Related papers: Diffusion, Long-Time Tails, and Localization in Cl…
An overview is given of the long-time and long-distance behavior of correlation functions in both classical and quantum statistical mechanics. After a simple derivation of the classical long-time tails in equilibrium time correlation…
Alder and Wainwright discovered the slow power decay $\sim t^{-d/2}$ ($d$:dimension) of the velocity autocorrelation function in moderately dense hard sphere fluids using the event-driven molecular dynamics simulations. In the…
An overview is given of the limitations of Luttinger liquid theory in describing the real time equilibrium dynamics of critical one-dimensional systems with nonlinear dispersion relation. After exposing the singularities of perturbation…
Generic short-range interacting quantum systems with a conserved quantity exhibit universal diffusive transport at late times. We employ non-equilibrium quantum field theory and semi-classical phase-space simulations to show how this…
The 1970 paper, "Decay of the Velocity Correlation Function" [Phys. Rev. A1, 18 (1970), see also Phys. Rev. Lett. 18, 988 (1967)] by Berni Alder and Tom Wainwright, demonstrated, by means of computer simulations, that the velocity…
When a particle moves through a spatially-random force field, its momentum may change at a rate which grows with its speed. Suppose moreover that a thermal bath provides friction which gets weaker for large speeds, enabling high-energy…
The universal power law tails of single particle and multi-particle time correlation functions are derived from a unifying point of view, solely using the hydrodynamic modes of the system. The theory applies to general correlation…
We study the formation and the evolution of velocity distribution tails for systems with long-range interactions. In the thermal bath approximation, the evolution of the distribution function of a test particle is governed by a…
Exact analytic calculations in spin-1/2 XY chains, show the presence of long-time tails in the asymptotic dynamics of spatially inhomogeneous excitations. The decay of inhomogeneities, for $t\to \infty $, is given in the form of a power law…
We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo…
Unified description on the long-time tail of velocity autocorrelation function and the long-range correlation for the equal-time spatial correlation functions is developed based on the generalized fluctuating hydrodynamics. The cross-over…
After a quantum quench, a sudden change of parameters, generic many particle quantum systems are expected to equilibrate. A few collisions of quasiparticles are usually sufficient to establish approximately local equilibrium. Reaching…
We study a lattice model describing the non-equilibrium dynamics emerging from the pulling of a tracer particle through a disordered medium occupied by randomly placed obstacles. The model is considered in a restricted geometry pertinent…
The long-time behavior of transport coefficients in a model for spatially heterogeneous media in two and three dimensions is investigated by Molecular Dynamics simulations. The behavior of the velocity auto-correlation function is…
Diffusion models have achieved impressive performance in generating high-quality and diverse synthetic data. However, their success typically assumes a class-balanced training distribution. In real-world settings, multi-class data often…
Time correlation functions in the Lebwohl-Lasher model of nematic liquid crystals are studied using theory and molecular dynamics simulations. In particular, the autocorrelation functions of angular momentum and nematic director…
We investigate the dynamics of a single tracer particle performing Brownian motion in a two-dimensional course of randomly distributed hard obstacles. At a certain critical obstacle density, the motion of the tracer becomes anomalous over…
We investigate the relaxation of long-tailed distributions under stochastic dynamics that do not support such tails. Linear relaxation is found to be a borderline case in which long tails are exponentially suppressed in time but not…
In transport processes across materials like glasses, living cells, and porous media, the probability density function of displacements exhibits exponential decay rather than Gaussian behavior. We show that this universal behavior of rare…
Hydrodynamic fluctuations at non-zero temperature can cause slow relaxation toward equilibrium even in observables which are not locally conserved. A classic example is the stress-stress correlator in a normal fluid, which, at zero…