Abstract:
We investigate the effects of wave localization on the delay time tau (frequency sensitivity of the scattering phase shift) of a wave transmitted through a disordered wave guide. Localization results in a separation tau=chi+chi' of the delay time into two independent but equivalent contributions, associated to the left and right end of the wave guide. For N=1 propagating modes, chi and chi' are identical to half the reflection delay time of each end of the wave guide. In this case the distribution function P(tau) in an ensemble of random disorder can be obtained analytically. For $N>1$ propagating modes the distribution function can be approximated by a simple heuristic modification of the single-channel problem. We find a strong correlation between channels with long reflection delay times and the dominant transmission channel.

Abstract:
Weyl's law approximates the number of states in a quantum system by partitioning the energetically accessible phase-space volume into Planck cells. Here we show that typical resonances in generic open quantum systems follow a modified, fractal Weyl law, even though their classical dynamics is not globally chaotic but also contains domains of regular motion. Besides the obvious ramifications for quantum decay, this delivers detailed insight into quantum-to-classical correspondence, a phenomenon which is poorly understood for generic quantum-dynamical systems.

Abstract:
We investigate the short-distance statistics of the local density of states nu in long one-dimensional disordered systems, which display Anderson localization. It is shown that the probability distribution function P(nu) can be recovered from the long-distance wavefunction statistics, if one also uses parameters that are irrelevant from the perspective of two-parameter scaling theory.

Abstract:
Within a general framework, we discuss the wave function statistics in the Lloyd model of Anderson localization on a one-dimensional lattice with a Cauchy distribution for the random on-site potential. We demonstrate that already in leading order in the disorder strength, there exists a hierarchy of anomalies in the probability distributions of the wave function, the conductance, and the local density of states, for every energy which corresponds to a rational ratio of wave length to the lattice constant. We also show that these distribution functions do have power-law rather then log-normal tails and do not display universal single-parameter scaling. These peculiarities persist in any model with power-law tails of the disorder distribution function.

Abstract:
We provide an analytic theory of Anderson localization on a lattice with a weak short-range correlated disordered potential. Contrary to the general belief we demonstrate that even next-neighbor statistical correlations in the potential can give rise to strong anomalies in the localization length and the density of states, and to the complete violation of single parameter scaling. Such anomalies originate in additional symmetries of the lattice model in the limit of weak disorder. The results of numerical simulations are in full agreement with our theory, with no adjustable parameters.

Abstract:
We study analytically the local density of states in a disordered normal-metal wire at ballistic distance to a superconductor. Our calculation is based on a scattering-matrix approach, which concerns for wave-function localisation in the normal metal, and extends beyond the conventional semiclassical theory based on Usadel and Eilenberger equations. We also analyse how a finite transparency of the NS interface modifies the spectral proximity effect and demonstrate that our results agree in the dirty diffusive limit with those obtained from the Usadel equation.

Abstract:
We analyze the conductance distribution function in the one-dimensional Anderson model of localization, for arbitrary energy. For energy at the band center the distribution function deviates from the universal form assumed in single-parameter scaling theory. A direct link to the break-down of the random-phase approximation is established. Our findings are confirmed by a parameter-free comparison to the results of numerical simulations.

Abstract:
The sensitivity of trajectories over finite time intervals t to perturbations of the initial conditions can be associated with a finite-time Lyapunov exponent lambda, obtained from the elements M_{ij} of the stability matrix M. For globally chaotic dynamics lambda tends to a unique value (the usual Lyapunov exponent lambda_infty) as t is sent to infinity, but for finite t it depends on the initial conditions of the trajectory and can be considered as a statistical quantity. We compute for a particle moving in a random time-dependent potential how the distribution function P(lambda;t) approaches the limiting distribution P(lambda;infty)=delta(lambda-lambda_infty). Our method also applies to the tail of the distribution, which determines the growth rates of positive moments of M_{ij}. The results are also applicable to the problem of wave-function localization in a disordered one-dimensional potential.

Abstract:
We present a theory for the nonequilibrium current in a mesoscopic Josephson junction which is coupled to a normal electron reservoir, and apply it to a chaotic junction. Large sample-to-sample fluctuations of the critical current $I_{\rm c}$ are found, with ${rms} I_{\rm c} \simeq \sqrt{N}e\Delta/\hbar$, when the voltage difference eV between the electron reservoir and the junction exceeds the superconducting gap $\Delta$ and the number of modes N connecting the junction to the superconducting electrodes is large.

Abstract:
We discuss curvature corrections to Fresnel's laws for the reflection and transmission of light at a non-planar refractive-index boundary. The reflection coefficients are obtained from the resonances of a dielectric disk within a sequential-reflection model. The Goos-H\"anchen effect for curved light fronts at a planar interface can be adapted to provide a qualitative and quantitative extension of the ray model which explains the observed deviations from Fresnel's laws.