Space-Time Velocity Correlation Function for Random Walks

Zaburdaev, Vasily; Denisov, S.; Haenggi, P.

doi:10.1103/PhysRevLett.110.170604

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Space-Time Velocity Correlation Function for Random Walks

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Zaburdaev, V., Denisov, S., & Haenggi, P. (2013). Space-Time Velocity Correlation Function for Random Walks. Physical Review Letters, 110(17): 170604. doi:10.1103/PhysRevLett.110.170604.

Cite as: https://hdl.handle.net/21.11116/0000-0008-619D-A

Abstract

Space-time correlation functions constitute a useful instrument from the research toolkit of continuous-media and many-body physics. Here we adopt this concept for single-particle random walks and demonstrate that the corresponding space-time velocity autocorrelation 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 nanoscales. DOI: 10.1103/PhysRevLett.110.170604