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Universality and beyond in Optical Microcavity Billiards with Source-Induced Dynamics.

Entropy (Basel, Switzerland)·2023

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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.

Keywords:

anisotropy bilayer graphene birefringence dispersion relation index ellipsoid mesoscopic billiards optical microcavities phase-space dynamics ray–wave correspondence

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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.