Universal Extremal Statistics in a Freely Expanding Jepsen Gas BENA

We study the extremal dynamics emerging in an out-of-equilibrium one-dimensional Jepsen gas of $(N+1)$ hard-point particles. The particles undergo binary elastic collisions, but move ballistically in-between collisions. The gas is initally uniformly distributed in a box $[-L,0]$ with the "leader" (or the rightmost particle) at X=0, and a random positive velocity, independently drawn from a distribution $phi(V)$, is assigned to each particle. The gas expands freely at subsequent times. We compute analytically the distribution of the leader's velocity at time $t$, and also the mean and the variance of the number of collisions that are undergone by the leader up to time $t$. We show that in the thermodynamic limit and at fixed time $tgg 1$ (the so-called "growing regime"), when interactions are strongly manifest, the velocity distribution exhibits universal scaling behavior of only three possible varieties, depending on the tail of $phi(V)$. The associated scaling functions are novel and different from the usual extreme-value distributions of uncorrelated random variables. In this growing regime the mean and the variance of [...] BENA COPPEX, Ioana Carla, MAJUMDAR, Satya N. Universal Extremal Statistics in a Freely Expanding Jepsen Gas. Physical Review. E, 2007, vol. 75, no. 051103, p. 13 p. DOI : 10.1103/PhysRevE.75.051103 arxiv : cond-mat/0701130