论文标题
一维促进的不对称排除过程的固定状态
Stationary States of the One-dimensional Facilitated Asymmetric Exclusion Process
论文作者
论文摘要
We describe the translation invariant stationary states (TIS) of the one-dimensional facilitated asymmetric exclusion process in continuous time, in which a particle at site $i\in\mathbb{Z}$ jumps to site $i+1$ (respectively $i-1$) with rate $p$ (resp. $1-p$), provided that site $i-1$ (resp. $i+1$) is occupied and site $i+1$ （分别为$ i-1 $）是空的。所有具有密度$ρ\ le1/2 $的tis状态都在未占据两个相邻站点的被困配置上支持；我们证明，如果在这种情况下，初始状态为i.i.d.〜bernoulli，那么最终状态将独立于$ p $。这种独立性也适用于有限环上的系统。对于$ρ> 1/2 $，只有一个tis。概率分布的无限体积限制使所有没有两个孔相邻的配置都使重量均匀，并且与Gibbs的同构相构象，用于与最接近邻居排除的硬核粒子的测量。
We describe the translation invariant stationary states (TIS) of the one-dimensional facilitated asymmetric exclusion process in continuous time, in which a particle at site $i\in\mathbb{Z}$ jumps to site $i+1$ (respectively $i-1$) with rate $p$ (resp. $1-p$), provided that site $i-1$ (resp. $i+1$) is occupied and site $i+1$ (resp. $i-1$) is empty. All TIS states with density $ρ\le1/2$ are supported on trapped configurations in which no two adjacent sites are occupied; we prove that if in this case the initial state is i.i.d.~Bernoulli then the final state is independent of $p$. This independence also holds for the system on a finite ring. For $ρ>1/2$ there is only one TIS. It is the infinite volume limit of the probability distribution that gives uniform weight to all configurations in which no two holes are adjacent, and is isomorphic to the Gibbs measure for hard core particles with nearest neighbor exclusion.
