Related papers: Diffusion, Long-Time Tails, and Localization in Cl…
It has been observed in numerous experiments, simulations, and various theoretical treatments that the spreading of particles can be modeled by the continuous-time random walk. We consider two well-known cases, i.e., Gaussian displacements…
Finite-size effects are challenging in molecular dynamics simulations because they have significant effects on computed static and dynamic properties, in particular diffusion constants, friction coefficients and time- or frequency-dependent…
We study the nonlinear energy diffusion through the SYK chain in the framework of Schwinger-Keldysh effective field theory. We analytically construct the interacting effective Lagrangian up to $40^{th}$ order in the derivative expansion.…
This contribution addresses the question commonly asked in scientific literature about the sources of multifractality in time series. Two primary sources are typically considered. These are temporal correlations and heavy tails in the…
Long-term temporal correlations observed in event sequences of natural and social phenomena have been characterized by algebraically decaying autocorrelation functions. Such temporal correlations can be understood not only by heterogeneous…
The localization transition and the critical properties of the Lorentz model in three dimensions are investigated by computer simulations. We give a coherent and quantitative explanation of the dynamics in terms of continuum percolation…
The Lorenz 1963 dynamical system is known to reduce in the steady state to a one-dimensional motion of a classical particle subjected to viscous damping in a past history-dependent potential field. If the potential field is substituted by a…
We propose a unified diffusion-mobility relation which quantifies both quantum and classical levels of understanding on electron dynamics in ordered and disordered materials. This attempt overcomes the inability of classical Einstein…
We review and complete the existing literature on the kinetic theory of spatially homogeneous systems with long-range interactions taking collective effects into account. The evolution of the system as a whole is described by the…
The phenomenon of wave tails has attracted much attention over the years from both physicists and mathematicians. However, our understanding of this fascinating phenomenon is not complete yet. In particular, most former studies of the tail…
Long tails in the velocity distribution are observed in plasmas and gravitational systems. Some experiments and observations in far-from-equilibrium conditions show that these tails behave as 1/v^(5/2). We show here that such heavy tails…
We present the detailed analysis of the diffusive transport of spatially inhomogeneous fluid mixtures and the interplay between structural and dynamical properties varying on the atomic scale. The present treatment is based on different…
We study synthetic temporal networks whose evolution is determined by stochastically evolving node variables - synthetic analogues of, e.g., temporal proximity networks of mobile agents. We quantify the long-timescale correlations of these…
The L\'evy-Lorentz gas describes the motion of a particle on the real line in the presence of a random array of scattering points, whose distances between neighboring points are heavy-tailed i.i.d. random variables with finite mean. The…
We consider the increase of the spatial variance of some inhomogeneous, non-equilibrium density (particles, energy, etc.) in a periodic quantum system of condensed matter-type. This is done for a certain class of initial quantum states…
An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…
Localization and delocalization of quantum diffusion in time-continuous one-dimensional Anderson model perturbed by the quasi-periodic harmonic oscillations of $M$ colors is investigated systematically, which has been partly reported by the…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
We analyse the long time tails of a charged quantum Brownian particle in a harmonic potential in the presence of a magnetic field using the Quantum Langevin Equation as a starting point. We analyse the long time tails in the position…
We generalize nonlinear Luttinger liquid theory to describe the dynamics of one-dimensional quantum critical systems at low temperatures. Analyzing density-matrix renormalization group results for the spin autocorrelation function in the…