The two dimensional harmonic oscillator on a noncommutative space with minimal uncertainties
High Energy Physics - Theory
2013-07-04 v1 Mathematical Physics
math.MP
Quantum Physics
Abstract
The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat noncommutative space and employ it to study the eigenvalue spectrum for the harmonic oscillator on this space. The perturbative expression for the eigenenergy indicates that the model might possess an exceptional point at which the spectrum becomes complex and its PT-symmetry is spontaneously broken.
Cite
@article{arxiv.1207.3303,
title = {The two dimensional harmonic oscillator on a noncommutative space with minimal uncertainties},
author = {Sanjib Dey and Andreas Fring},
journal= {arXiv preprint arXiv:1207.3303},
year = {2013}
}
Comments
4 pages, contribution to proceedings of "Analytic and algebraic methods in physics X", Prague