Local Wigner-Mass Maps and Integrated Negativity as Measures of nonclassicality in Quantum Chaotic Billiards

TL;DR

This paper introduces local Wigner-mass maps and integrated negativity to quantify nonclassicality in quantum chaotic billiards, revealing how phase space structures and coherences contribute to quantum signatures.

Contribution

It presents a novel framework using local Wigner-mass maps and negativity measures to analyze nonclassicality in wave-chaotic systems, applicable beyond billiards.

Findings

Negative Wigner regions indicate nonclassicality.

Hybridization enhances negativity in chaotic eigenmodes.

Framework validated across different billiard geometries.

Abstract

The Wigner function is a phase space quasi-probability distribution whose negative regions provide a direct, local signature of nonclassicality. To identify where phase-sensitive structure concentrates, we introduce local positive- and negative Wigner-mass maps and adopt the integrated Wigner negativity as a compact scalar measure of nonclassical phase space structure. A decomposition of the density operator reveals that off-diagonal coherences between hybridizing components generate oscillatory, sign-alternating patterns, with the negative contribution maximized when component weights are comparable. Non-Gaussian chaotic eigenmodes exhibit a baseline negativity that is further amplified by such hybridization. We validate these diagnostics across two billiard geometries and argue that the framework is transferable to other wave-chaotic platforms, where it can aid mode engineering and coherence control.