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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MDPI AG
2025-01-01
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| author | Martina Hentschel Samuel Schlötzer Lukas Seemann |
| author_facet | Martina Hentschel Samuel Schlötzer Lukas Seemann |
| author_sort | Martina Hentschel |
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| 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. |
| format | Article |
| id | doaj-art-045c42decc7941e689d933dac9c0dce0 |
| institution | DOAJ |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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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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