Opposite amplitude phase entropy responses at a non Hermitian avoided crossing

TL;DR

This paper introduces a novel information-theoretic approach analyzing local amplitude and phase statistics in non-Hermitian open resonators, revealing unique sector-dependent responses at avoided crossings and spatial heterogeneity effects.

Contribution

It presents a new field-level analysis combining amplitude and phase statistics, uncovering sector-resolved behaviors and the role of spatial heterogeneity in non-Hermitian mode interactions.

Findings

Amplitude statistics tighten at the mixing point.

Phase statistics broaden maximally at the mixing point.

Global amplitude-phase coupling is shaped by spatial heterogeneity.

Abstract

Avoided crossings (A.C.) in open resonators arise from non-Hermitian mode interaction, where leakage produces complex spectra and biorthogonal eigenmodes. Intensity-based entropies are robust markers of mode mixing but discard the phase structure of the complex field. Here we introduce a field-level information-theoretic analysis based on the joint statistics of local amplitude and phase under Born-weighted sampling on the cavity grid. For an open elliptical microcavity in the strong-interaction A.C. regime, we find a distinctive sector-resolved response: amplitude statistics tighten while phase statistics broaden maximally at the mixing point, and conditioning reveals strong amplitude-phase dependence. By introducing a coarse position label and the associated co-information, we further show that the enhancement of global amplitude-phase coupling is strongly shaped by spatial heterogeneity across the cavity.