but in non-crystalline systems it is commonly observed to change sign at low temperatures. In spite of its apparent universality this change has been interpreted in a variety of ways in different systems. We have developed a Green{\textquoteright}s function recursion algorithm based on the Chester-Thelling-Kubo-Greenwood formula for calculating the kinetic coefficients on long strips or bars. From these we can deduce the electrical conductivity, the Seebeck and Peltier coefficients and the thermal conductivity, as well as the Lorenz number. We present initial results for 1D systems. We observe a Lorentzian distribution for the thermopower which is modified by the presence of inelastic scattering. This could give rise to non-negligible quantum fluctuations in macroscopic systems at low temperatures.

},
doi = {10.1143/JPSJS.72SA.167},
author = {Rudolf A R{\"o}mer and Angus MacKinnon and Cristine Villagonzalo}
}
@article {Villagonzalo200016446,
title = {Behavior of the thermopower in amorphous materials at the metal-insulator transition},
journal = {Phys. Rev. B},
volume = {62},
number = {24},
year = {2000},
note = {cited By 4},
pages = {16446-16452},
abstract = {We study the behavior of the thermal transport properties in three-dimensional disordered systems close to the metal-insulator transition within linear response. Using a suitable form for the energy-dependent conductivity σ, we show that the value of the dynamical scaling exponent for noninteracting disordered systems such as the Anderson model of localization can be reproduced. Furthermore, the values of the thermopower *S* have the right order of magnitude close to the transition as compared to the experimental results. A sign change in the thermoelectric power *S* {\textemdash} as is often observed in experiments {\textemdash} can also be modeled within the linear response formulation using modified experimental σ data as input.

},
doi = {10.1103/PhysRevB.62.16446},
author = {Cristine Villagonzalo and Rudolf A R{\"o}mer and Michael Schreiber and Angus MacKinnon}
}
@article {Villagonzalo1999179,
title = {Thermoelectric transport properties in disordered systems near the Anderson transition},
journal = {Eur. Phys. J. B},
volume = {12},
number = {2},
year = {1999},
note = {cited By 12},
pages = {179-189},
abstract = {We study the thermoelectric transport properties in the three-dimensional Anderson model of localization near the metal-insulator transition (MIT). In particular, we investigate the dependence of the thermoelectric power *S*, the thermal conductivity *K*, and the Lorenz number *L*0 on temperature *T*. We first calculate the *T* dependence of the chemical potential μ from the number density *n* of electrons at the MIT using an averaged density of states obtained by diagonalization. Without any additional approximation, we determine from the behavior of *S*, *K* and *L*0 at low *T* as the MIT is approached. We find that the d.c. conductivity and *K* decrease to zero at the MIT as *T* -\> 0 and show that *S* does not diverge. Both *S* and *L*0 become temperature independent at the MIT and depend only on the critical behavior of the conductivity.

},
doi = {10.1007/s100510050994},
author = {Cristine Villagonzalo and Rudolf A R{\"o}mer and Michael Schreiber}
}
@article {Villagonzalo1998394,
title = {Low temperature behavior of the thermopower in disordered systems near the Anderson transition},
journal = {Ann. Phys. (Leipzig)},
volume = {7},
number = {5-6},
year = {1998},
note = {cited By 5},
pages = {394-399},
abstract = {We investigate the behavior of the thermoelectric power *S* in disordered systems close to the Anderson-type metal-insulator transition (MIT) at low temperatures. In the literature, we find contradictory results for *S*. It is either argued to diverge or to remain a constant as the MIT is approached. To resolve this dilemma, we calculate the number density of electrons at the MIT in disordered systems using an averaged density of states obtained by diagonalizing the three-dimensional Anderson model of localization. From the number density we obtain the temperature dependence of the chemical potential necessary to solve for *S*. Without any additional approximation, we use the Chester-Thellung-Kubo-Greenwood formulation and numerically obtain the behavior of *S* at low *T* as the Anderson transition is approached from the metallic side. We show that indeed *S* does not diverge.

},
doi = {10.1002/(SICI)1521-3889(199811)7:5/6<394::AID-ANDP394>3.0.CO;2-Q},
author = {Cristine Villagonzalo and Rudolf A R{\"o}mer}
}