A one dimensional model showing a quantum phase transition based on a singular potential
Abstract
We study a one-dimensional singular potential plus three types of regular interactions: constant electric field, harmonic oscillator and infinite square well. We use the Lippman-Schwinger Green function technique in order to search for the bound state energies. In the electric field case the unique bound state coincides with that found in an earlier study as the field is switched off. For non-zero field the ground state is shifted and positive energy "quasibound states" appear. For the harmonic oscillator we find a quantum phase transition of a novel type. This behavior does not occur in the corresponding case of an infinite square well and demonstrates the influence of quantum non-locality.
Keywords
Cite
@article{arxiv.0906.5331,
title = {A one dimensional model showing a quantum phase transition based on a singular potential},
author = {M. L. Glasser and M. Gadella and L. M. Nieto},
journal= {arXiv preprint arXiv:0906.5331},
year = {2015}
}
Comments
We have realized that one of the main conclusions of the paper is wrong: Due to an erroneous calculation, we have concluded that some states in the harmonic oscillator with a point interaction evaporate, which is simple impossible due to the structure of the potential. As this manuscript contains major errors, we consider convenient its withdrawal