相关论文: Quantum billiards and constrained random wave corr…

In specific types of partially rectangular billiards we estimate the mass of an eigenfunction of energy $E$ in the region outside the rectangular set in the high-energy limit. We use the adiabatic ansatz to compare the Dirichlet energy form…

We study a two-particle circular billiard containing two finite-size circular particles that collide elastically with the billiard boundary and with each other. Such a two-particle circular billiard provides a clean example of an…

Quantum ergodicity of classically chaotic systems has been studied extensively both theoretically and experimentally, in mathematics, and in physics. Despite this long tradition we are able to present a new rigorous result using only…

We consider the radially vibrating spherical quantum billiard as a representative example of vibrating quantum billiards. We derive necessary conditions for quantum chaos in $d$-term superposition states. These conditions are symmetry…

We study the quantum behaviour of the stadium billiard. We discuss how the interplay between quantum localization and the rich structure of the classical phase space influences the quantum dynamics. The analysis of this model leads to new…

In a previous Letter [Phys. Rev. Lett. 77, 4158 (1996)], a new correlation measure was introduced that sensitively probes phase space localization properties of eigenstates. It is based on a system's response to varying an external…

Similar to the Berry conjecture of quantum chaos we consider elastic analogue which incorporates longitudinal and transverse elastic displacements with corresponding wave vectors. Based on that we derive the correlation functions for…

We study numerically quantum transport through a billiard with a classically mixed phase space. In particular, we calculate the conductance and Wigner delay time by employing a recursive Green's function method. We find sharp, isolated…

We present quasi-analytical and numerical calculations of Gaussian wave packet solutions of the Schr\"odinger equation for two-dimensional infinite well and quantum billiard problems with equilateral triangle, square, and circular…

For two-dimensional quantum billiards we derive the partial Weyl law, i.e. the average density of states, for a subset of eigenstates concentrating on an invariant region $\Gamma$ of phase space. The leading term is proportional to the area…

A two-dimensional circular quantum billiard with unusual boundary conditions introduced by Berry and Dennis (\emph{J Phys A} {\bf 41} (2008) 135203) is considered in detail. It is demonstrated that most of its eigenfunctions are strongly…

We present an extensive numerical study of spectral statistics and eigenfunctions of quantized triangular billiards. We compute two million consecutive eigenvalues for six representative cases of triangular billiards, three with generic…

We study the isolated resonances occurring in conductance fluctuations of ballistic electron systems with a classically mixed phase space. In particular, we calculate the conductance and Wigner-Smith time as well as scattering states and…

For a large class of quantized ergodic flows the quantum ergodicity theorem due to Shnirelman, Zelditch, Colin de Verdi\`ere and others states that almost all eigenfunctions become equidistributed in the semiclassical limit. In this work we…

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…

Using the fact that the energy eigenstates of the equilateral triangle infinite well (or billiard) are available in closed form, we examine the connections between the energy eigenvalue spectrum and the classical closed paths in this…

We consider the time evolution of a wave packet representing a quantum particle moving in a geometrically open billiard that consists of a number of fixed hard-disk or hard-sphere scatterers. Using the technique of multiple collision…

We study the coupling of bouncing-ball modes to chaotic modes in two-dimensional billiards with two parallel boundary segments. Analytically, we predict the corresponding decay rates using the fictitious integrable system approach.…

We consider the distribution of eigenvalues for the wave equation in annular (electromagnetic or acoustic) ray-splitting billiards. These systems are interesting in that the derivation of the associated smoothed spectral counting function…

We consider the free motion of a point particle inside a circular billiard with periodically moving boundary, with the assumption that the collisions of the particle with the boundary are elastic so that the energy of the particle is not…