Classical limit of non-Hermitian quantum dynamics - a generalised canonical structure

TL;DR

This paper derives a generalized canonical structure describing the classical limit of non-Hermitian quantum systems, incorporating both conservative and dissipative dynamics, and demonstrates its application to systems with Euclidean and spherical phase spaces.

Contribution

It introduces a unified framework for classical dynamics of non-Hermitian quantum systems, extending to nontrivial phase space geometries like spheres.

Findings

Classical dynamics combine symplectic and metric gradient flows.

The structure applies to Euclidean and spherical phase spaces.

Damped and driven oscillators are modeled within this framework.

Abstract

We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion, for both conservative and dissipative motion. The dynamical equations combine a symplectic flow associated with the Hermitian part of the Hamiltonian with a metric gradient flow associated with the anti-Hermitian part of the Hamiltonian. We derive this structure of the classical limit of quantum systems in the case of a Euclidean phase space geometry. As an example we show that the classical dynamics of a damped and driven oscillator can be linked to a non-Hermitian quantum system, and investigate the quantum classical correspondence. Furthermore, we present an example of an angular momentum system whose classical phase space is spherical and show that the generalised canonical structure persists for this nontrivial phase space geometry.