Space-time velocity correlation function for random walks

Abstract

Space-time correlation functions constitute a useful instrument from the research toolkit of continuous-media and many-body physics. We adopt here this concept for single-particle random walks and demonstrate that the corresponding space-time velocity auto-correlation functions reveal correlations which extend in time much longer than estimated with the commonly employed temporal correlation functions. A generic feature of considered random-walk processes is an effect of velocity echo identified by the existence of time-dependent regions where most of the walkers are moving in the direction opposite to their initial motion. We discuss the relevance of the space-time velocity correlation functions for the experimental studies of cold atom dynamics in an optical potential and charge transport on micro- and nano-scales.

Phys. Rev. Lett., in press

References in corpus (14)

• Observation of anomalous diffusion and fractional self-similarity in one dimension
• Controllable soliton emission from a Bose-Einstein condensate
• From anomalous energy diffusion to Levy walks and heat conductivity in one-dimensional systems
• Theory of fractional-Lévy kinetics for cold atoms diffusing in optical lattices
• Time averaged Einstein relation and fluctuating diffusivities for the Lévy walk
• Exact solution of a Levy walk model for anomalous heat transport
• Perturbation spreading in many-particle systems: a random walk approach
• Electron injection in a nanotube: noise correlations and entanglement
• Energy diffusion in hard-point systems
• Density Profiles in Open Superdiffusive Systems
• Anomalous Infiltration
• Levy walks with velocity fluctuations
• Direct observation of Levy flight of holes in bulk n-InP
• Tomography of correlation functions for ultracold atoms via time-of-flight images

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• Infinite densities for Lévy walks
• Lévy-walk-like Langevin dynamics
• Random walks with thermalizing collisions in bounded regions; physical applications valid from the ballistic to diffusive regimes
• Langevin dynamics for Lévy walk with memory
• Langevin picture of Lévy walk in a constant force field
• Lévy-walk-like Langevin dynamics affected by a time-dependent force
• Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices
• Large deviations of the ballistic Lévy walk model
• Memory-dependent noise-induced resonance and diffusion in non-markovian systems