Perry Esguerra | University of the Philippines Diliman (original) (raw)
Papers by Perry Esguerra
We address the problem of stitching together the vacuum, static, planar-symmetric Taub spacetime ... more We address the problem of stitching together the vacuum, static, planar-symmetric Taub spacetime and the flat Friedmann-Robertson-Walker cosmology using the Israel thin-shell formalism. The joining of Taub and FRW spacetimes is reminiscent of the Oppenheimer-Snyder collapse used in modeling the formation of a singularity from a collapsing spherical ball of dust. A possible mechanism for the formation of a planar singularity is provided. It is hoped that tackling such example will improve our intuition on planar-symmetric
systems in Einstein’s general relativity.
Physica D: Nonlinear Phenomena, 1998
The average thermodynamic power of a time-dependent external potential in the white-noise Langevi... more The average thermodynamic power of a time-dependent external potential in the white-noise Langevin model is derived using a Green's function solution. The power appears as a driving term in the differential equation for the average energy and determines whether the solution is stationary or non-stationary. Different dynamics are illustrated with explicit models: a linear potential with a static magnetic field, a linear potential perturbed with an oscillating component and a magnetic field switch modeled using a tanh\tanhtanh protocol.
The average thermodynamic power of a time-dependent external potential in the white-noise Langevi... more The average thermodynamic power of a time-dependent external potential in the white-noise Langevin model is derived using a Green's function solution. The power appears as a driving term in the differential equation for the average energy and determines whether the solution is stationary or non-stationary. Different dynamics are illustrated with explicit models: a linear potential with a static magnetic field, a linear potential perturbed with an oscillating component and a magnetic field switch modeled using a tanh\tanhtanh protocol.
The single-particle tunneling current is calculated for normal metal–superconductor and supercond... more The single-particle tunneling current is calculated for normal metal–superconductor and superconductor–superconductor junctions using the spin polaron theory.
Journal of Mathematical Physics, 2014
ABSTRACT Using the momentum-space approach, we obtain bound states for multiple Dirac-δ wells in ... more ABSTRACT Using the momentum-space approach, we obtain bound states for multiple Dirac-δ wells in the framework of space-fractional quantum mechanics. Introducing first an attractive Dirac-comb potential, i.e., Dirac comb with strength -g (g > 0), in the space-fractional Schrödinger equation we show that the problem of obtaining eigenenergies of a system with N Dirac-δ wells can be reduced to a problem of obtaining the eigenvalues of an N × N matrix. As an illustration we use the present matrix formulation to derive expressions satisfied by the bound-state energies of N = 1, 2, 3 delta wells. We also obtain the corresponding wave functions and express them in terms of Fox's H-function.
Journal of Superconductivity and Novel Magnetism, 2014
ABSTRACT The single-particle tunneling current is calculated for normal metal–superconductor and ... more ABSTRACT The single-particle tunneling current is calculated for normal metal–superconductor and superconductor–superconductor junctions using the spin polaron theory.
Physica A: Statistical Mechanics and its Applications, 2014
ABSTRACT We study transmission through locally periodic potentials in the framework of space-frac... more ABSTRACT We study transmission through locally periodic potentials in the framework of space-fractional quantum mechanics (SFQM). In particular, we calculate the transmission probabilities T(N)T(N) for a particle in a chain of NN Dirac-δδ barriers and, for the other case, a chain of NN square barriers. We use a transfer-matrix (M-matrix) approach in the context of SFQM to obtain equations for T(N)T(N). For both systems, bandlike structures emerge even for a small number of barriers of as low as N=4N=4 and are more apparent for lower values of Lévy index αα considered.
The lattice gauge theory for curved spacetime is formulated. A discretized action is derived for ... more The lattice gauge theory for curved spacetime is formulated. A discretized action is derived for both gluon and quark fields which reduces to the generally covariant form in the continuum limit. Using the Wilson action, it is shown analytically that for a general curved spacetime background, two propagating gluons are always color-confined. The fermion-doubling problem is discussed in the specific case of Friedman-Robertson-Walker metric. Lastly, we discussed possible future numerical implementation of lattice QCD in curved spacetime.
The lattice gauge theory (LGT) for curved spacetime is formulated. A discretized action is derive... more The lattice gauge theory (LGT) for curved spacetime is formulated. A discretized action is derived for both gluon and quark fields which reduces to the generally covariant form in the continuum limit. Using the Wilson action, it is shown analytically that for a general curved spacetime background, two propagating gluons are always color-confined. The fermion-doubling problem is discussed in the specific case of Friedman–Robertson–Walker (FRW) metric. Last, we discussed possible future numerical implementation of lattice QCD in curved spacetime.
We present exact analytical solutions to the classical equations of motion and analyze the dynami... more We present exact analytical solutions to the classical equations of motion and analyze the dynamical consequences of the existence of a minimal length for the free particle, particle in a linear potential, anti-symmetric constant force oscillator, harmonic oscillator, vertical harmonic oscillator, linear diatomic chain, and linear triatomic chain. It turns out that the speed of a free particle and the magnitude of the acceleration of a particle in a linear potential have larger values compared to the non-minimal length counterparts - the increase in magnitudes come from multiplicative factors proportional to what is known as the generalized uncertainty principle parameter. Our analysis of oscillator systems suggests that the characteristic frequencies of systems also have larger values than the non-minimal length counterparts. In connection with this, we discuss a kind of experimental test with which the existence of a minimal length may be detected on a classical level.
We solved the wind-influenced projectile motion problem with the same initial and final heights a... more We solved the wind-influenced projectile motion problem with the same initial and final heights and obtained exact analytical expressions for the shape of the trajectory, range, maximum height, time of flight, time of ascent, and time of descent with the help of the Lambert W function. It turns out that the range and maximum horizontal displacement are not always equal. When launched at a critical angle, the projectile will return to its starting position. It turns out that a launch angle of 90° maximizes the time of flight, time of ascent, time of descent, and maximum height and that the launch angle corresponding to maximum range can be obtained by solving a transcendental equation. Finally, we expressed in a parametric equation the locus of points corresponding to maximum heights for projectiles launched from the ground with the same initial speed in all directions. We used the results to estimate how much a moderate wind can modify a golf ball's range and suggested other possible applications.
Using a path integral approach, we consider a fractional Schrödinger equation with delta- perturb... more Using a path integral approach, we consider a fractional Schrödinger equation with delta-
perturbed infinite square well. The Lévy path integral, which is generalized from the
Feynman path intergal for the propagator, is expanded into a perturbation series. From this,
the energy-dependent Green's function is obtained.
We solve the space-fractional Schrödinger equation for a quadrupolar triple Dirac-δ (QTD-δ) poten... more We solve the space-fractional Schrödinger equation for a quadrupolar triple Dirac-δ (QTD-δ)
potential for all energies using the momentum-space approach. For the E< 0 solution, we
consider two cases, ie, when the strengths of the potential are V0> 0 (QTD-δ potential with
central Dirac-δ well) and V0< 0 (QTD-δ potential with central Dirac-δ barrier) and derive
expressions satisfied by the bound-state energy. For all fractional orders α considered, we
find that there is one eigenenergy when V0> 0, and there are two eigenenergies when V0
We solve the space-fractional Schrödinger equation for a quadrupolar triple Dirac-δ (QTD-δ) poten... more We solve the space-fractional Schrödinger equation for a quadrupolar triple Dirac-δ (QTD-δ)
potential for all energies using the momentum-space approach. For the E< 0 solution, we
consider two cases, ie, when the strengths of the potential are V0> 0 (QTD-δ potential with
central Dirac-δ well) and V0< 0 (QTD-δ potential with central Dirac-δ barrier) and derive
expressions satisfied by the bound-state energy. For all fractional orders α considered, we
find that there is one eigenenergy when V0> 0, and there are two eigenenergies when V0
We introduce zealots of one opinion in the voter model on a complete graph and examine how they a... more We introduce zealots of one opinion in the voter model on a complete graph and examine how they affect consensus achievement. Using first-step analysis for Markov chains to obtain an exact solution, we find that the mean consensus time scales with the population size NN. Increasing the number of zealots, ZZ, will decrease the consensus time in a power law fashion for large ZZ. The mean magnetization was also analytically obtained and was found to contain an exponential dependence on ZZ. The dynamics for the complete graph are qualitatively similar to those obtained in another study for the Barabasi–Albert network. In general, the existence of zealots serves to hasten consensus, except in the case where only a few zealots oppose the vast majority.
We address the problem of stitching together the vacuum, static, planar-symmetric Taub spacetime ... more We address the problem of stitching together the vacuum, static, planar-symmetric Taub spacetime and the flat Friedmann-Robertson-Walker cosmology using the Israel thin-shell formalism. The joining of Taub and FRW spacetimes is reminiscent of the Oppenheimer-Snyder collapse used in modeling the formation of a singularity from a collapsing spherical ball of dust. A possible mechanism for the formation of a planar singularity is provided. It is hoped that tackling such example will improve our intuition on planar-symmetric
systems in Einstein’s general relativity.
Physica D: Nonlinear Phenomena, 1998
The average thermodynamic power of a time-dependent external potential in the white-noise Langevi... more The average thermodynamic power of a time-dependent external potential in the white-noise Langevin model is derived using a Green's function solution. The power appears as a driving term in the differential equation for the average energy and determines whether the solution is stationary or non-stationary. Different dynamics are illustrated with explicit models: a linear potential with a static magnetic field, a linear potential perturbed with an oscillating component and a magnetic field switch modeled using a tanh\tanhtanh protocol.
The average thermodynamic power of a time-dependent external potential in the white-noise Langevi... more The average thermodynamic power of a time-dependent external potential in the white-noise Langevin model is derived using a Green's function solution. The power appears as a driving term in the differential equation for the average energy and determines whether the solution is stationary or non-stationary. Different dynamics are illustrated with explicit models: a linear potential with a static magnetic field, a linear potential perturbed with an oscillating component and a magnetic field switch modeled using a tanh\tanhtanh protocol.
The single-particle tunneling current is calculated for normal metal–superconductor and supercond... more The single-particle tunneling current is calculated for normal metal–superconductor and superconductor–superconductor junctions using the spin polaron theory.
Journal of Mathematical Physics, 2014
ABSTRACT Using the momentum-space approach, we obtain bound states for multiple Dirac-δ wells in ... more ABSTRACT Using the momentum-space approach, we obtain bound states for multiple Dirac-δ wells in the framework of space-fractional quantum mechanics. Introducing first an attractive Dirac-comb potential, i.e., Dirac comb with strength -g (g > 0), in the space-fractional Schrödinger equation we show that the problem of obtaining eigenenergies of a system with N Dirac-δ wells can be reduced to a problem of obtaining the eigenvalues of an N × N matrix. As an illustration we use the present matrix formulation to derive expressions satisfied by the bound-state energies of N = 1, 2, 3 delta wells. We also obtain the corresponding wave functions and express them in terms of Fox's H-function.
Journal of Superconductivity and Novel Magnetism, 2014
ABSTRACT The single-particle tunneling current is calculated for normal metal–superconductor and ... more ABSTRACT The single-particle tunneling current is calculated for normal metal–superconductor and superconductor–superconductor junctions using the spin polaron theory.
Physica A: Statistical Mechanics and its Applications, 2014
ABSTRACT We study transmission through locally periodic potentials in the framework of space-frac... more ABSTRACT We study transmission through locally periodic potentials in the framework of space-fractional quantum mechanics (SFQM). In particular, we calculate the transmission probabilities T(N)T(N) for a particle in a chain of NN Dirac-δδ barriers and, for the other case, a chain of NN square barriers. We use a transfer-matrix (M-matrix) approach in the context of SFQM to obtain equations for T(N)T(N). For both systems, bandlike structures emerge even for a small number of barriers of as low as N=4N=4 and are more apparent for lower values of Lévy index αα considered.
The lattice gauge theory for curved spacetime is formulated. A discretized action is derived for ... more The lattice gauge theory for curved spacetime is formulated. A discretized action is derived for both gluon and quark fields which reduces to the generally covariant form in the continuum limit. Using the Wilson action, it is shown analytically that for a general curved spacetime background, two propagating gluons are always color-confined. The fermion-doubling problem is discussed in the specific case of Friedman-Robertson-Walker metric. Lastly, we discussed possible future numerical implementation of lattice QCD in curved spacetime.
The lattice gauge theory (LGT) for curved spacetime is formulated. A discretized action is derive... more The lattice gauge theory (LGT) for curved spacetime is formulated. A discretized action is derived for both gluon and quark fields which reduces to the generally covariant form in the continuum limit. Using the Wilson action, it is shown analytically that for a general curved spacetime background, two propagating gluons are always color-confined. The fermion-doubling problem is discussed in the specific case of Friedman–Robertson–Walker (FRW) metric. Last, we discussed possible future numerical implementation of lattice QCD in curved spacetime.
We present exact analytical solutions to the classical equations of motion and analyze the dynami... more We present exact analytical solutions to the classical equations of motion and analyze the dynamical consequences of the existence of a minimal length for the free particle, particle in a linear potential, anti-symmetric constant force oscillator, harmonic oscillator, vertical harmonic oscillator, linear diatomic chain, and linear triatomic chain. It turns out that the speed of a free particle and the magnitude of the acceleration of a particle in a linear potential have larger values compared to the non-minimal length counterparts - the increase in magnitudes come from multiplicative factors proportional to what is known as the generalized uncertainty principle parameter. Our analysis of oscillator systems suggests that the characteristic frequencies of systems also have larger values than the non-minimal length counterparts. In connection with this, we discuss a kind of experimental test with which the existence of a minimal length may be detected on a classical level.
We solved the wind-influenced projectile motion problem with the same initial and final heights a... more We solved the wind-influenced projectile motion problem with the same initial and final heights and obtained exact analytical expressions for the shape of the trajectory, range, maximum height, time of flight, time of ascent, and time of descent with the help of the Lambert W function. It turns out that the range and maximum horizontal displacement are not always equal. When launched at a critical angle, the projectile will return to its starting position. It turns out that a launch angle of 90° maximizes the time of flight, time of ascent, time of descent, and maximum height and that the launch angle corresponding to maximum range can be obtained by solving a transcendental equation. Finally, we expressed in a parametric equation the locus of points corresponding to maximum heights for projectiles launched from the ground with the same initial speed in all directions. We used the results to estimate how much a moderate wind can modify a golf ball's range and suggested other possible applications.
Using a path integral approach, we consider a fractional Schrödinger equation with delta- perturb... more Using a path integral approach, we consider a fractional Schrödinger equation with delta-
perturbed infinite square well. The Lévy path integral, which is generalized from the
Feynman path intergal for the propagator, is expanded into a perturbation series. From this,
the energy-dependent Green's function is obtained.
We solve the space-fractional Schrödinger equation for a quadrupolar triple Dirac-δ (QTD-δ) poten... more We solve the space-fractional Schrödinger equation for a quadrupolar triple Dirac-δ (QTD-δ)
potential for all energies using the momentum-space approach. For the E< 0 solution, we
consider two cases, ie, when the strengths of the potential are V0> 0 (QTD-δ potential with
central Dirac-δ well) and V0< 0 (QTD-δ potential with central Dirac-δ barrier) and derive
expressions satisfied by the bound-state energy. For all fractional orders α considered, we
find that there is one eigenenergy when V0> 0, and there are two eigenenergies when V0
We solve the space-fractional Schrödinger equation for a quadrupolar triple Dirac-δ (QTD-δ) poten... more We solve the space-fractional Schrödinger equation for a quadrupolar triple Dirac-δ (QTD-δ)
potential for all energies using the momentum-space approach. For the E< 0 solution, we
consider two cases, ie, when the strengths of the potential are V0> 0 (QTD-δ potential with
central Dirac-δ well) and V0< 0 (QTD-δ potential with central Dirac-δ barrier) and derive
expressions satisfied by the bound-state energy. For all fractional orders α considered, we
find that there is one eigenenergy when V0> 0, and there are two eigenenergies when V0
We introduce zealots of one opinion in the voter model on a complete graph and examine how they a... more We introduce zealots of one opinion in the voter model on a complete graph and examine how they affect consensus achievement. Using first-step analysis for Markov chains to obtain an exact solution, we find that the mean consensus time scales with the population size NN. Increasing the number of zealots, ZZ, will decrease the consensus time in a power law fashion for large ZZ. The mean magnetization was also analytically obtained and was found to contain an exponential dependence on ZZ. The dynamics for the complete graph are qualitatively similar to those obtained in another study for the Barabasi–Albert network. In general, the existence of zealots serves to hasten consensus, except in the case where only a few zealots oppose the vast majority.