arXiv subjects

Daniel O-Campa

Publications and source records attributed to Daniel O-Campa.

7 recordsLinked to original sources

arXiv2026

Spectral design of confining optical structures by supersymmetry techniques

In this work, we apply supersymmetric transformations to an optical medium with quadratic index distributions on both transversal coordinates defining an elliptic profile. In particular, we implement first- and second-order transformations to construct new multi-parametric gradient index patterns that may host one or two subsidiary guided modes with a wide range of spectral properties and transversal intensity and phase distributions. These transformations may be continued up to an arbitrary order enabling the possibility to control the spectral and propagation properties of light beams.

physics.optics↗

arXiv2025

Spectral analysis of Dirac materials in position-dependent magnetic and electric fields via Heun functions

This work focuses on the study of the spectral problem for Dirac materials immersed in position-dependent magnetic and electric fields. To achieve this, the system of differential equations satisfied by the eigenfunction components of the Hamiltonian has been decoupled, and the solutions for some specific cases have been analyzed using Heun functions, which provide us with a quantization relation and allow us to determine the solutions for the bound states.

math-ph↗

arXiv2024

Phase-space representation of coherent states generated through SUSY QM for tilted anisotropic Dirac materials

In this paper, we examine the electron interaction within tilted anisotropic Dirac materials when subjected to external electric and magnetic fields possessing translational symmetry. Specifically, we focus on a distinct non-zero electric field magnitude, enabling the decoupling of the differential equation system inherent in the eigenvalue problem. Subsequently, employing supersymmetric quantum mechanics facilitates the determination of eigenstates and eigenvalues corresponding to the Hamiltonian operator. To delve into a semi-classical analysis of the system, we identify a set of coherent states. Finally, we assess the characteristics of these states using fidelity and the phase-space representation through the Wigner function.

cond-mat.mtrl-sci↗

arXiv2024

An algorithm for exact analytical solutions for tilted anisotropic Dirac materials

In this article, we obtain the exact solutions for bound states of tilted anisotropic Dirac materials under the action of external electric and magnetic fields with translational symmetry. In order to solve the eigenvalue equation that arises from the effective Hamiltonian of these materials, we describe an algorithm that allow us to decouple the differential equations that are obtained for the spinor components.

cond-mat.mes-hall↗

arXiv2022

Graphene generalized coherent states

In this paper we construct the generalized coherent states for an electron in monolayer or bilayer graphene placed in an external magnetic field. At first we define an appropriate set of ladder operators acting on the eigenfunctions for each Hamiltonian, afterwards we derive the generalized coherent states through several definitions and analyze the commutation relationship between the ladder operators. Then we determine the conditions leading to the mutual equivalence between coherent states. Finally, some physical quantities are calculated and we study the time evolution for the generalized graphene coherent states.

quant-ph↗

arXiv2021

Bilayer graphene in magnetic fields generated by supersymmetry

The effective Hamiltonian for electrons in bilayer graphene with applied magnetic fields is solved through second-order supersymmetric quantum mechanics. This method transforms the corresponding eigenvalue problem into two intertwined one dimensional stationary Schrödinger equations whose potentials are determined by choosing at most two seed solutions. In this paper new kinds of magnetic fields associated to non-shape-invariant SUSY partner potentials are generated. Analytic solutions for these magnetic fields are found, the associated spectrum is analyzed, and the probability and current densities are explored.

math-ph↗

arXiv2020

Electron in bilayer graphene with magnetic fields leading to shape invariant potentials

The quantum behavior of electrons in bilayer graphene with applied magnetic fields is addressed. By using second-order supersymmetric quantum mechanics the problem is transformed into two intertwined one dimensional stationary Schrödinger equations whose potentials are required to be shape invariant. Analytical solutions for the energy bound states are obtained for several magnetic fields. The associated spectrum is analyzed, and the probability and current densities are determined.

math-ph↗