Husimi dynamics generated by non-Hermitian Hamiltonians

TL;DR

This paper explores the complex dynamics of Husimi distributions under non-Hermitian Hamiltonians, revealing surprising behaviors and providing a semiclassical analysis that bridges classical and quantum evolution.

Contribution

It introduces a detailed analysis of Husimi distribution dynamics in non-Hermitian systems, highlighting the interplay between classical trajectories and quantum effects.

Findings

Classical Husimi evolution involves phase-space trajectories and norm factors.

Full quantum dynamics can be understood as an extension of classical Husimi behavior.

Surprising dynamical features emerge from the interplay of classical and quantum effects.

Abstract

The dynamics generated by non-Hermitian Hamiltonians are often less intuitive than those of conventional Hermitian systems. Even for models as simple as a complexified harmonic oscillator, the dynamics for generic initial states shows surprising features. Here we analyse the dynamics of the Husimi distribution in a semiclassical limit, illuminating the foundations of the full quantum evolution. The classical Husimi evolution is composed of two factors, (i) the initial Husimi distribution evaluated along phase-space trajectories, and (ii) the final value of the norm corresponding to each phase-space point. Both factors conspire to lead to intriguing dynamical behaviours. We demonstrate how the full quantum dynamics unfolds on top of the classical Husimi dynamics for two instructive examples.