Related papers: Statistics of resonances in one-dimensional disord…
Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…
Resonances, or scattering poles, are complex numbers which mathematically describe meta-stable states: the real part of a resonance gives the rest energy, and its imaginary part, the rate of decay of a meta-stable state. This description…
In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…
The paper deals with the interaction between buckling and resonance instabilities of mechanical systems. Taking into account the effect of geometric nonlinearity in the equations of motion through the geometric stiffness matrix, the problem…
I review recent work on the ``phase diagram'' of the one-dimensional complex Ginzburg-Landau equation for system sizes at which chaos is extensive. Particular attention is paid to a detailed description of the spatiotemporally disordered…
The Wigner-Smith (WS) time delay matrix relates a lossless system's scattering matrix to its frequency derivative. First proposed in the realm of quantum mechanics to characterize time delays experienced by particles during a collision,…
The propagation of light through a disordered layered system is studied. It is shown that distribution function of the transmission coefficient phase tends to stationary non-uniform distribution as the number of layers increases. The…
We study one-dimensional systems with random diagonal disorder but off-diagonal short-range correlations imposed by structural constraints. We find that these correlations generate effective conduction channels for finite systems. At a…
The Wigner time delay is a measure of the time spent by a particle inside the scattering region of an open system. For chaotic systems, the statistics of the individual delay times (whose average is the Wigner time delay) are thought to be…
We use particle dynamics simulations to probe the correlations between noise and dynamics in a variety of disordered systems, including superconducting vortices, 2D electron liquid crystals, colloids, domain walls, and granular media. The…
We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…
Algorithms increasingly operate within complex physical, social, and engineering systems where they are exposed to disturbances, noise, and interconnections with other dynamical systems. This article extends known convergence guarantees of…
It has become increasingly clear that a full understanding of the physics of electrons in disordered systems requires an approach in which both disorder and interactions are taken into account. Work on small numbers of electrons has…
We present a method for numerically obtaining the positions, widths and wavefunctions of resonance states in a two dimensional billiard connected to a waveguide. For a rectangular billiard, we study the dynamics of three resonance poles…
In this paper, we study the decoherence of a wave described by the solution to a Schroedinger equation with a time-dependent random potential. The random potential is assumed to have slowly decaying correlations. The main tool to analyze…
Disorder can profoundly influence synchronization in networks of nonlinear oscillators, sometimes enhancing coherence through external tuning. In semiconductor lasers, however, achieving high-quality steady-state synchronization is desired,…
The distortion of the regular motion in a quantum system by its coupling to the continuum of decay channels is investigated. The regular motion is described by means of a Poissonian ensemble. We focus on the case of only few channels K<10.…
We study the correlations of time delays in a model of chaotic resonance scattering based on the random matrix approach. Analytical formulae which are valid for arbitrary number of open channels and arbitrary coupling strength between…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…
The presence of resonances modifies the passage of light or of electrons through a disordered medium. We generalize random matrix theory to account for this effect. Using supersymmetry, we calculate analytically the mean density of states,…