The Dirac-Moshinsky oscillator: theory and applications

Abstract

This work summarizes the most important developments in the construction and application of the Dirac-Moshinsky oscillator (DMO) with which the author has come in contact. The literature on the subject is voluminous, mostly because of the avenues that exact solvability opens towards our understanding of relativistic quantum mechanics. Here we make an effort to present the subject in chronological order and also in increasing degree of complexity of its parts. We start our discussion with the seminal paper by Moshinsky and Szczepaniak and the immediate implications stemming from it. Then we analyze the extensions of this model to many particles. The one-particle DMO is revisited in the light of the Jaynes-Cummings model in quantum optics and exactly solvable extensions are presented. Applications and implementations in hexagonal lattices are given, with a particular emphasis in the emulation of graphene in electromagnetic billiards.

Relativistic Measurement Backaction in the Quantum Dirac Oscillator

“…It is characterized by fast Zitterbewegung oscillations of small amplitude superposed to slow oscillations at frequency ω Ω zb and of amplitude proportional to 2 f , essentially still given by Eq. (8). Detecting a signal at the bare frequency of the oscillator results, therefore, in an effective smearing f ± ∆ of the measured force, with ∆ = √ 2nεg b †b .…”

Self-Adjoint Extension Approach for Singular Hamiltonians in (2 + 1) Dimensions

“…The Dirac oscillator is an exactly soluble model and can be an excellent example in the context of many-particle models in relativistic and nonrelativistic quantum mechanics [40]. In Ref.…”

First Experimental Realization of the Dirac Oscillator

“…Pm, 07.57.Pt, 73.22.Pr The relativistic version of the harmonic oscillator has been touched upon occasionally [1,2], but became a widely used model for relativistic equations with the appearance of the seminal paper [3]. Originally it was known as the Dirac oscillator (DO) [4,5]. Indeed since then the number of papers using this model has increased rapidly, mainly in mathematical physics [6][7][8][9][10][11][12][13][14][15][16][17][18][19], but also in nuclear physics [20][21][22], subnuclear physics [23,24] and quantum optics [25][26][27][28].…”