Supersymmetry and PT-Symmetric Spectral Bifurcation

TL;DR

This paper explores the interplay of supersymmetry and PT-symmetry in dynamical systems, revealing conditions under which ground states respect or break PT-symmetry and providing methods to generate exactly solvable complex potentials.

Contribution

It introduces a general framework for analyzing supersymmetry and PT-symmetry in dynamical systems, including novel insights into potential bifurcations and solution methods for complex potentials.

Findings

Ground state may or may not respect PT-symmetry depending on parameters.

Two superpotentials can generate one potential in non-PT-symmetric cases.

Exact eigenfunctions and eigenstates can be obtained via shape-invariance.

Abstract

Dynamical systems exhibiting both PT and Supersymmetry are analyzed in a general scenario. It is found that, in an appropriate parameter domain, the ground state may or may not respect PT-symmetry. Interestingly, in the domain where PT-symmetry is not respected, two superpotentials give rise to one potential; whereas when the ground state respects PT, this correspondence is unique. In both scenarios, supersymmetry and shape-invariance are intact, through which one can obtain eigenfunctions and eigenstates exactly. Our procedure enables one to generate a host of complex potentials which are not PT-symmetric, and can be exactly solved.