arXiv subjects

Gabriel Gonzalez

Publications and source records attributed to Gabriel Gonzalez.

At least 19 recordsLinked to original sources

arXiv2026

Commutative Factorization of Nonlinear Second-Order Differential Equations: Theory and Applications

This work presents a generalization of the commutative factorization framework for a broad class of second-order nonlinear ordinary differential equations. The main objective was to extend the commutative factorization procedure in order to use the Riccati-Bernoulli equation and the B\"acklund transformation. This provides a systematic route for constructing both particular and general solutions of the original second-order nonlinear equation. The theoretical development is illustrated through several nonlinear models of physical and mathematical interest, including equations arising in classical mechanics and nonlinear oscillatory systems. The results demonstrate that commutative factorization constitutes an effective analytical tool for solving nonlinear differential equations.

math-ph↗

arXiv2026

Berry-phase in a periodically driven single molecule magnet transistor

We consider the electron transport through a single molecule magnet transistor in the presence of a local transverse magnetic field and ac-driven gate voltage. We calculate the conductance as a function of the electron energy and transverse magnetic field by using the Floquet and Landauer formalism. We show that the time periodic potential causes zero transmission resonances that oscillate as a function of the transverse magnetic field due to the Berry phase interference associated with two quantum tunneling paths. We find that these Berry phase oscillations can be detected in the conductance as a function of the transverse magnetic field for an incoming electron with a specific energy.

cond-mat.mes-hall↗

arXiv2026

Berry-phase effect in single molecule magnets: analytical and numerical results

In this paper we theoretically and numerically investigate transport signatures of quantum interference on the current through a single molecule magnet transistor tunnel coupled to oppositely polarized leads in the presence of a local transverse and longitudinal magnetic field. Our calculations are based in a density matrix approach where we treat the ground state energy splitting induced by tunneling of the spin between different paths with the aid of perturbation theory. Using this approach we show that it is possible to use an effective Hamiltonian which describes the Berry phase interference as a function of the transverse magnetic field which completely blocks the current flow when we place the single molecule magnet between oppositely polarized leads. Finally, we use this effective Hamiltonian in an open source Python software (QmeQ) that allows us to calculate the current through the single molecule magnet with oppositely polarized leads tunnel coupled to the single molecule magnet. The analytical results are well reproduced by our numerical simulations.

cond-mat.mes-hall↗

arXiv2026

Dimensional consistency in fractional differential equations with non singular kernels

The purpose of this article is to address the issues of dimensional consistency that arise in the process of replacing the ordinary time derivative operator by a fractional derivative operator in order to write a fractional differential equation. We show that by performing a simple change of variables fulfilling certain conditions ensures the consistency in physical dimensions for fractional differential equations with non singular kernels. An example of the proposed method is given.

math-ph↗

arXiv2024

Deep Neural Network for Constraint Acquisition through Tailored Loss Function

The significance of learning constraints from data is underscored by its potential applications in real-world problem-solving. While constraints are popular for modeling and solving, the approaches to learning constraints from data remain relatively scarce. Furthermore, the intricate task of modeling demands expertise and is prone to errors, thus constraint acquisition methods offer a solution by automating this process through learnt constraints from examples or behaviours of solutions and non-solutions. This work introduces a novel approach grounded in Deep Neural Network (DNN) based on Symbolic Regression that, by setting suitable loss functions, constraints can be extracted directly from datasets. Using the present approach, direct formulation of constraints was achieved. Furthermore, given the broad pre-developed architectures and functionalities of DNN, connections and extensions with other frameworks could be foreseen.

cs.LG↗

arXiv2022

Lie symmetries, Jacobi last multipliers and new non-standard Lagrangians for dissipative dynamical systems

We present a new method based on Lie symmetries and Jacobi last multipliers which allows one to find many non-standard Lagrangians for dissipative dynamical systems. In particular, it is demonstrated that for every non-standard Lagrangian one can generate a new non-standard Lagrangian associated to a new equation of motion. We point out that the knowledge of Lie symmetries for a given dynamical system generates Jacobi last multipliers which can be used to obtain new non-standard Lagrangians for dissipative dynamical systems in a simple and straightforward way. We exemplify the new method by applying it to the case of the free particle and the simple harmonic oscillator in order to obtain new non-standard Lagrangians for dissipative systems.

physics.class-ph↗

arXiv2020

Rabi oscillations at the exceptional point in anti-parity-time symmetric diffusive systems

The motivation for this theoretical paper comes from recent experiments of a heat transfer system of two thermally coupled rings rotating in opposite directions with equal angular velocities that present anti-parity-time (APT) symmetry. The theoretical model predicted a rest-to-motion temperature distribution phase transition during the symmetry breaking for a particular rotation speed. In this work we show that the system exhibits a parity-time ($\mathcal{PT}$) phase transition at the exceptional point in which eigenvalues and eigenvectors of the corresponding non-Hermitian Hamiltonian coalesce. We analytically solve the heat diffusive system at the exceptional point and show that one can pass through the phase transition that separates the unbroken and broken phases by changing the radii of the rings. In the case of unbroken $\mathcal{PT}$ symmetry the temperature profiles exhibit damped Rabi oscillations at the exceptional point. Our results unveils the behavior of the system at the exceptional point in heat diffusive systems.

quant-ph↗

arXiv2019

Invariance of Witten's quantum mechanics under point canonical transformations

We show that the supersymmetric algebra of Witten's quantum mechanics is invariant under a given point canonical transformation. It is shown that Witten's supersymmetric quantum mechanics can be isospectral or not to the seed Hamiltonian depending on the space coordinate you work on. We illustrate our results by generating a new class of exactly solvable supersymmetric partner Hamiltonians which are not isospectral to the seed Hamiltonian.

math-ph↗

arXiv2017

Electrostatic analogy of the Jackiw-Rebbi zero energy state

We present an analogy between the one dimensional Poisson equation in inhomogeneous media and the Dirac equation in one space dimension with a Lorentz scalar potential for zero energy. We illustrate how the zero energy state in the Jackiw-Rebbi model can be implemented in a simple one dimensional electrostatic setting by using an inhomogeneous electric permittivity and an infinite charged sheet. Our approach provides a novel insight into the Jackiw-Rebbi zero energy state and provides a helpful view in teaching this important quantum field theory model using basic electrostatics.

cond-mat.other↗

arXiv2017

Effect of radiation damping on the Child-Langmuir law in open diodes

We present a microscopic derivation of the space charge limited current for the motion of non-relativistic charged particles inside a parallel vacuum tube diode taking into account the radiation reaction force. We study the space charged limited current for two different limiting cases. Our results reveal that in the low field regime the space charge current does not follow the Child-Langmuir law, while in the high field regime the space charge current follows the Child-Langmuir law with and effective electrostatic field, i.e. the so called modified Child-Langmuir law.

physics.plasm-ph↗

arXiv2017

Dirac equation in one dimensional transformation optics

We show that the propagation of transverse electric (TE) polarized waves in one dimensional inhomogeneous settings can be written in the form of the Dirac equation in one space dimension with a Lorentz scalar potential, and consequently perform photonic simulations of the Dirac equation in optical structures. In particular, we propose how the zero energy state of the Jackiw-Rebbi model can be implemented in a optical set up by controlling the refractive index landscape, where TE polarized waves mimic the Dirac particles and the soliton field can be implemented and tuned by adjusting the refractive index.

physics.optics↗

arXiv2016

Exact Partition Function for the Random Walk of an Electrostatic Field

The partition function for the random walk of an electrostatic field produced by several static parallel infinite charged planes in which the charge distribution could be either $\pmσ$ is obtained. We find the electrostatic energy of the system and show that it can be analyzed through generalized Dyck paths. The relation between the electrostatic field and generalized Dyck paths allows us to sum over all possible electrostatic field configurations and is used for obtaining the partition function of the system. We illustrate our results with one example.

cond-mat.stat-mech↗

arXiv2015

A new approach to the Child-Langmuir law

We analyze the motion of charged particles in a vacuum tube diode using a new set of variables. We obtain the space charge limited current for a charged particle moving non-relativistically in one dimension for the case of zero and non zero initial velocity. Our approach gives a new physical insight into the Child-Langmuir law and avoids the need of solving a nonlinear differential equation.

physics.plasm-ph↗

arXiv2015

The random walk of an electrostatic field using parallel infinite charged planes

We show that it is possible to generate a random walk with an electrostatic field by means of several parallel infinite charged planes in which the surface charge distribution could be either $\pmσ$. We formulate the problem of this stochastic process by using a rate equation for the most probable value for the electrostatic field subject to the appropriate transition probabilities according to the electrostatic boundary conditions. Our model gives rise to a stochastic law when the charge distribution is not deterministic. The probability distribution of the electrostatic field intensity, the mean value of the electrostatic force and the energy density are obtained.

cond-mat.stat-mech↗

arXiv2015

Eigenvalue bounds in one dimensional Schrodinger's equation with ultra-short potentials

The problem of a particle localized in a ultra-short potential in one dimension is considered. By proposing a general solution to Schrodinger;s equation we show that the energy spectra and the probability of the particle have definite bounds for an arbitrary ultra-short potential. These results are relevant for the confinement of particles in nanodevices.

quant-ph↗

arXiv2014

Quantum theory of space charge limited current in solids

We present a quantum model of space charge limited current transport inside trap-free solids with planar geometry in the mean field approximation. We use a simple transformation which allows us to find the exact analytical solution for the steady state current case. We use our approach to find a Mott-Gurney like behavior and the mobility for single charge carriers in the quantum regime in solids.

cond-mat.other↗

arXiv2014

Magnetic quantum coherence effect in Ni4 molecular transistors

We consider the electron transport in single molecule magnet transistors in the presence of Zeeman spin splitting and magnetic quantum coherence (MQC). The Zeeman interaction is extended along the leads, thereby producing gaps in the energy spectrum which allow electron transport with spin polarized along a certain direction. The MQC induces an effective coupling between localized spin states and continuum spin states in the single molecule magnet and leads, respectively. We investigate the conductance at zero temperature as a function of the applied bias and magnetic field, and show that the MQC is responsible for the appearence of resonances. Accordingly, we name them MQC resonances.

cond-mat.mes-hall↗

arXiv2013

Electron dynamics inside a vacuum tube diode through linear differential equations

In this paper we analyze the motion of charged particles in a vacuum tube diode by solving linear differential equations. Our analysis is based on expressing the volume charge density as a function of the current density and coordinates only, while in the usual scheme the volume charge density is expressed as a function of the current density and electrostatic potential. Our approach gives the well known behavior of the classical current density proportional to the three-halves power of the bias potential and inversely proportional to the square of the gap distance between the electrodes, and does not require the solution of the nonlinear differential equation normally associated with the Child-Langmuir formulation.

physics.plasm-ph↗