相关论文: Experimental studies of Chaos and Localization in …
We consider Gaussian random waves on hyperbolic spaces and establish variance asymptotics and central limit theorems for a large class of their integral functionals, both in the high-frequency and large domain limits. Our strategy of proof…
We study the quantum behaviour of chaotic billiards which exhibit classically diffusive behaviour. In particular we consider the stadium billiard and discuss how the interplay between quantum localization and the rich structure of the…
We consider the motion of a particle subjected to the constant gravitational field and scattered inelasticaly by hard boundaries which possess the shape of parabola, wedge, and hyperbola. The billiard itself performs oscillations. The…
We study chaotic properties of eigenstates depending on the degree of complexity in boundaries of a 2D periodic billiard. Main attention is paid to the situation when the motion of a classical particle is strongly chaotic. Our approach…
Understanding properties of quantum matter is an outstanding challenge in science. In this paper, we demonstrate how machine-learning methods can be successfully applied for the classification of various regimes in single-particle and…
We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth disorder. The conjecture of Gaussian fluctuations of wave functions put forward by Berry and generalized by…
We study the quantum-interference effect in the ballistic Aharonov-Bohm (AB) billiard. The wave-number averaged conductance and the correlation function of the non-averaged conductance are calculated by use of semiclassical theory. Chaotic…
The wavefunctions in phase-space representation can be expressed as entire functions of their zeros if the phase space is compact. These zeros seem to hide a lot of relevant and explicit information about the underlying classical dynamics.…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
In the present work we explore the concept of solitary wave billiards. I.e., instead of a point particle, we examine a solitary wave in an enclosed region and explore its collision with the boundaries and the resulting trajectories in cases…
In a recent letter [Phys. Rev. Lett. {\bf 100}, 164101 (2008)] and within the context of quantized chaotic billiards, random plane wave and semiclassical theoretical approaches were applied to an example of a relatively new class of…
Reflection of particles from a disordered or chaotic medium is characterized by a scattering matrix that can be represented as a superposition of resonances. Each resonance corresponds to an eigenstate inside the medium and has a width…
The dynamics of chaotic billiards is significantly influenced by coexisting regions of regular motion. Here we investigate the prevalence of a different fundamental structure, which is formed by marginally unstable periodic orbits and…
We review the random matrix theory describing elastic scattering through zero-dimensional ballistic cavities (having chaotic classical dynamics) and quasi-one dimensional disordered systems. In zero dimension, general symmetry…
We present first measurements on a superconducting three-dimensional, partly chaotic microwave billiard shaped like a small deformed cup. We analyze the statistical properties of the measured spectrum in terms of several methods originally…
Anderson localization is the ubiquitous phenomenon of inhibition of transport of classical and quantum waves in a disordered medium. In dimension one, it is well known that all states are localized, implying that the distribution of an…
We discuss recent developments in the study of quantum wavefunctions and transport in classically ergodic systems. Surprisingly, short-time classical dynamics leaves permanent imprints on long-time and stationary quantum behavior, which are…
Statistical properties of billiards with diffusive boundary scattering are investigated by means of the supersymmetric sigma-model in a formulation appropriate for chaotic ballistic systems. We study level statistics, parametric level…
The explicit analytical expression for the distribution function of parametric derivatives of energy levels ("level velocities") with respect to a random change of scattering potential is derived for the chaotic quantum systems belonging to…
We study chaotic eigenfunctions in wedge-shaped and rectangular regions using a generalization of Berry's conjecture. An expression for the two-point correlation function is derived and verified numerically.