Related papers: Classical dynamics on graphs
We report new results about the two-time dynamics of an anomalously diffusing classical particle, as described by the generalized Langevin equation with a frequency-dependent noise and the associated friction. The noise is defined by its…
We study the classical and quantum mechanics of a free particle that collides elastically with the walls of a circular disk with the radius varying periodically in time. The quasi-energy spectral properties of the model are obtained from…
The problem of deriving a gradient flow structure for the porous medium equation which is {\em thermodynamic}, in that it arises from the large deviations of some microscopic particle system, is studied. To this end, a rescaled zero-range…
We study the dynamics of a self-propelled particle advected by a steady laminar flow. The persistent motion of the self-propelled particle is described by an active Ornstein-Uhlenbeck process. We focus on the diffusivity properties of the…
We investigate dynamically and statistically diffusive motion in a Klein-Gordon particle chain in the presence of disorder. In particular, we examine a low energy (subdiffusive) and a higher energy (self-trapping) case and verify that…
We address continuous-time quantum walks on graphs in the presence of time- and space-dependent noise. Noise is modeled as generalized dynamical percolation, i.e. classical time-dependent fluctuations affecting the tunneling amplitudes of…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
The theoretical study of the self-organization of two-dimensional and geophysical turbulent flows is addressed based on statistical mechanics methods. This review is a self-contained presentation of classical and recent works on this…
Quantum Brownian motion in a periodic cosine potential is studied and a simple estimate of the tunneling effect is obtained in the frames of a quasi-equilibrium semiclassical approach. It is shown that the latter is applicable for heavy…
We consider the quantum mechanical behavior of a driven particle in an infinite 1D potential well. We show that the time dependent perturbation series is induced by the delicate non-trivial properties of the momentum operator in this case,…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
We study continuous time Glauber dynamics for random configurations with local constraints (e.g. proper coloring, Ising and Potts models) on finite graphs with $n$ vertices and of bounded degree. We show that the relaxation time (defined as…
We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time--reversal…
The dynamics of a molecule immersed in a superfluid medium are considered. Results are derived using a classical hydrodynamic approach followed by canonical quantization. The classical model, a rigid body immersed in incompressible fluid,…
We study the autophoretic motion of a spherical active particle interacting chemically and hydrodynamically with its fluctuating environment in the limit of rapid diffusion and slow viscous flow. Then, the chemical and hydrodynamic fields…
Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…
Resonances of the time evolution (Frobenius-Perron) operator P for phase space densities have recently been shown to play a key role for the interrelations of classical, semiclassical and quantum dynamics. Efficient methods to determine…
A one-dimensional long-range model of classical rotators with an extended degree of complexity, as compared to paradigmatic long-range systems, is introduced and studied. Working at constant density, in the thermodynamic limit one can prove…
Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power law form for spectra of temporal fluctuations. Such non-local connections…
We discuss the transition from a quantum to a classical domain for a model where a separation into environment and system is explicitely not given. Utilizing the coarse graining procedure for free quantum fields we also apply the projection…