Frequency-dependent fluctuation-dissipation relations in granular gases

Guy Bunin*, Yair Shokef, Dov Levine

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The Green-Kubo relation for two models of granular gases is discussed. In the Maxwell model in any dimension, the effective temperature obtained from the Green-Kubo relation is shown to be frequency independent and equal to the average kinetic energy, known as the granular temperature. In the second model analyzed, a mean-field granular gas, the collision rate of a particle is taken to be proportional to its velocity. The Green-Kubo relation in the high-frequency limit is calculated for this model, and the effective temperature in this limit is shown to be equal to the granular temperature. This result, taken together with previous results showing a difference between the effective temperature at zero frequency (the Einstein relation) and the granular temperature, shows that the Green-Kubo relation for granular gases is violated.

Original languageEnglish
Article number051301
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number5
StatePublished - 9 May 2008
Externally publishedYes


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