相关论文: Statistical properties of random scattering matric…

By calculating all terms of the high-density expansion of the euclidean random matrix theory (up to second-order in the inverse density) for the vibrational spectrum of a topologically disordered system we show that the low-frequency…

The Wigner time delay of slow particles in the process of their elastic scattering by complex targets formed by several zero-range potentials is investigated. It is shown that at asymptotically large distances from the target, the…

We study the statistical properties of the time delay matrix $Q$ in the context of quantum transport through a chaotic cavity, in the absence of time-reversal invariance. First, we approach the problem from the point of view of random…

Although many physical arguments account for using a modified definition of time delay in multichannel-type scattering processes, one can hardly find rigorous results on that issue in the literature. We try to fill in this gap by showing,…

Elastic scattering of a wave can be quantified by a shift in the phase with respect to the incoming wave phase. A qualitative measure of the time during which the effect occurs is given by the Wigner time delay. The tunneling time in turn…

The scattering matrix approach is employed to determine a joint probability density function of reflection eigenvalues for chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Derived under…

Motivated by recent studies of the phenomenon of Coherent Perfect Absorption, we develop the random matrix theory framework for understanding statistics of the zeros of the (subunitary) scattering matrices in the complex energy plane, as…

We investigate the eigenstructure of matrix formulations used for modeling scattering processes within materials in transmission electron microscopy. Dynamical scattering is crucial for describing the interaction between an electron wave…

We review the random matrix description of electron transport through open quantum dots, subject to time-dependent perturbations. All characteristics of the current linear in the bias can be expressed in terms of the scattering matrix,…

We consider quantum walks on a finite graphs to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The S-matrix for such graphs is defined. Its unitarity is proved…

We review recent progress in analysing wave scattering in systems with both intrinsic chaos and/or disorder and internal losses, when the scattering matrix is no longer unitary. By mapping the problem onto a nonlinear supersymmetric…

Within a random matrix theory approach, we obtain spectral statistics of the Wigner time delay matrix $Q$, for arbitrary channels number $M$ and for all symmetry classes, in fact for general Dyson parameter $\beta$. We also put forth two…

We investigate the low-frequency dynamics for transmission or reflection of a wave by a cavity with chaotic scattering. We compute the probability distribution of the phase derivative phi'=d phi/d omega of the scattered wave amplitude,…

We propose to analyse the statistical properties of a sequence of vectors using the spectrum of the associated Gram matrix. Such sequences arise e.g. by the repeated action of a deterministic kicked quantum dynamics on an initial condition…

We study the effects of an arbitrary external perturbation in the statistical properties of the S-matrix of quantum chaotic scattering systems in the limit of isolated resonances. We derive, using supersymmetry, an exact non-perturbative…

We analyze the distribution of eigenvectors for mesoscopic, mean-field perturbations of diagonal matrices in the bulk of the spectrum. Our results apply to a generalized $N\times N$ Rosenzweig-Porter model. We prove that the eigenvectors…

The K-matrix, also known as the "Wigner reaction matrix" in nuclear scattering or "impedance matrix" in the electromagnetic wave scattering, is given essentially by an M x M diagonal block of the resolvent (E-H)^{-1} of a Hamiltonian H. For…

We study chaotic scattering outside the wide band limit, as the Fermi energy $E_F$ approaches the band edges $E_B$ of a one-dimensional lattice embedding a scattering region of M sites. We show that the delay-time and thermopower…

We consider the empirical eigenvalue distribution of random real symmetric matrices with stochastically independent skew-diagonals and study its limit if the matrix size tends to infinity. We allow correlations between entries on the same…

We develop the scattering theory of general conformally compact metrics. For low frequencies, the domain of the scattering matrix is shown to be frequency dependent. In particular, generalized eigenfunctions exhibit L^2 decay in directions…