Exceptional Points and Dynamical Phase Transitions

I Rotter

doi:10.14311/1273

Abstract

In the framework of non-Hermitian quantum physics, the relation between exceptional points,dynamical phase transitions and the counter intuitive behavior of quantum systems at high level density is considered. The theoretical results obtained for open quantum systems and proven experimentally some years ago on a microwave cavity, may explain environmentally induce deffects (including dynamical phase transitions), which have been observed in various experimental studies. They also agree(qualitatively) with the experimental results reported recently in PT symmetric optical lattices.

Highlights

In the framework of non-Hermitian quantum physics, the relation between exceptional points, dynamical phase transitions and the counterintuitive behavior of quantum systems at high level density is considered
Kato [1] introduced the notation exceptional points for singularities appearing in the perturbation theory for linear operators
According to Kato, the number of eigenvalues and the number of eigenfunctions is reduced at the exceptional point

Summary

Introduction

In the framework of non-Hermitian quantum physics, the relation between exceptional points, dynamical phase transitions and the counterintuitive behavior of quantum systems at high level density is considered. This means that the k are considered to be eigenvalues of a non-Hermitian Hamilton operator H0 which contains both the direct interaction V between the two states and the coupling of each of the two individual states to the environment of scattering wavefunctions. This means that the non-Hermitian quantum physics is able to describe environmentally induced effects, for example spectroscopic redistribution processes induced by the mixing of the states via the continuum of scattering wavefunctions, which is described by ω in (3).

Results

Conclusion