Physics of PT-Symmetric Quantum Systems at Finite Temperature

TL;DR

This paper develops a new quantum statistics framework to analyze finite-temperature PT-symmetric non-Hermitian quantum systems, revealing a continuous phase transition at the exceptional point and a zero-temperature anomaly.

Contribution

It introduces the quantum Liouvillian statistics theory, replacing the Boltzmann law, to study thermodynamics of PT-symmetric systems at finite temperature.

Findings

Discovered a continuous thermodynamic phase transition at the exceptional point.

Identified a zero-temperature anomaly in PT-symmetric systems.

Derived analytical thermodynamic properties using the new theory.

Abstract

We study parity-time-symmetric non-Hermitian quantum systems at finite temperature, where the Boltzmann distribution law fails to hold. To characterize their abnormal physical properties, a new quantum statistics theory (the so-called quantum Liouvillian statistics theory) was developed, in which the Boltzmann distribution law was replaced by the Liouvillian-Boltzmann distribution law. Using it, we derived analytical results of thermodynamic properties for thermal PT systems and found that a "continuous" thermodynamic phase transition occurs at the exceptional point, where a zero-temperature anomaly exists.