Related papers: Universal diffusion near the golden chaos border
Chaotic systems exhibit rich quantum dynamical behaviors ranging from dynamical localization to normal diffusion to ballistic motion. Dynamical localization and normal diffusion simulate electron motion in an impure crystal with a vanishing…
Resonance states in quantum chaotic scattering systems have a multifractal structure that depends on their decay rate. We show how classical dynamics describes this structure for all decay rates in the semiclassical limit. This result for…
We study the probability distributions of interface roughness, sampled among successive equilibrium configurations of a single-interface model used for the description of Barkhausen noise in disordered magnets, in space dimensionalities…
We consider the classical map proposed previously to be the exact classical analogue of Rydberg Molecules calculated with the approximations relevant to the multi-channel quantum defect theory. The resulting classical map is analyzed at…
We consider Hermitian and symmetric random band matrices $H$ in $d \geq 1$ dimensions. The matrix elements $H_{xy}$, indexed by $x,y \in \Lambda \subset \Z^d$, are independent, uniformly distributed random variables if $\abs{x-y}$ is less…
We consider the isochrone curves in first-passage percolation on a 2D square lattice, i.e. the boundary of the set of points which can be reached in less than a given time from a certain origin. The occurrence of an instantaneous average…
Motivated by the Central Limit Theorem, in this paper, we study both universal and non-universal simulations of random variables with an arbitrary target distribution $Q_{Y}$ by general mappings, not limited to linear ones (as in the…
We consider large random matrices $X$ with centered, independent entries which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical…
Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on…
The theory of diffusion in many-dimensional Hamiltonian system is applied to asteroidal dynamics. The general formulations developed by Chirikov is applied to the Nesvorn\'{y}-Morbidelli analytic model of three-body (three-orbit)…
We experimentally investigate theoretical predictions of universal impedance fluctuations in wave chaotic systems using a microwave analog of a quantum chaotic infinite square well potential. Our approach emphasizes the use of the radiation…
We investigate the boundary separating regular and chaotic dynamics in the generalized Chirikov map, an extension of the standard map with phase-shifted secondary kicks. Lyapunov maps were computed across the parameter space (K, K{\alpha},…
Random matrix theory (RMT) universality is the defining property of quantum mechanical chaotic systems, and can be probed by observables like the spectral form factor (SFF). In this paper, we describe systematic deviations from RMT…
Chirikov's celebrated criterion of resonance overlap has been widely used in celestial mechanics and Hamiltonian dynamics to detect global instability, but is rarely rigourous. We introduce two simple Hamiltonian systems, each depending on…
We report on a numerical study of gravitational waves undergoing gravitational collapse due to their self-interaction. We consider several families of asymptotically flat initial data which, similar to the well known Choptuik's discovery,…
We consider transport properties of the chaotic (strange) attractor along unfolded trajectories of the dissipative standard map. It is shown that the diffusion process is normal except of the cases when a control parameter is close to some…
We study the critical behavior of the pair annihilation model (PAM) with diffusion in one, two and three dimensions, using the pair approximation (PA) and Monte Carlo simulation. Of principal interest is the dependence of the critical…
We consider the generalized Langevin equation (GLE) in a harmonic potential with power law decay memory. We study the anomalous diffusion of the particle's displacement and velocity. By comparison with the free particle situation in which…
We study resonance distributions in a circular dielectric cavity. It is shown that the decay-rate distribution has a peak structure and the details of the peak are consistent with the classical survival probability time distribution. We…
We study numerically statistical distributions of sums of orbit coordinates, viewed as independent random variables in the spirit of the Central Limit Theorem, in weakly chaotic regimes associated with the excitation of the first ($k=1$)…