Related papers: Level Repulsion in Integrable Systems
Inspired by continuum mechanical contact problems with geological fault networks, we consider elliptic second order differential equations with jump conditions on a sequence of multiscale networks of interfaces with a finite number of…
I survey physics theories involving parallel universes, arguing that they form a natural four-level hierarchy of multiverses allowing progressively greater diversity. Level I: A generic prediction of inflation is an infinite ergodic…
A new master equation to mimic the dynamics of a collection of interacting random walkers in an open system is proposed and solved numerically.In this model, the random walkers interact through excluded volume interaction (single-file…
We argue that the random-matrix like energy spectra found in pseudointegrable billiards with pointlike scatterers are related to the quantum violation of scale invariance of classical analogue system. It is shown that the behavior of the…
Disorder-induced spectral correlations of mesoscopic quantum systems in the non-diffusive regime and their effect on the magnetic susceptibility are studied. We perform impurity averaging for non-translational invariant systems by combining…
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…
We develop a mean-field theory of dropout as a perturbation of critical signal propagation at the edge of chaos. Dropout shifts the perfect-alignment fixed point, making the depth scale for information propagation finite even at critical…
We conjecture that in chaotic quantum systems with escape the intensity statistics for resonance states universally follows an exponential distribution. This requires a scaling by the multifractal mean intensity which depends on the system…
In a recent letter [Phys. Rev. Lett. {\bf 100}, 164101 (2008)] and within the context of quantized chaotic billiards, random plane wave and semiclassical theoretical approaches were applied to an example of a relatively new class of…
The level set method is a widely used tool for solving reachability and invariance problems. However, some shortcomings, such as the difficulties of handling dissipation function and constructing terminal conditions for solving the…
Steady statistics of a passive scalar advected by a random two-dimensional flow of an incompressible fluid is described in the range of scales between the correlation length of the flow and the diffusion scale. That corresponds to the…
This paper studies large deviations of a ``fully coupled" finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment…
We develop a new perturbative method for studying any steady states of quantum impurities, in or out of equilibrium. We show that steady-state averages are completely fixed by basic properties of the steady-state (Hershfield's) density…
We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties…
We present a systematic expansion in the ratio between the level spacing and temperature and employ it to evaluate differences between statistical mechanics and thermodynamics in finite disordered systems. These differences are related to…
The statistical properties of a Hamiltonian $H_0$ perturbed by a localized scatterer are considered. We prove that when $H_0$ describes a bounded chaotic motion, the universal part of the spectral statistics are not changed by the…
An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems.…
The topological nature of the disorder of glasses and supercooled liquids strongly affects their high-frequency dynamics. In order to understand its main features, we analytically studied a simple topologically disordered model, where the…
We establish an analytical link between the level density obtained by means of the Strutinsky averaging method, and the semiclassical level density. This link occurs only in the so-called "asymptotic limit". It turns out that the Strutinsky…
The logarithmic mean-velocity profile is a key experimental and theoretical result in wall-bounded turbulence. Similarly, here we show that the topographic surface emerging between parallel zero-elevation boundaries presents an intermediate…