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DY: Fachverband Dynamik und Statistische Physik

DY 8: Focus Session: Nonlinear Dynamics and Stochastic Processes – Advances in Theory and Applications II

DY 8.4: Vortrag

Montag, 17. März 2025, 16:00–16:15, H43

Momentum space induced complex billiard dynamics — •Lukas Seemann, Jana Lukin, and Martina Hentschel — Institut für Physik, TU Chemnitz, Deutschland

While billiard models have always been a paradigm to study nonlinear dynamics, their class has been enriched by realistic models such as optical cavities, ballistic quantum dots, or graphene systems over the past decades. The originally hard billiard walls are replaced by confinement through total internal reflection of light or potential wells trapping electrons. They are well-known model systems in the field of mesoscopic physics, quantum chaos, and wave-ray correspondence exhibiting a broad range of dynamical behavior, ranging from regular and mixed to purely chaotic dynamics depending on their geometric shape. However, employing their material-specific properties allows one to influence and even control their complex dynamics in more ways. Using an anisotropy (as for electrons in bilayer graphene systems), one can induce chaotic motion even in a circularly shaped cavity [1]. We develop a ray tracing algorithm for anisotropic media and illustrate how anisotropy affects the billiards dynamics in real and phase space. In particular we show how deformation away from the circular shape in real and momentum space, changes the phase space structure and can be optimized to the formation of large stable island [2] that we quantify using Lyapunov exponents.

[1] L. Seemann, A. Knothe, M. Hentschel, Phys. Rev. B 107, 205404 (2023)

[2] L. Seemann, A. Knothe, M. Hentschel, NJP 26, 10 (2024)

Keywords: billiards; anisotropy; ray-wave correspondence; ray tracing