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Article

Ray–Wave Correspondence in Anisotropic Mesoscopic Billiards

Institute of Physics, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
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Entropy 2025, 27(2), 132; https://doi.org/10.3390/e27020132
Submission received: 14 December 2024 / Revised: 19 January 2025 / Accepted: 22 January 2025 / Published: 26 January 2025
(This article belongs to the Special Issue Recent Advances in the Theory of Nonlinear Lattices)

Abstract

Mesoscopic billiard systems for electrons and light, realized as quantum dots or optical microcavities, have enriched the fields of quantum chaos and nonlinear dynamics not only by enlarging the class of model systems, but also by providing access to their experimental realization. Here, we add yet another system class, two-dimensional billiards with anisotropies. One example is the anisotropic dispersion relation relevant in bilayer graphene known as trigonal warping, and another is the birefringent closed optical disk cavity. We demonstrate that the established concept of ray–wave correspondence also provides useful insight for anisotropic billiard systems. First, we approach the dynamics of the anisotropic disk from the ray-tracing side that takes the anisotropy in momentum space into account, based on the non-spherical index ellipsoid. Second, we use transformation optics to solve the wave problem and find the resonances to be those of the isotropic elliptical cavity. We illustrate ray–wave correspondence and mark differences in the description of optical and electronic anisotropic systems.
Keywords: mesoscopic billiards; anisotropy; birefringence; ray–wave correspondence; phase-space dynamics; optical microcavities; bilayer graphene; index ellipsoid; dispersion relation mesoscopic billiards; anisotropy; birefringence; ray–wave correspondence; phase-space dynamics; optical microcavities; bilayer graphene; index ellipsoid; dispersion relation

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MDPI and ACS Style

Hentschel, M.; Schlötzer, S.; Seemann, L. Ray–Wave Correspondence in Anisotropic Mesoscopic Billiards. Entropy 2025, 27, 132. https://doi.org/10.3390/e27020132

AMA Style

Hentschel M, Schlötzer S, Seemann L. Ray–Wave Correspondence in Anisotropic Mesoscopic Billiards. Entropy. 2025; 27(2):132. https://doi.org/10.3390/e27020132

Chicago/Turabian Style

Hentschel, Martina, Samuel Schlötzer, and Lukas Seemann. 2025. "Ray–Wave Correspondence in Anisotropic Mesoscopic Billiards" Entropy 27, no. 2: 132. https://doi.org/10.3390/e27020132

APA Style

Hentschel, M., Schlötzer, S., & Seemann, L. (2025). Ray–Wave Correspondence in Anisotropic Mesoscopic Billiards. Entropy, 27(2), 132. https://doi.org/10.3390/e27020132

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