相关论文: Intermediate wave-function statistics
We obtain general predictions for the distribution of wave function intensities in position space on the periodic orbits of chaotic ballistic systems. The expressions depend on effective system size N, instability exponent lambda of the…
We investigate quantised maps of the torus whose classical analogues are ergodic but not mixing. Their quantum spectral statistics shows non-generic behaviour, i.e.it does not follow random matrix theory (RMT). By coupling the map to a spin…
Certain wave functions of non-interacting quantum chaotic systems can exhibit "scars" in the fabric of their real-space density profile. Quantum scarred wave functions concentrate in the vicinity of unstable periodic classical trajectories.…
Spectral statistics of hermitian random Toeplitz matrices with independent identically distributed elements is investigated numerically. It is found that the eigenvalue statistics of complex Toeplitz matrices is surprisingly well…
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…
Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of…
We apply a recently developed semiclassical theory of short peridic orbits to the stadium billiard. We give explicit expresions for the resonances of periodic orbits and for the application of the semiclassical Hamiltonian operator to them.…
Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of an isolated system which is determined to calculate molecular properties and to…
A discrete analog of quantum unique ergodicity was proved for Cayley graphs of quasirandom groups by Magee, Thomas and Zhao. They show that for large graphs there exist real orthonormal basis of eigenfunctions of the adjacency matrix such…
We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide…
We present a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to distinguish not only between regular and…
We consider the Faraday surface waves of a fluid in a container with a non-integrable boundary shape. We show that, at sufficiently low frequencies, the wave patterns are ``scars'' selected by the instability of the corresponding periodic…
A novel approach is suggested for the statistical description of quantum systems of interacting particles. The key point of this approach is that a typical eigenstate in the energy representation (shape of eigenstates, SE) has a well…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
The states of an open quantum system are coupled via the environment of scattering wavefunctions. The complex coupling coefficients $\omega$ between system and environment arise from the principal value integral and the residuum. At high…
We estimate the distribution of the eigenvalues of a family of time-frequency localization operators whose eigenfunctions are the well-known Prolate Spheroidal Wave Functions from mathematical physics. These operators are fundamental to the…
Quantum statistics have a profound impact on the properties of systems composed of identical particles. In this Letter, we demonstrate that the quantum statistics of a pair of identical massive particles can be probed by a direct…
The properties of energy levels in a family of classically pseudointegrable systems, the barrier billiards, are investigated. An extensive numerical study of nearest-neighbor spacing distributions, next-to-nearest spacing distributions,…
We show that in the semiclassical limit, classically chaotic systems have universal spectral statistics. Concentrating on short-time statistics, we identify the pairs of classical periodic orbits determining the small-$\tau$ behavior of the…
The eigenvalue density of a quantum-mechanical system exhibits oscillations, determined by the closed orbits of the corresponding classical system; this relationship is simple and strong for waves in billiards or on manifolds, but becomes…