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We discuss a modification to Random Matrix Theory eigenstate statistics, that systematically takes into account the non-universal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead…
The foundations for a thermo-statistical description of the called non extensive Hamiltonian systems are reconsidered. The relevance of the parametric resonance as a fundamental mechanism of the Hamiltonian chaoticity in those systems with…
It is shown that the asymptotic spectra of finite-time Lyapunov exponents of a variety of fully chaotic dynamical systems can be understood in terms of a statistical analysis. Using random matrix theory we derive numerical and in particular…
Motivated by the rich variety of complex periodic and quasi-periodic patterns found in systems such as two-frequency forced Faraday waves, we study the interaction of two spatially periodic modes that are nearly resonant. Within the…
The eigenvalues of the transmission matrix provide the basis for a full description of the statistics of steady-state transmission and conductance. At the same time, the ability to excite the sample with the waveform of specific…
We study the spectrum of quantized open maps, as a model for the resonance spectrum of quantum scattering systems. We are particularly interested in open maps admitting a fractal repeller. Using the ``open baker's map'' as an example, we…
Ensembles of quantum chaotic systems are expected to exhibit energy eigenvalues with random-matrix-like level repulsion between pairs of energies separated by less than the inverse Thouless time. Recent research has shown that exact and…
We consider a model for systems perturbed by dichotomous noise, in which the hazard rate function of a random lifetime is subject to additive time-alternating perturbations described by the telegraph process. This leads us to define a…
A general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. The evolution equation for the multimode characteristic…
We theoretically investigate the Aharonov-Bohm effect in a thick-walled Weyl semimetal (WSM) cylinder subject to an external axial magnetic field. By employing a low-energy effective Hamiltonian, we analytically solve the eigenvalue problem…
We analyze an approach aiming at determining statistical properties of spectra of time-periodic quantum chaotic system based on the parameter dynamics of their quasienergies. In particular we show that application of the methods of…
We discuss the effect of stochastic resonance in a simple model of magnetic reversals. The model exhibits statistically stationary solutions and bimodal distribution of the large scale magnetic field. We observe a non trivial amplification…
The problem of parameter estimation by the continuous time observations of a deterministic signal in white gaussian noise is considered. The asymptotic properties of the maximul likelihood estimator are described in the asymptotics of small…
Biological systems can rely on collective formation of a metachronal wave in an ensemble of oscillators for locomotion and for fluid transport. We consider one-dimensional chains of phase oscillators with nearest neighbor interactions,…
We present a result relating the density of quantum resonances for an open chaotic system to the fractal dimension of the associated classical repeller. The result is supported by numerical computation of the resonances of the system of n…
The Random Coupling Model (RCM) is a statistical approach for studying the scattering properties of linear wave chaotic systems in the semi-classical regime. Its success has been experimentally verified in various over-moded wave settings,…
We examine the time dependent defect fluctuations and lifetimes for a bidisperse disordered assembly of Yukawa particles. At high temperatures, the noise spectrum of fluctuations is white and the coordination number lifetimes have a…
The effect of spatial correlations on the Purcell effect in a bidimensional dispersion of resonant nanoparticles is analyzed. We perform extensive calculations on the fluorescence decay rate of a point emitter embedded in a system of…
Chaotic systems, presenting complex and non-reproducible dynamics, may be found in nature from the interaction between planets to the evolution of the weather, but can also be tailored using current technologies for advanced signal…
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…