Statistics of the total number of collisions and the ordering time in a freely expanding hard-point gas

自由膨胀Kipnis-Marchioro-Presutti气体中正则化局域能量密度的完整统计

Full Statistics of Regularized Local Energy Density in a Freely Expanding Kipnis-Marchioro-Presutti Gas

本文结合宏观涨落理论与逆散射方法，研究自由膨胀KMP晶格气体中局域平均能量密度的长时间大偏差统计，证明其大偏差函数在适当变量下趋于与区间长度无关的普适形式，并给出条件最可能能量密度构型。

Magnetic ordering of random dense packings of freely rotating dipoles

We study random dense packings of Heisenberg dipoles by numerical simulation. The dipoles are at the centers of identical spheres that occupy fixed random positions in space and fill a fraction $Φ$ of the spatial volume. The parameter $Φ$ ranges from rather low values, typical of amorphous ensembles, to the maximum $Φ$=0.64 that occurs in the random-close-packed limit. We assume that the dipoles can freely rotate and have no local anisotropies. As well as the usual thermodynamical variables, the physics of such systems depends on $Φ$. Concretely, we explore the magnetic ordering of these syste…

A rigourous demonstration of the validity of Boltzmann's scenario for the spatial homogenization of a freely expanding gas and the equilibration of the Kac ring

Boltzmann provided a scenario to explain why individual macroscopic systems composed of a large number $N$ of microscopic constituents are inevitably (i.e., with overwhelming probability) observed to approach a unique macroscopic state of thermodynamic equilibrium, and why after having done so, they are then observed to remain in that state, apparently forever. We provide here rigourous new results that mathematically prove the basic features of Boltzmann's scenario for two classical models: a simple boundary-free model for the spatial homogenization of a non-interacting gas of point particles…

Universal Extremal Statistics in a Freely Expanding Jepsen Gas

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 $ϕ(V)$, 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 varianc…

Violation of Porod law in a freely cooling granular gas in one dimension

We study a model of freely cooling inelastic granular gas in one dimension, with a restitution coefficient which approaches the elastic limit below a relative velocity scale v. While at early times (t << 1/v) the gas behaves as a completely inelastic sticky gas conforming to predictions of earlier studies, at late times (t >> 1/v) it exhibits a new fluctuation dominated phase ordering state. We find distinct scaling behavior for the (i) density distribution function, (ii) occupied and empty gap distribution functions, (iii) the density structure function and (iv) the velocity structure functio…

自由膨胀费米气体类Page曲线动力学的广义流体动力学描述

Generalised Hydrodynamics description of the Page curve-like dynamics of a freely expanding fermionic gas

提出晶格非相互作用费米气体从带缺陷盒中释放的可解模型，用广义流体动力学准确刻画类Page曲线纠缠动力学及密度、电流。