Statistical Properties of Random Banded Matrices with Strongly Fluctuating Diagonal Elements

The random banded matrices (RBM) whose diagonal elements fluctuate much stronger than the off-diagonal ones were introduced recently by Shepelyansky as a convenient model for coherent propagation of two interacting particles in a random potential. We treat the problem analytically by using the mapping onto the same supersymmetric nonlinear $\sigma-$model that appeared earlier in consideration of the standard RBM ensemble, but with renormalized parameters. A Lorentzian form of the local density of states and a two-scale spatial structure of the eigenfunctions revealed recently by Jacquod and Shepelyansky are confirmed by direct calculation of the distribution of eigenfunction components.Comment: 7 pages,RevTex, no figures Submitted to Phys.Rev.

Correlation functions of impedance and scattering matrix elements in chaotic absorbing cavities

Wave scattering in chaotic systems with a uniform energy loss (absorption) is considered. Within the random matrix approach we calculate exactly the energy correlation functions of different matrix elements of impedance or scattering matrices for systems with preserved or broken time-reversal symmetry. The obtained results are valid at any number of arbitrary open scattering channels and arbitrary absorption. Elastic enhancement factors (defined through the ratio of the corresponding variance in reflection to that in transmission) are also discussed.Comment: 10 pages, 2 figures (misprints corrected and references updated in ver.2); to appear in Acta Phys. Pol. A (Proceedings of the 2nd Workshop on Quantum Chaos and Localization Phenomena, May 19-22, 2005, Warsaw

The decay of photoexcited quantum systems: a description within the statistical scattering model

The decay of photoexcited quantum systems (examples are photodissociation of molecules and autoionization of atoms) can be viewed as a half-collision process (an incoming photon excites the system which subsequently decays by dissociation or autoionization). For this reason, the standard statistical approach to quantum scattering, originally developed to describe nuclear compound reactions, is not directly applicable. Using an alternative approach, correlations and fluctuations of observables characterizing this process were first derived in [Fyodorov YV and Alhassid Y 1998 Phys. Rev. A 58, R3375]. Here we show how the results cited above, and more recent results incorporating direct decay processes, can be obtained from the standard statistical scattering approach by introducing one additional channel.Comment: 7 pages, 2 figure

Induced vs Spontaneous Breakdown of S-matrix Unitarity: Probability of No Return in Quantum Chaotic and Disordered Systems

We investigate systematically sample-to sample fluctuations of the probability $\tau$ of no return into a given entrance channel for wave scattering from disordered systems. For zero-dimensional ("quantum chaotic") and quasi one-dimensional systems with broken time-reversal invariance we derive explicit formulas for the distribution of $\tau$, and investigate particular cases. Finally, relating $\tau$ to violation of S-matrix unitarity induced by internal dissipation, we use the same quantity to identify the Anderson delocalisation transition as the phenomenon of spontaneous breakdown of S-matrix unitarity.Comment: This is the published version, with a few modifications added to the last par

Distribution of "level velocities" in quasi 1D disordered or chaotic systems with localization

The explicit analytical expression for the distribution function of parametric derivatives of energy levels ("level velocities") with respect to a random change of scattering potential is derived for the chaotic quantum systems belonging to the quasi 1D universality class (quantum kicked rotator, "domino" billiard, disordered wire, etc.).Comment: 11 pages, REVTEX 3.

Inhomogeneous losses and complexness of wave functions in chaotic cavities

In a two-dimensional microwave chaotic cavity Ohmic losses located at the contour of the cavity result in different broadenings of different modes. We provide an analytic description and establish the link between such an inhomogeneous damping and the complex (non-real) character of biorthogonal wave functions. This substantiates the corresponding recent experimental findings of Barthélemy et al. (Europhys. Lett., 70 (2005) 162)

Strong eigenfunction correlations near the Anderson localization transition

We study overlap of two different eigenfunctions as compared with self-overlap in the framework of an infinite-dimensional version of the disordered tight-binding model. Despite a very sparse structure of the eigenstates in the vicinity of Anderson transition their mutual overlap is still found to be of the same order as self-overlap as long as energy separation is smaller than a critical value. The latter fact explains robustness of the Wigner-Dyson level statistics everywhere in the phase of extended states. The same picture is expected to hold for usual d-dimensional conductors, ensuring the $s^{\beta}$ form of the level repulsion at critical point.Comment: 4 pages, RevTe

Wigner Random Banded Matrices with Sparse Structure: Local Spectral Density of States

Random banded matrices with linearly increasing diagonal elements are recently considered as an attractive model for complex nuclei and atoms. Apart from early papers by Wigner \cite{Wig} there were no analytical studies on the subject. In this letter we present analytical and numerical results for local spectral density of states (LDOS) for more general case of matrices with a sparsity inside the band. The crossover from the semicircle form of LDOS to that given by the Breit-Wigner formula is studied in detail.Comment: Misprints are corrected and stylistic changes are made. To be published in PR