Complex Wigner entropy and Fisher control of negativity in an oval quantum billiard

TL;DR

This paper introduces a complex-entropy framework for analyzing Wigner negativity in quantum billiards, revealing how negativity responds to control parameters and identifying signatures of mode hybridization.

Contribution

It develops a novel complex-entropy approach for Wigner negativity, including a negative-channel Fisher information, and applies it to oval quantum billiards to detect mode hybridization effects.

Findings

Wigner negativity can be quantified via a complex entropy functional.

Enhanced negativity correlates with avoided crossings in the billiard.

The negative-channel Fisher information measures sensitivity of negativity to parameter changes.

Abstract

We develop a complex-entropy framework for Wigner negativity and apply it to avoided crossings in an oval quantum billiard. For a real Wigner function the Gibbs--Shannon functional becomes complex; its imaginary part, proportional to the Wigner-negative volume, serves as an entropy-like measure of phase-space nonclassicality. A sign-resolved decomposition separates the total negative weight from its phase-space distribution and defines a negative-channel Fisher information that quantifies how sensitively the negative lobe reshapes as a control parameter is varied. This structure yields a Cauchy--Schwarz bound that limits how rapidly the imaginary entropy, and hence the Wigner negativity, can change with the parameter. In the oval billiard, avoided crossings display enhanced negativity and an amplified negative-channel Fisher response, providing a clear phase-space signature of mode hybridization. The construction is generic and extends to other wave-chaotic and mesoscopic systems with phase-space representations.