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Title: Local Wigner-weight maps and integrated negativity as measures of nonclassicality in quantum chaotic billiards

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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