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Ray-Wave Correspondence in Anisotropic Mesoscopic Billiards
Martina Hentschel1, Samuel Schlötzer1, Lukas Seemann1
1Institute of Physics, Technische Universität Chemnitz, D-09107 Chemnitz, Germany.
Entropy (Basel, Switzerland)
|February 26, 2025
Summary
We introduce anisotropic billiard systems, such as those in bilayer graphene and optical cavities, to quantum chaos studies. Ray-wave correspondence offers insights into these systems, bridging classical and quantum descriptions.
Area of Science:
- Quantum chaos
- Nonlinear dynamics
- Mesoscopic physics
Background:
- Mesoscopic billiard systems (quantum dots, optical microcavities) are crucial in quantum chaos and nonlinear dynamics.
- Existing models primarily focus on isotropic systems, limiting the scope of experimental realization and theoretical understanding.
Purpose of the Study:
- To introduce and investigate two-dimensional anisotropic billiard systems.
- To explore the applicability of ray-wave correspondence in anisotropic systems.
- To compare optical and electronic anisotropic systems.
Main Methods:
- Ray-tracing analysis incorporating anisotropic momentum space, using a non-spherical index ellipsoid model.
- Transformation optics to solve the wave problem and identify system resonances.
- Comparative analysis of optical and electronic anisotropic systems.
Main Results:
- Ray-wave correspondence provides valuable insights into anisotropic billiard dynamics.
- Resonances in anisotropic disk cavities correspond to those of isotropic elliptical cavities.
- Distinct descriptions arise for optical and electronic anisotropic systems.
Conclusions:
- Anisotropic billiard systems expand the toolkit for studying quantum chaos and nonlinear dynamics.
- Ray-wave correspondence is a unifying concept applicable to both isotropic and anisotropic mesoscopic systems.
- Understanding the differences between optical and electronic anisotropic systems is key for future research.
Keywords:
anisotropybilayer graphenebirefringencedispersion relationindex ellipsoidmesoscopic billiardsoptical microcavitiesphase-space dynamicsray–wave correspondenceMore Related Videos
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