Brownian motion under annihilation dynamics

Abstract

The behavior of a heavy tagged intruder immersed in a bath of particles evolving under ballistic annihilation dynamics is investigated. The Fokker-Planck equation for this system is derived and the peculiarities of the corresponding diffusive behavior are worked out. In the long time limit, the intruder velocity distribution function approaches a Gaussian form, but with a different temperature from its bath counterpart. As a consequence of the continuous decay of particles in the bath, the mean squared displacement increases exponentially in the collision per particle time scale. Analytical results are finally successfully tested against Monte Carlo numerical simulations.

Transport properties for driven granular fluids in situations close to homogeneous steady states

“…As will show below, in the low-density limit, our results agree with those obtained in Ref. [19] showing the equivalence between the Chapman-Enskog and linear response methods for driven granular gases.…”

“…( 62) and (68), respectively, with χ = 1. The expressions (80) and (81) agree with recent results [19] derived from the linearized Boltzmann equation for a granular gas heated by the stochastic thermostat (β = 0). In addition, as mentioned before, when β = 1 2 in Eq.…”

“…Although for granular gases the drag parameter γ b and the white noise parameter ξ 2 b can be considered in general as independent parameters, to make contact here with previous results obtained for dilute gases [19,23] we will assume that both parameters are related by…”

“…where β is an arbitrary constant. Thus, when β = 0 our thermostat reduces to the usual stochastic thermostat [19] while the choice β = 1 2 reduces to the conventional Fokker-Planck model for ordinary gases [23]. According to Eq.…”

“…On the other hand, much less is known in the case of driven granular fluids. To the best of our knowledge, the only derivation of Green-Kubo formula for Navier-Stokes transport coefficients of a granular dilute gas heated by the stochastic thermostat has been recently carried out by García de Soria et al [19]. Starting from the Boltzmann equation, these authors obtain explicit expressions for the transport coefficients as a function of the inelasticity and the spatial dimension.…”