Distribution of scattering matrix elements in quantum chaotic scattering.

Scattering is an important phenomenon which is observed in systems ranging from the micro- to macroscale. In the context of nuclear reaction theory, the Heidelberg approach was proposed and later demonstrated to be applicable to many chaotic scattering systems. To model the universal properties, stochasticity is introduced to the scattering matrix on the level of the Hamiltonian by using random matrices.

Truncations of random orthogonal matrices.

Statistical properties of nonsymmetric real random matrices of size M, obtained as truncations of random orthogonal N×N matrices, are investigated. We derive an exact formula for the density of eigenvalues which consists of two components: finite fraction of eigenvalues are real, while the remaining part of the spectrum is located inside the unit disk symmetrically with respect to the real axis. In the case of strong nonorthogonality, M/N=const, the behavior typical to real Ginibre ensemble is found.

Universality of spectra for interacting quantum chaotic systems.

We analyze a model quantum dynamical system subjected to periodic interaction with an environment, which can describe quantum measurements. Under the condition of strong classical chaos and strong decoherence due to large coupling with the measurement device, the spectra of the evolution operator exhibit an universal behavior. A generic spectrum consists of a single eigenvalue equal to unity, which corresponds to the invariant state of the system, while all other eigenvalues are contained in a disk in the complex plane.

Exact fidelity and full fidelity statistics in regular and chaotic surroundings.

For a prepared state exact expressions for the time-dependent mean fidelity as well as for the mean inverse participation ratio are obtained analytically. The prepared state is taken as an eigenstate of the unperturbed system, and the studied fidelity is identical to the survival probability. The full distribution functions of fidelity in the long-time limit and of inverse participation ratio are studied numerically and analytically.

Distribution of reflection eigenvalues in many-channel chaotic cavities with absorption.

The reflection matrix R=S(dagger)S, with S being the scattering matrix, differs from the unit matrix when absorption is finite. Using the random matrix approach, we calculate analytically the distribution function of its eigenvalues in the limit of a large number of propagating modes in the leads attached to a chaotic cavity. The obtained result is independent of the presence of time-reversal symmetry in the system, being valid at finite absorption and arbitrary openness of the system.

Delay times and reflection in chaotic cavities with absorption.

Absorption yields an additional exponential decay in open quantum systems which can be described by shifting the (scattering) energy E along the imaginary axis, E+i variant Planck's over 2pi /2tau(a). Using the random-matrix approach, we calculate analytically the distribution of proper delay times (eigenvalues of the time-delay matrix) in chaotic systems with broken time-reversal symmetry that is valid for an arbitrary number of generally nonequivalent channels and an arbitrary absorption rate tau(-1)(a). The relation between the average delay time and the "norm-leakage" decay function is found.

Is the concept of the non-Hermitian effective Hamiltonian relevant in the case of potential scattering?

We examine the notion and properties of the non-Hermitian effective Hamiltonian of an unstable system using as an example potential resonance scattering with a fixed angular momentum. We present a consistent self-adjoint formulation of the problem of scattering on a finite-range potential, which is based on the separation of the configuration space into two segments, internal and external. The scattering amplitude is expressed in terms of the resolvent of a non-Hermitian operator H.

Distribution of proper delay times in quantum chaotic scattering: a crossover from ideal to weak coupling.

The probability distribution of the proper delay times during scattering on a chaotic system is derived in the framework of the random matrix approach and the supersymmetry method. The result obtained is valid for an arbitrary number of scattering channels as well as arbitrary coupling to the energy continuum. The case of statistically equivalent channels is studied in detail.

Reducing nonideal to ideal coupling in random matrix description of chaotic scattering: application to the time-delay problem.

We write explicitly a transformation of the scattering phases reducing the problem of quantum chaotic scattering for systems with M statistically equivalent channels at nonideal coupling to that for ideal coupling. Unfolding the phases by their local density leads to universality of their local fluctuations for large M. A relation between the partial time delays and diagonal matrix elements of the Wigner-Smith matrix is revealed for ideal coupling.