相关论文: On the distribution of matrix elements for the qua…

The scattering matrix S of a ballistic chaotic cavity is the direct sum of a `classical' and a `quantum' part, which describe the scattering of channels with typical dwell time smaller and larger than the Ehrenfest time, respectively.…

We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the `energy'--average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric non--linear $\sigma$--model…

Statistical fluctuations in the eigenvalues of the scattering, impedance and admittance matrices of 2-Port wave-chaotic systems are studied experimentally using a chaotic microwave cavity. These fluctuations are universal in that their…

The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…

We derive the Eigenstate Thermalization Hypothesis (ETH) from a random matrix Hamiltonian by extending the model introduced by J. M. Deutsch [Phys. Rev. A 43, 2046 (1991)]. We approximate the coupling between a subsystem and a many-body…

The quantum baker's map is the quantization of a simple classically chaotic system, and has many generic features that have been studied over the last few years. While there exists a semiclassical theory of this map, a more rigorous study…

We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…

With the decline of the Copenhagen interpretation of quantum mechanics and the recent experiments indicating that quantum mechanics does actually embody 'objective reality', one might ask if a 'mechanical', conceptual model for quantum…

We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties…

We investigate the spectral fluctuation properties of constrained ensembles of random matrices (defined by the condition that a number N(Q) of matrix elements vanish identically; that condition is imposed in unitarily invariant form) in the…

The Walsh-quantized baker's maps are models for quantum chaos on the torus. We show that for all baker's map scaling factors $D\ge2$ except for $D=4$, typically (in the sense of Haar measure on the eigenspaces, which are degenerate) the…

This work deals with the average scattering entropy of quantum graphs. We explore this concept in several distinct scenarios that involve periodic, aperiodic and random distribution of vertices of distinct degrees. In particular, we compare…

Classical counterparts of a great variety of quantum systems, from atomic physics to quantum wells and quantum dots, to optical, microwave, and acoustic resonators exhibit partially chaotic dynamics. Since it is often impossible to measure…

We demonstrate the connection between an operator's matrix element distribution and entangling power via numerical simulations of random, pseudo-random, and quantum chaotic operators. Creating operators with a random distribution of matrix…

We study the matrix elements of local and nonlocal operators in the single-particle eigenstates of two paradigmatic quantum-chaotic quadratic Hamiltonians; the quadratic Sachdev-Ye-Kitaev (SYK2) model and the three-dimensional Anderson…

The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…

Random band matrices relevant for open chaotic systems are introduced and studied. The scattering model based on such matrices may serve for the description of preequilibrium chaotic scattering. In the limit of a large number of open…

We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…

Consider a classically chaotic system which is described by a Hamiltonian H_0. At t=0 the Hamiltonian undergoes a sudden-change H_0 -> H. We consider the quantum-mechanical spreading of the evolving energy distribution, and argue that it…

The energy evolution of a quantum chaotic system under the perturbation that harmonically depends on time is studied for the case of large perturbation, in which the rate of transition calculated from the Fermi golden rule (FGR) is about or…