V. Zaburdaev, S. Denisov, P. Hanggi
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 proposed space-time velocity auto-correlation function reveals correlations which extend in time much longer than estimated with the commonly employed temporal correlation functions. We uncover a generic feature of random-walk processes which is the presence of a region of strong velocity anti-correlations around the starting point and relate these correlations to the density of walkers. To highlight the practical relevance of our findings we outline a setup to measure the space-time velocity correlation function of an ensemble of cold atoms evolving in a laser-created optical potential.
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http://arxiv.org/abs/1212.4451
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