Imaginary Interactions with Minimum Length

TL;DR

This paper investigates how imposing a minimum length affects a PT-symmetric quantum harmonic oscillator, showing that PT symmetry and phase transition characteristics are preserved under this deformation.

Contribution

It provides an analytical perturbative analysis of a two-dimensional PT-symmetric oscillator with minimum length, demonstrating the invariance of PT symmetry and phase transition features.

Findings

First order correction remains real under unbroken PT symmetry

PT phase transition characteristics are unchanged

Minimum length deformation does not break PT symmetry

Abstract

We analyze the effect of having minimum length on a two dimensional anisotropic simple harmonic oscillator with PT symmetric imaginary interaction perturbatively. First order correction to the general state is calculated analytically to show that it remains real as long as PT symmetry is unbroken. The characteristics of PT phase transition remain unaltered in this deformed formulation of quantum mechanics.