arXiv subjects

David J Fernández C

Publications and source records attributed to David J Fernández C.

3 recordsLinked to original sources

arXiv2023

Supersymmetric Quantum Mechanics, multiphoton algebras and coherent states

The multiphoton algebras for one-dimensional Hamiltonians with infinite discrete spectrum, and for their associated kth-order SUSY partners are studied. In both cases, such an algebra is generated by the multiphoton annihilation and creation operators, as well as by Hamiltonians which are functions of an appropriate number operator. The algebras obtained turn out to be polynomial deformations of the corresponding single-photon algebra previously studied. The Barut-Girardello coherent states, which are eigenstates of the annihilation operator, are obtained and their uncertainty relations are explored by means of the associated quadratures.

quant-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↗

arXiv2019

Multiphoton supercoherent states

In this paper we are going to build the multiphoton supercoherent states for the supersymmetric harmonic oscillator as eigenstates of the $m$-th power of a special form (but still with a free parameter) of the Kornbluth-Zypman supersymmetric annihilation operator. They become expressed in terms of the multiphoton coherent states for the standard harmonic oscillator. The Heisenberg uncertainty relation and some statistical properties for these states will be studied. Since the multiphoton supercoherent states turn out to be periodic, then the associated geometric phases will be as well evaluated.

quant-ph↗