arXiv subjects

J. Negro

Publications and source records attributed to J. Negro.

At least 19 recordsLinked to original sources

arXiv2025

Planar Dirac equation with radial contact potentials

We investigate the planar Dirac equation with the most general time-independent contact (singular) potential supported on a circumference. Taking advantage of the radial symmetry, the problem is effectively reduced to a one-dimensional one (the radial), and the contact potential is addressed in a mathematically rigorous way using a distributional approach that was originally developed to treat point interactions in one dimension, providing a physical interpretation for the interaction parameters. The most general contact interaction for this system is obtained in terms of four physical parameters: the strengths of a scalar and the three components of a singular Lorentz vector potential supported on the circumference. We then investigate the bound and scattering solutions for several choices of the physical parameters, and analyze the confinement properties of the corresponding potentials.

math-ph↗

arXiv2025

The role of the effective mass in two-dimensional Dirac electric quantum dots

We investigate the influence of a different effective mass inside and outside an electric quantum dot on in its energy spectrum. Depending on the different values we give to the mass, we have found quite different spectra. Specifically, when the mass is positive but lighter inside the dot than outside it, the spectrum increases and splits into two types of states separated by a gap. Conversely, if the mass inside the quantum dot is heavier than the mass outside, the spectrum has fewer states and needs stronger fields in order to confine states. Finally, the case of inverted mass (ie, negative mass inside the quantum dot and positive outside it or vice versa) gives rise to a new spectral curve of edge states. All these cases have been analyzed in detail along this paper.

cond-mat.mes-hall↗

arXiv2024

Solutions of an extended Duffing-van der Pol equation with variable coefficients

In this work, exact solutions of the nonlinear cubic-quintic Duffing-van der Pol oscillator with variable coefficients are obtained. Two approaches have been applied, one based on the factorization method combined with the Field Method, and a second one relying on Painlev\'e analysis. Both procedures allow us to find the same exact solutions to the problem. The Lagrangian formalism for this system is also derived. Moreover, some examples for particular choices of the time-dependent coefficients, and their corresponding general and particular exact solutions are presented.

nlin.SI↗

arXiv2024

Exploring Supersymmetry: Interchangeability Between Jaynes-Cummings and Anti-Jaynes-Cummings Models

The supersymmetric connection that exists between the Jaynes-Cummings (JC) and anti-Jaynes Cummings (AJC) models in quantum optics is unraveled entirely. A new method is proposed to obtain the temporal evolution of observables in the AJC model using supersymmetric techniques, providing an overview of its dynamics and extending the calculation to full photon counting statistics. The approach is general and can be applied to determine the high-order cumulants given an initial state. The analysis reveals that engineering the collapse-revival behavior and the quantum properties of the interacting field is possible by controlling the initial state of the atomic subsystem and the corresponding atomic frequency in the AJC model. The substantial potential for applications of supersymmetric techniques in the context of photonic quantum technologies is thus demonstrated.

quant-ph↗

arXiv2023

Polar coherent states in bilayer graphene under a constant uniform magnetic field

Symmetries associated with the Hamiltonian describing bilayer graphene subjected to a constant magnetic field perpendicular to the plane of the bilayer are calculated using polar coordinates. These symmetries are then applied to explain some fundamental properties, such as the spectrum and the integer pseudo-spin character of the eigenfunctions. The probability and current densities of the bilayer Hamiltonian have also been calculated in polar coordinates and shown to be gauge invariant and scalar under generalized rotations. We also define appropriate coherent states of this system as eigenfunctions, with complex eigenvalues, of a suitable chose annihilation operator. In this framework, symmetries are also useful to show the meaning of the complex eigenvalue in terms of expected values. The local current density of these coherent states is shown to exhibit a kind of radial component interference effect, something that has gone unnoticed until now. Some of these results that have just been exposed are graphically illustrated throughout the manuscript.

cond-mat.mes-hall↗

arXiv2021

Massive and massless two-dimensional Dirac particles in electric quantum dots

In this work we investigate the confining properties of charged particles of a Dirac material in the plane subject to an electrostatic potential well, that is, in an electric quantum dot. Our study focuses on the effect of mass and angular momenta on such confining properties. To have a global picture of confinement, both bound and resonance states are considered. The resonances will be examined by means of the Wigner time delay of the scattering states, as well as through the complex eigenvalues of outgoing states in order to show that they are physically meaningful. By tuning the potential intensity of the well, electron captures and atomic collapses are observed for critical values. In these processes, the bound states of the discrete spectrum become resonances of the continuous spectrum or vice versa. For massive charges, the atomic collapse phenomenon keeps the number of bound levels in the quantum dot below a maximum value. In the massless case, the bound states have zero energy and occur only for some discrete values of the potential depth, as is known. We also show that although the intensity of the resonances for massive particles is not significantly influenced by angular momenta, on the contrary, for massless particles they are quite sensitive to angular momenta, as it is the case of graphene.

quant-ph↗

arXiv2021

Dirac-like Hamiltonians associated to Schr\"odinger factorizations

In this work, we have extended the factorization method of scalar shape-invariant Schr\"o\-din\-ger Hamiltonians to a class of Dirac-like matrix Hamiltonians. The intertwining operators of the Schr\"odinger equations have been implemented in the Dirac-like shape invariant equations. We have considered also another kind of anti-intertwining operators changing the sign of energy. The Dirac-like Hamiltonians can be obtained from reduction of higher dimensional spin systems. Two examples have been worked out, one obtained from the sphere ${\cal S}^2$ and a second one, having a non-Hermitian character, from the hyperbolic space ${\cal H}^2$.

math-ph↗

arXiv2020

Tavis-Cummings models and their quasi-exactly solvable Schr\"odinger Hamiltonians

We study in detail the relationship between the Tavis-Cummings Hamiltonian of quantum optics and a family of quasi-exactly solvable Schr\"odinger equations. The connection between them is stablished through the biconfluent Heun equation. We found that each invariant $n$-dimensional subspace of Tavis-Cummings Hamiltonian corresponds either to $n$ potentials, each with one known solution, or to one potential with $n$-known solutions. Among these Schr\"odinger potentials appear the quarkonium and the sextic oscillator.

quant-ph↗

arXiv2020

Redundant poles of the $S$-matrix for the one dimensional Morse potential

We analyze the structure of the scattering matrix, $S(k)$, for the one dimensional Morse potential. We show that, in addition to a finite number of bound state poles and an infinite number of anti-bound poles, there exist an infinite number of redundant poles, on the positive imaginary axis, which do not correspond to either of the other types. This can be solved analytically and exactly. In addition, we obtain wave functions for all these poles and ladder operators connecting them. Wave functions for redundant state poles are connected via two different series. We also study some exceptional cases.

math-ph↗

arXiv2020

The general Racah algebra as the symmetry algebra of generic systems on pseudo--spheres

We characterize the symmetry algebra of the generic superintegrable system on a pseudo-sphere corresponding to the homogeneous space $SO(p,q+1)/SO(p,q)$ where $p+q={\cal N}$, ${\cal N}\in\mathbb N$. We show that this algebra is independent of the signature $(p,q+1)$ of the metric and that it is the same as the Racah algebra ${\cal R}({\cal N}+1)$. The spectrum obtained from ${\cal R}({\cal N}+1)$ via the Daskaloyannis method depends on undetermined signs that can be associated to the signatures. Two examples are worked out explicitly for the cases $SO(2,1)/SO(2)$ and $SO(3)/SO(2)$ where it is shown that their spectrum obtained by means of separation of variables coincide with particular choices of the signs corresponding to the specific signatures of the spectrum for the symmetry algebra ${\cal R}(3)$.

math-ph↗

arXiv2018

Classical ladder functions for Rosen-Morse and curved Kepler-Coulomb systems

Ladder functions in classical mechanics are defined in a similar way as ladder operators in the context of quantum mechanics. In the present paper, we develop a new method for obtaining ladder functions of one dimensional systems by means of a product of two `factor functions'. We apply this method to the curved Kepler-Coulomb and Rosen-Morse II systems whose ladder functions were not found yet. The ladder functions here obtained are applied to get the motion of the system.

math-ph↗

arXiv2017

The Perlick system type I: from the algebra of symmetries to the geometry of the trajectories

In this paper, we investigate the main algebraic properties of the maximally superintegrable system known as "Perlick system type I". All possible values of the relevant parameters, $K$ and $β$, are considered. In particular, depending on the sign of the parameter $K$ entering in the metrics, the motion will take place on compact or non compact Riemannian manifolds. To perform our analysis we follow a classical variant of the so called factorization method. Accordingly, we derive the full set of constants of motion and construct their Poisson algebra. As it is expected for maximally superintegrable systems, the algebraic structure will actually shed light also on the geometric features of the trajectories, that will be depicted for different values of the initial data and of the parameters. Especially, the crucial role played by the rational parameter $β$ will be seen "in action".

math-ph↗

arXiv2017

Superintegrability of the Fock-Darwin system

The Fock-Darwin system is analysed from the point of view of its symmetry properties in the quantum and classical frameworks. The quantum Fock-Darwin system is known to have two sets of ladder operators, a fact which guarantees its solvability. We show that for rational values of the quotient of two relevant frequencies, this system is superintegrable, the quantum symmetries being responsible for the degeneracy of the energy levels. These symmetries are of higher order and close a polynomial algebra. In the classical case, the ladder operators are replaced by ladder functions and the symmetries by constants of motion. We also prove that the rational classical system is superintegrable and its trajectories are closed. The constants of motion are also generators of symmetry transformations in the phase space that have been integrated for some special cases. These transformations connect different trajectories with the same energy. The coherent states of the quantum superintegrable system are found and they reproduce the closed trajectories of the classical one.

math-ph↗

arXiv2017

Heisenberg-type higher order symmetries of superintegrable systems separable in cartesian coordinates

Heisenberg-type higher order symmetries are studied for both classical and quantum mechanical systems separable in cartesian coordinates. A few particular cases of this type of superintegrable systems were already considered in the literature, but here they are characterized in full generality together with their integrability properties. Some of these systems are defined only in a region of $\mathbb R^n$, and in general they do not include bounded solutions. The quantum symmetries and potentials are shown to reduce to their superintegrable classical analogs in the $\hbar \to0$ limit.

nlin.SI↗

arXiv2016

Approximation methods for the calculation of eigenvalues in ODE with periodic or anti periodic boundary conditions: Application to nanotubes

We compare three different methods to obtain solutions of Sturm-Liouville problems: a successive approximation method and two other iterative methods. We look for solutions with periodic or anti periodic boundary conditions. With some numerical test over the Mathieu equation, we compare the efficiency of these three methods. As an application, we make a numerical analysis on a model for carbon nanotubes.

physics.comp-ph↗

arXiv2016

Resonances and antibound states of Pöschl-Teller potential: Ladder operators and SUSY partners

We analyze the one dimensional scattering produced by all variations of the Pöschl-Teller potential, i.e., potential well, low and high barriers. We show that the Pöschl-Teller well and low barrier potentials have no resonance poles, but an infinite number of simple poles along the imaginary axis corresponding to bound and antibound states. A quite different situation arises on the Pöschl-Teller high barrier potential, which shows an infinite number of resonance poles and no other singularities. We have obtained the explicit form of their associated Gamow states. We have also constructed ladder operators connecting wave functions for bound and antibound states as well as for resonance states. Finally, using wave functions of Gamow and antibound states in the factorization method, we construct some examples of supersymmetric partners of the Pöschl-Teller Hamiltonian.

math-ph↗

arXiv2014

Superintegrable Lissajous systems on the sphere

A kind of systems on the sphere, whose trajectories are similar to the Lissajous curves, are studied by means of one example. The symmetries are constructed following a unified and straightforward procedure for both the quantum and the classical versions of the model. In the quantum case it is stressed how the symmetries give the degeneracy of each energy level. In the classical case it is shown how the constants of motion supply the orbits, the motion and the frequencies in a natural way.

math-ph↗

arXiv2014

Polynomial symmetries of spherical Lissajous systems

In a previous work, both the constants of motion of a classical system and the symmetries of the corresponding quantum version have been computed with the help of factorizations. As their expressions were not polynomial, in this paper the question of finding an equivalent set of polynomial constants of motion and symmetries is addressed. The general algebraic relations as well as the appropriate Hermitian relations will also be found.

math-ph↗