Semiclassical Husimi distributions for non-Hermitian quantum systems

TL;DR

This paper develops a semiclassical phase-space approach for non-Hermitian quantum systems using Husimi distributions of Schur vectors, linking quantum states to classical phase-space features and lifetimes.

Contribution

It introduces a novel semiclassical phase-space density of Schur vectors for non-Hermitian systems, applicable to complex dynamics like PT-symmetric kicked rotors.

Findings

Successfully applied to PT-symmetric kicked rotor

Revealed classical norm landscape correlates with quantum lifetimes

Demonstrated generality in mixed and chaotic regimes

Abstract

We construct a semiclassical phase-space density of Schur vectors in non-Hermitian quantum systems. Each Schur vector is associated to a single Planck cell. The Schur states are organised according to a classical norm landscape on phase space - a classical manifestation of the lifetimes which are characteristic of non-Hermitian systems. To demonstrate the generality of this construction we apply it to a highly non-trivial example, a PT-symmetric kicked rotor in the regimes of mixed and chaotic classical dynamics.