Quantum-to-semiclassical Husimi dynamics of non-Hermitian localization transitions

TL;DR

This paper explores the relationship between classical phase-space dynamics and quantum localization transitions in non-Hermitian quasiperiodic systems, revealing that classical analysis can approximate quantum behavior only under specific conditions.

Contribution

It demonstrates that classical phase-space analysis partially captures non-Hermitian localization transitions, highlighting the lack of a universal classical-quantum correspondence in these systems.

Findings

Localization transitions persist in semiclassical limit

Classical transition points do not match quantum critical points

Classical dynamics can mimic quantum behavior temporarily

Abstract

The localization transition in the Hermitian Aubry-Andr\'e model is known to have a clear classical origin, with the critical point being exactly predictable from an analysis of classical phase-space trajectories. Motivated by this correspondence, we investigate whether a similar classical origin exists for localization transitions in non-Hermitian quasiperiodic Hamiltonians. Using semiclassical Husimi dynamics together with a detailed phase-space stability analysis, we show that localization transitions persist even in the semiclassical limit of such non-Hermitian models. However, in sharp contrast to the Hermitian Aubry-Andr\'e case, the transition point inferred from classical phase-space analysis does not coincide with the quantum critical point. Instead, we find that the semiclassical transition depends sensitively on the choice of the irrational parameter defining the quasiperiodic potential, indicating the absence of a universal classical-quantum correspondence for the localization transition in the non-Hermitian setting. Nonetheless, we identify a suitable parameter regime in which the classical dynamics can faithfully mimic the quantum dynamics over a finite but appreciable time window.