Ray–Wave Correspondence in Anisotropic Mesoscopic Billiards

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...

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Main Authors: Martina Hentschel, Samuel Schlötzer, Lukas Seemann
Format: Article
Language:English
Published: MDPI AG 2025-01-01
Series:Entropy
Subjects:
Online Access:https://www.mdpi.com/1099-4300/27/2/132
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author Martina Hentschel
Samuel Schlötzer
Lukas Seemann
author_facet Martina Hentschel
Samuel Schlötzer
Lukas Seemann
author_sort Martina Hentschel
collection DOAJ
description 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.
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spelling doaj-art-045c42decc7941e689d933dac9c0dce02025-08-20T02:44:42ZengMDPI AGEntropy1099-43002025-01-0127213210.3390/e27020132Ray–Wave Correspondence in Anisotropic Mesoscopic BilliardsMartina Hentschel0Samuel Schlötzer1Lukas Seemann2Institute of Physics, Technische Universität Chemnitz, D-09107 Chemnitz, GermanyInstitute of Physics, Technische Universität Chemnitz, D-09107 Chemnitz, GermanyInstitute of Physics, Technische Universität Chemnitz, D-09107 Chemnitz, GermanyMesoscopic 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.https://www.mdpi.com/1099-4300/27/2/132mesoscopic billiardsanisotropybirefringenceray–wave correspondencephase-space dynamicsoptical microcavities
spellingShingle Martina Hentschel
Samuel Schlötzer
Lukas Seemann
Ray–Wave Correspondence in Anisotropic Mesoscopic Billiards
Entropy
mesoscopic billiards
anisotropy
birefringence
ray–wave correspondence
phase-space dynamics
optical microcavities
title Ray–Wave Correspondence in Anisotropic Mesoscopic Billiards
title_full Ray–Wave Correspondence in Anisotropic Mesoscopic Billiards
title_fullStr Ray–Wave Correspondence in Anisotropic Mesoscopic Billiards
title_full_unstemmed Ray–Wave Correspondence in Anisotropic Mesoscopic Billiards
title_short Ray–Wave Correspondence in Anisotropic Mesoscopic Billiards
title_sort ray wave correspondence in anisotropic mesoscopic billiards
topic mesoscopic billiards
anisotropy
birefringence
ray–wave correspondence
phase-space dynamics
optical microcavities
url https://www.mdpi.com/1099-4300/27/2/132
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AT samuelschlotzer raywavecorrespondenceinanisotropicmesoscopicbilliards
AT lukasseemann raywavecorrespondenceinanisotropicmesoscopicbilliards