Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume -, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/2008/10/L10001
Keywords
Brownian motion; granular matter; fluctuations (theory); diffusion
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We study a gas of hard rods on a ring, driven by an external thermostat, with either elastic or inelastic collisions, which exhibits sub-diffusive behavior, < x(2)> similar to t(1/2). We show the validity of the usual fluctuation-dissipation (FD) relation, i.e. the proportionality between the response function and the correlation function, when the gas is elastic or diluted. In contrast, in strongly inelastic or dense cases, when the tracer velocity is no longer independent of the other degrees of freedom, the Einstein formula fails and must be replaced by a more general FD relation.
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