Related papers: Short-Time Effects on Eigenstate Structure in Sina…
We present a comprehensive semiclassical investigation of the three-dimensional Sinai billiard, addressing a few outstanding problems in "quantum chaos". We were mainly concerned with the accuracy of the semiclassical trace formula in two…
We study the spectral rigidity problem for Sinai billiards with finite horizon, specifically asking whether the geometry of the billiard table can be recovered from the lengths of its (marked) periodic trajectories. To address this, we…
Statistical equilibration of energies in a slow-fast system is a fundamental open problem in physics. In a recent paper, it was shown that the equilibration rate in a springy billiard can remain strictly positive in the limit of vanishing…
We discuss a modification to Random Matrix Theory eigenstate statistics, that systematically takes into account the non-universal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead…
The Sinai billiard map $T$ on the two-torus, i.e., the periodic Lorentz gaz, is a discontinuous map. Assuming finite horizon and another condition we introduce -- namely \emph{negligible singularities} -- we prove that the metric pressure…
Sinai chaos is characterized by exponential divergence between neighboring trajectories of a point billiard. If the repulsive potential of the finite-diameter fixed particle in the middle of the table is made smooth, the Sinai divergence…
We study approximations of billiard systems by lattice graphs. It is demonstrated that under natural assumptions the graph wavefunctions approximate solutions of the Schroedinger equation with energy rescaled by the billiard dimension. As…
We examine the consequences of classical ergodicity for the localization properties of individual quantum eigenstates in the classical limit. We note that the well known Schnirelman result is a weaker form of quantum ergodicity than the one…
We propose a model of Sinai billiards with moving scatterers, in which the locations and shapes of the scatterers may change by small amounts between collisions. Our main result is the exponential loss of memory of initial data at uniform…
It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. In this Letter we show that the level fluctuations of experimental realizations of the Sinai billiard exhibit…
We discuss general aspects of non-relativistic quantum chaos theory of scattering of a quantum particle on a system of a large number of naked singularities. We define such a system space-temporal Sinai billiard We dis- cuss the problem in…
We obtain sharp error rates in the local limit theorem for the Sinai billiard map (one and two dimensional) with infinite horizon. This result allows us to further obtain higher order terms and thus, sharp mixing rates in the speed of…
Quantum cavities or dots have markedly different properties depending on whether their classical counterparts are chaotic or not. Connecting a superconductor to such a cavity leads to notable proximity effects, particularly the appearance,…
An effective random matrix theory description is developed for the universal gap fluctuations and the ensemble averaged density of states of chaotic Andreev billiards for finite Ehrenfest time. It yields a very good agreement with the…
For classical billiards we suggest that a matrix of action or length of trajectories in conjunction with statistical measures, level spacing distribution and spectral rigidity, can be used to distinguish chaotic from integrable systems. As…
We use scanning near-field optical microscopy to image hyperbolic phonon polaritons in hexagonal boron nitride (hBN) billiards with integrable and chaotic geometries. In Sinai billiards, we observe irregular mode patterns consistent with…
The Lorentz gas of $\mathbb{Z}^2$-periodic scatterers (or the so called Sinai billiards) can be used to model motion of electrons on an ionized medal. We investigate the linear response for the system under various external forces (during…
We discuss the impact of recent developments in the theory of chaotic dynamical systems, particularly the results of Sinai and Ruelle, on microwave experiments designed to study quantum chaos. The properties of closed Sinai billiard…
Finite horizon Sinai billiard maps are examples of uniformly hyperbolic systems with singularities. These discontinuities make it more difficult to develop the classical theory of thermodynamic formalism. Nevertheless, Baladi and Demers…
We report on the stationary dynamics in classical Sinai billiard (SB) corresponding to the unit cell of the periodic Lorentz gas (LG) formed by square lattice of length $L$ and dispersing circles of radius $R$ placed in the center of unit…