PT-symmetric quantum Liouvillian dynamics

TL;DR

This paper explores PT-symmetric properties of quantum Liouvillian dynamics in open quantum systems, revealing a D2 symmetry in the spectrum and uniform decay rates for coherences under weak coupling, exemplified by boundary-driven XXZ spin chains.

Contribution

It introduces the concept of PT-symmetry in quantum Liouvillian dynamics and analyzes its spectral implications and effects on coherence decay in open systems.

Findings

D2 symmetry of the Liouvillian spectrum due to PT-symmetry

Uniform decay rates for off-diagonal density matrix elements under weak coupling

Application to boundary-driven XXZ spin chains

Abstract

We discuss a combination of unitary and anti-unitary symmetry of quantum Liouvillian dynamics, in the context of open quantum systems, which implies a D2 symmetry of the complex Liovillean spectrum. For sufficiently weak system-bath coupling it implies a uniform decay rate for all coherences, i.e. off-diagonal elements of the system's density matrix taken in the eigenbasis of the Hamiltonian. As an example we discuss symmetrically boundary driven open XXZ spin 1/2 chains.