论文标题
离散的时间促进了完全不对称的简单排除过程
The Discrete-Time Facilitated Totally Asymmetric Simple Exclusion Process
论文作者
论文摘要
我们描述了一维离散时间的翻译不变固定状态，促进了完全不对称的简单排除过程（F-TASEP）。在此系统中，$ j $ z $跳跃的网站$ j $ in Integer times $ j+1 $，前提是占用$ j-1 $，并且网站$ j+1 $是空的。这定义了从$ \ {0,1 \}^{z} $上的任何指定的初始配置中的确定性的非可逆动力学演变。当从密度$ρ$的Bernoulli产品度量开始时，系统将接近固定状态，相转换为$ρ= 1/2 $，$ρ= 2/3 $。我们在不同密度制度中讨论这些状态的各种属性$ 0 <ρ<1/2 $，$ 1/2 <ρ<2/3 $，$ 2/3 <ρ<1 $;例如，我们表明这对相关性$ g（j）= \langleη（i）η（i+j）\ rangle $满足，对于z $中的所有$ n \，$ n \ in z $，$ \ sum_ {j = kn+1}^{k（n+1）} $ 2/3 \leρ\ le 1 $，并猜想（基于模拟），当$ 1/2 \ leρ\ le 2/3 $时，相同的身份与$ k = 6 $保持。上面提到的$ρ<1/2 $固定状态也是确定性离散时间在密度$ρ$（带有Bernoulli初始状态）的固定状态，或者在交换粒子和孔后，密度为$ 1-ρ$。
We describe the translation invariant stationary states of the one dimensional discrete-time facilitated totally asymmetric simple exclusion process (F-TASEP). In this system a particle at site $j$ in $Z$ jumps, at integer times, to site $j+1$, provided site $j-1$ is occupied and site $j+1$ is empty. This defines a deterministic noninvertible dynamical evolution from any specified initial configuration on $\{0,1\}^{Z}$. When started with a Bernoulli product measure at density $ρ$ the system approaches a stationary state, with phase transitions at $ρ=1/2$ and $ρ=2/3$. We discuss various properties of these states in the different density regimes $0<ρ<1/2$, $1/2<ρ<2/3$, and $2/3<ρ<1$; for example, we show that the pair correlation $g(j)=\langleη(i)η(i+j)\rangle$ satisfies, for all $n\in Z$, $\sum_{j=kn+1}^{k(n+1)}g(j)=kρ^2$, with $k=2$ when $0 \le ρ\le 1/2$ and $k=3$ when $2/3 \le ρ\le 1$, and conjecture (on the basis of simulations) that the same identity holds with $k=6$ when $1/2 \le ρ\le 2/3$. The $ρ<1/2$ stationary state referred to above is also the stationary state for the deterministic discrete-time TASEP at density $ρ$ (with Bernoulli initial state) or, after exchange of particles and holes, at density $1-ρ$.
