Related papers: Distribution of the wave function inside chaotic p…
By an inductive reasoning, and based on recent results of the joint moments of proper delay times of open chaotic systems for ideal coupling to leads, we obtain a general expression for the distribution of the partial delay times for an…
We analyse universal statistical properties of phase shifts and time delays for open chaotic systems in the crossover regime of partly broken time-reversal invariance. In particular, we find that the distribution of the time delay shows…
Unstable periodic orbits scar wave functions in chaotic systems. This also influences the associated spectra, that follow the otherwise universal Porter--Thomas intensity distribution. We show here how this deviation extend to other longer…
We develop a statistical theory of waveform shaping of incident waves that aim to efficiently deliver energy at weakly lossy targets which are embedded inside chaotic enclosures. Our approach utilizes the universal features of chaotic…
This article presents results on the concentration properties of the smoothing and filtering distributions of some partially observed chaotic dynamical systems. We show that, rather surprisingly, for the geometric model of the Lorenz…
A semiclassical diagrammatic approach is constructed for calculating correlation functions of observables in open chaotic systems with time reversal symmetry. The results are expressed in terms of classical correlation functions involving…
We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on…
Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first…
Exploiting the time-reversal invariance and reciprocal properties of the lossless wave equation enables elegantly simple solutions to complex wave-scattering problems, and is embodied in the time-reversal mirror. A time-reversal mirror…
We study correlations of the amplitudes of wave functions of a chaotic system at large distances. For this purpose, a joint distribution function of the amplitudes at two distant points in a sample is calculated analytically using the…
Work in closed quantum systems is usually defined by a two-point measurement. This definition of work is compatible with quantum fluctuation theorems but it fundamentally differs from its classical counterpart. In this paper, we study the…
In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic…
The wavefunctions in phase-space representation can be expressed as entire functions of their zeros if the phase space is compact. These zeros seem to hide a lot of relevant and explicit information about the underlying classical dynamics.…
The application of random matrix theory to scattering requires introduction of system-specific information. This paper shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically…
This paper develops a theory of propagation of chaos for a system of weakly interacting particles whose terminal configuration is fixed as opposed to the initial configuration as customary. Such systems are modeled by backward stochastic…
By analysing an n-dimensional generalisation of Thomas's cyclically symmetric attractor we find that this chaotic dynamical system behaves like a random walk constrained onto the surface of a hypersphere. The growth of error is limited,…
The correlation between the values of wavefunctions at two different spatial points is examined for chaotic systems with time-reversal symmetry. Employing a supermatrix method, we find that there exist long-range Friedel oscillations of the…
We report on experimental studies of the distribution of the off-diagonal elements of the scattering matrix of open microwave networks with symplectic symmetry and a chaotic wave dynamics. These consist of two geometrically identical…
Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs. chaotic), and is often instrumental to identify…
In this paper, we study random features manifested in components of energy eigenfunctions of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on semiclassical analysis, particularly on Berry's…