https://doi.org/10.1140/epjp/s13360-026-07462-6
Regular Article
Wigner-entropy and negativity signatures of tunneling in a sextic double well
1
Departamento de Física, Universidad Autónoma Metropolitana, Iztapalapa, Rafael Atlixco 186, CDMX, 09340, Ciudad de México, Mexico
2
Departamento de Química, Universidad Autónoma Metropolitana, Iztapalapa, Rafael Atlixco 186, CDMX, 09340, Ciudad de México, Mexico
3
Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, 3001, Boulevard Juriquilla, 76230, Querétaro, Mexico
a
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Received:
25
December
2025
Accepted:
18
February
2026
Published online:
6
March
2026
Abstract
We develop a phase-space description of tunneling in the quasi-exact sextic double well 
based on the Wigner quasiprobability. From high-accuracy wavefunctions, we introduce the complex Shannon entropy 
of the Wigner function W(x, p), whose imaginary part isolates coherence and negativity, and the entropy 
of its modulus, a strictly real indicator of phase-space spreading. Together with the mutual information 
, these measures yield sharp signatures of the transition into the double-well regime (
) and the emergence of tunneling-induced parity doublets. High-precision spectral data are supported by a smooth Gaussian-process interpolant anchored in asymptotic scaling, ensuring analytic control of level behavior. The resulting phase-space framework provides a compact and sensitive characterization of nonclassical structure beyond probability-density approaches.
Adrian M. Escobar Ruiz, Angelina N. Mendoza Tavera, Robin P. Sagar, C. Mateo Frausto-Avila and Mario A. Quiroz-Juárez are contributed equally to this work.
© The Author(s) 2026
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