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Local Wigner-mass maps and integrated negativity as measures of nonclassicality in quantum chaotic billiards

Kyu-Won Park, Soojoon Lee, Kabgyun Jeong

Published Jan 1, 2025• 0 citations
Publisher
DOI
10.2139/ssrn.5713668

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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.

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Abstract The Wigner function is a phase-space quasiprobability distribution whose negative regions provide a direct local signature of nonclassicality. To identify where phase-sensitive structure concentrates, we define local positive and negative Wigner-weight maps and use the integrated Wigner negativity as a compact scalar diagnostic 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 demonstrate the robustness of these diagnostics across two billiard geometries and suggest that the same sign-resolved analysis can be applied to other wave-chaotic platforms, where it may aid mode engineering and coherence control.

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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.
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.
Abstract The Wigner function is a phase-space quasiprobability distribution whose negative regions provide a direct local signature of nonclassicality. To identify where phase-sensitive structure concentrates, we define local positive and negative Wigner-weight maps and use the integrated Wigner negativity as a compact scalar diagnostic 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 demonstrate the robustness of these diagnostics across two billiard geometries and suggest that the same sign-resolved analysis can be applied to other wave-chaotic platforms, where it may aid mode engineering and coherence control.