arXiv subjects

David J. Fernández C.

Publications and source records attributed to David J. Fernández C..

15 recordsLinked to original sources

arXiv2025

Exact solutions of the inhomogeneous nonlinear Schrödinger equation through supersymmetric potentials

By employing supersymmetric quantum mechanics, we present a general algorithm to construct supersymmetric partner potentials and hence derive exact stationary solutions of the inhomogeneous nonlinear Schrödinger equation (INLSE). This is possible due to the connection between the INLSE and the nonlinear Schrödinger equation (NLSE), which can be established from a treatment based on Lie point symmetries and is related with Schrödinger equation, under certain conditions. As an illustrative example, we construct exact solutions for the INLSE through a Pösch-Teller potential with a single bound state.

quant-ph↗

arXiv2025

Confluent supersymmetric algorithm for bilayer graphene

External magnetic field profiles leading to equidistant and partially equidistant bilayer graphene spectra within the tight-binding model are obtained. This is achieved by implementing the integral and differential versions of the second-order confluent algorithm to the harmonic oscillator for arbitrary real factorization energies. Additionally, new Barut-Girardello and Gilmore-Perelomov coherent states for bilayer graphene are derived, for both diagonal and non-diagonal ladder operators. Their time evolution is analyzed, finding temporal stability and cyclic evolution in some cases. This fact is contrasted with the non-cyclic evolution of bilayer graphene coherent states obtained when using two different factorization energies. Likewise, the geometric phase and uncertainty product of the quadratures for the previously obtained coherent states are studied.

quant-ph↗

arXiv2024

Bilayer graphene in periodic and quasiperiodic magnetic superlattices

Starting from the effective Hamiltonian arising from the tight binding model, we study the behaviour of low-lying excitations for bilayer graphene placed in periodic external magnetic fields by using irreducible second order supersymmetry transformations. The coupled system of equations describing these excitations is reduced to a pair of periodic Schrödinger Hamiltonians intertwined by a second order differential operator. The direct implementation of more general second-order supersymmetry transformations allows to create nonsingular Schrödinger potentials with periodicity defects and bound states embedded in the forbidden bands, which turn out to be associated to quasiperiodic magnetic superlattices. Applications in quantum metamaterials stem from the ability to engineer and control such bound states which could lead to a fast development of the subject in the near future.

cond-mat.mes-hall↗

arXiv2022

Multiphoton coherent states for bilayer graphene

The multiphoton coherent states, a generalization to coherent sates, are derived for electrons in bilayer graphene placed in a constant homogeneous magnetic field which is orthogonal to the bilayer surface. For that purpose a generalized annihilation operator is constructed in order to determine the multiphoton coherent states as eigenstates of such operator with complex eigenvalue. In addition, some physical quantities are calculated for these states, as the Heisenberg uncertainty relation, probability density and mean energy value. Finally, in order to study the dynamics of the system the time evolution is explored and the time-correlation function is computed.

quant-ph↗

arXiv2022

Equivalent non-rational extensions of the harmonic oscillator, their ladder operators and coherent states

In this work, we generate a family of quantum potentials that are non-rational extensions of the harmonic oscillator. Such a family can be obtained via two different but equivalent supersymmetric transformations. We construct ladder operators for these extensions as the product of the intertwining operators of both transformations. Then, we generate families of Barut-Girardello coherent states and analyze some of their properties as temporal stability, continuity on the label, and completeness relation. Moreover, we calculate mean-energy values, time-dependent probability densities, Wigner functions, and the Mandel Q-parameter to uncover a general non-classical behavior of these states.

quant-ph↗

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

Spectral manipulation of the trigonometric Rosen-Morse potential through supersymmetry

The first and second-order supersymmetry transformations can be used to manipulate one or two energy levels of the initial spectrum when generating new exactly solvable Hamiltonians from a given initial potential. In this paper, we will construct the first and second-order supersymmetric partners of the trigonometric Rosen-Morse potential. Firstly, it is identified a set of solutions of the initial stationary Schrödinger equation which are appropriate for implementing in a simple way non-singular transformations, without inducing new singularities in the built potential. Then, the way the spectral manipulation works is illustrated through several specific examples.

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

Bilayer graphene coherent states

In this paper we consider the interaction of electrons in bilayer graphene with a constant homogeneous magnetic field which is orthogonal to the bilayer surface. Departing from the energy eigenstates of the effective Hamiltonian, the corresponding coherent states will be constructed. For doing this, first we will determine appropriate creation and annihilation operators in order to subsequently derive the coherent states as eigenstates of the annihilation operator with complex eigenvalue. Then, we will calculate some physical quantities, as the Heisenberg uncertainty relation, the probabilities and current density as well as the mean energy value. Finally, we will explore the time evolution for these states and we will compare it with the corresponding evolution for monolayer graphene coherent states.

quant-ph↗

arXiv2016

Solutions to the Painlevé V equation through supersymmetric quantum mechanics

In this paper we shall use the algebraic method known as supersymmetric quantum mechanics (SUSY QM) to obtain solutions to the Painlevé V (PV) equation, a second-order non-linear ordinary differential equation. For this purpose, we will apply first the SUSY QM treatment to the radial oscillator. In addition, we will revisit the polynomial Heisenberg algebras (PHAs) and we will study the general systems ruled by them: for first-order PHAs we obtain the radial oscillator, while for third-order PHAs the potential will be determined by solutions to the PV equation. This connection allows us to introduce a simple technique for generating solutions of the PV equation expressed in terms of confluent hypergeometric functions. Finally, we will classify them into several solution hierarchies.

math-ph↗

arXiv2013

Jacobi photonic lattices and their SUSY partners

We present a classical analog of quantum optical deformed oscillators in arrays of waveguides. The normal modes of these one-dimensional photonic crystals are given in terms of Jacobi polynomials. We show that it is possible to attack the problem via factorization by exploiting the quantum optical analogy. This allows us to provide an unbroken supersymmetric partner of the proposed Jacobi lattices. Thanks to the underlying SU(1,1) group symmetry of the lattices, we present the analytic propagators and impulse functions for these one-dimensional photonic crystals.

physics.optics↗

arXiv2012

Solutions of the Dirac Equation in a Magnetic Field and Intertwining Operators

The intertwining technique has been widely used to study the Schrödinger equation and to generate new Hamiltonians with known spectra. This technique can be adapted to find the bound states of certain Dirac Hamiltonians. In this paper the system to be solved is a relativistic particle placed in a magnetic field with cylindrical symmetry whose intensity decreases as the distance to the symmetry axis grows and its field lines are parallel to the $x-y$ plane. It will be shown that the Hamiltonian under study turns out to be shape invariant.

quant-ph↗

arXiv2011

Supersymmetry Transformations for Delta Potentials

We make a detailed study of the first and second-order SUSY partners of a one-dimensional free Hamiltonian with a singular perturbation proportional to a Dirac delta function. It is shown that the second-order transformations increase the spectral manipulation possibilities offered by the standard first-order supersymmetric quantum mechanics.

hep-th↗

arXiv2003

Group theoretical approach to the intertwined Hamiltonians

We show that the finite difference Bäcklund formula for the Schrödinger Hamiltonians is a particular element of the transformation group on the set of Riccati equations considered by two of us in a previous paper. Then, we give a group theoretical explanation to the problem of Hamiltonians related by a first order differential operator. A generalization of the finite difference algorithm relating eigenfunctions of {\emph three} different Hamiltonians is found, and some illustrative examples of the theory are analyzed, finding new potentials for which one eigenfunction and its corresponding eigenvalue is exactly known.

math-ph↗

arXiv1995

Distorted Heisenberg Algebra and Coherent States for Isospectral Oscillator Hamiltonians

The dynamical algebra associated to a family of isospectral oscillator Hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates. It is shown that this representation becomes similar to that of the standard Heisenberg algebra, and it is dependent of a parameter $w\geq 0$. We name it {\it distorted Heisenberg algebra}, where $w$ is the distortion parameter. The corresponding coherent states for an arbitrary $w$ are derived, and some particular examples are discussed in full detail. A prescription to produce the squeezing, by adequately selecting the initial state of the system, is given.

hep-th↗