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A "drivebelt" stadium billiard with boundary consisting of circular arcs of differing radius connected by their common tangents shares many properties with the conventional "straight" stadium, including hyperbolicity and mixing, as well as…
In this work, we perform a statistical study on Dirac Billiards in the extreme quantum limit (a single open channel on the leads). Our numerical analysis uses a large ensemble of random matrices and demonstrates the preponderant role of…
We study theoretically the Josephson current-phase relationship in a chaotic quantum dot coupled to superconductors by ballistic contacts. In this regime, strong proximity effect induces superconductivity in the quantum dot that leads to a…
Andreev billiards are finite, arbitrarily-shaped, normal-state regions, surrounded by superconductor. At energies below the superconducting energy gap, single-quasiparticle excitations are confined to the normal region and its vicinity, the…
The statistics of energy levels of a rectangular billiard, that is perturbed by a strong localized potential, are studied analytically and numerically, when this perturbation is at the center or at a typical position. Different results are…
Eigenstates and energy levels of a square quantum billiard in a magnetic field, or with an Aharonov-Bohm flux line, are found in quasiclassical approximation, that is, for high enough energy. Explicit formulas for the energy levels and…
Conductance fluctuations have been studied in a soft wall stadium and a Sinai billiard defined by electrostatic gates on a high mobility semiconductor heterojunction. These reproducible magnetoconductance fluctuations are found to be…
We prove the presence of topological chaos at high internal energies for a new class of mechanical refraction billiards coming from Celestial Mechanics. Given a smooth closed domain $D\in\mathbb{R}^2$, a central mass generates a Keplerian…
Uniform hyperbolicity is a strong chaotic property which holds, in particular, for Sinai billiards. In this paper, we consider the case of a nonflat billiard, that is, a Riemannian manifold with boundary. Each trajectory follows the…
Close to a spacelike singularity, pure gravity and supergravity in four to eleven spacetime dimensions admit a cosmological billiard description based on hyperbolic Kac-Moody groups. We investigate the quantum cosmological billiards of…
Nonlinear coupling between eigenmodes of a system leads to spectral energy redistribution. For multi-wavespeed chaotic billiards the average coupling strength can exhibit sharp discontinuities as a function of frequency related to…
Streamlines and distributions of nodal points are used as signatures of chaos in coherent electron transport through three types of billiards, Sinai, Bunimovich and rectangular. Numerical averaged distribution functions of nearest distances…
The coherent tunneling phenomenon is investigated in rectangular billiards divided into two domains by a classically unclimbable potential barrier. We show that by placing a pointlike scatterer inside the billiard, we can control the…
We investigate a semiclassical conductance for ballistic open three-dimensional (3-d) billiards. For partially or completely broken-ergodic 3-d billiards such as SO(2) symmetric billiards, the dependence of the conductance on the Fermi…
We study theoretically and numerically the velocity dynamics of fully chaotic time-dependent shape-preserving billiards. The average velocity of an ensemble of initial conditions generally asymptotically follows the power law $v =…
We present a computational scheme based on classical molecular dynamics to study chaotic billiards in static external magnetic fields. The method allows to treat arbitrary geometries and several interacting particles. We test the scheme for…
The problem of the quantizations of the $L$-shaped billiards and the like ones, i.e. each angle of which is equal to $\pi/2$ or $3\pi/2$, is considered using as a tool the Fourier series expansion method. The respective wave functions and…
The quantum dynamics of a chaotic billiard with moving boundary is considered in this work. We found a shape parameter Hamiltonian expansion which enables us to obtain the spectrum of the deformed billiard for deformations so large as the…
The Loschmidt echo (LE) measures the ability of a system to return to the initial state after a forward quantum evolution followed by a backward perturbed one. It has been conjectured that the echo of a classically chaotic system decays…
We consider a slowly rotating rectangular billiard with moving boundaries and use the canonical perturbation theory to describe the dynamics of a billiard particle. In the process of slow evolution certain resonance conditions can be…