Kinetic glass transition in granular gases and non-linear molecular fluids

Abstract

In this paper we investigate, both analytically and numerically, the emergence of a kinetic glass transition in two different model systems: a uniformly heated granular gas and a molecular fluid with nonlinear drag. Despite the profound differences between these two physical systems, their behavior in thermal cycles share strong similarities, which stem from the relaxation time diverging algebraically at low temperatures for both systems. When the driving intensity -- for the granular gas -- or the bath temperature -- for the molecular fluid -- is decreased to sufficiently low values, the kinetic temperature of both systems becomes ``frozen" at a value that depends on the cooling rate through a power law with the same exponent. Interestingly, this frozen glassy state is universal in the following sense: for a suitable rescaling of the relevant variables, its velocity distribution function becomes independent of the cooling rate. Upon reheating, i.e., when either the driving intensity or the bath temperature is increased from this frozen state, hysteresis cycles arise and the apparent heat capacity displays a maximum. The numerical results obtained from the simulations are well described by a perturbative approach.

21 pages, 13 figures, 1 table

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