论文标题
在一个维
Run-and-Tumble particle in inhomogeneous media in one dimension
论文作者
论文摘要
我们在一个维度上研究了运行和翻滚粒子（RTP），也称为持续的布朗运动。电报噪声$σ（t）$驱动粒子，该粒子在$ \ pm 1 $值之间以某些速率变化。以$ r_1 $为$ r_1 $的翻转速率从$ 1 $ $ -1 $和$ r_2 $表示，我们考虑$ r_1（x）= \ left的位置和方向率（\ frac {\ frac {\ mid x \ mid x \ mid} $ r_2（x）= \ left（\ frac {\ mid x \ mid} {l} \右）对于$γ_1>γ_2$，我们发现粒子即使在无限的线上也表现出稳态的概率分散，其确切形式取决于$α$。对于$α= 0 $和$ 1 $，我们完全解决了主方程，以$ t $的任意$γ_1$和$γ_2$。从我们对时间依赖性概率分布$ p（x，t）$的显式表达式中，我们发现它以$γ_1>γ_2$的形式放松到稳态分布。另一方面，对于$γ_1<γ_2$，$ p（x，t）$的大$ t $行为与$γ_1=γ_2$ case截然不同，其中分布衰减为$ t^{ - \ frac {1} {1} {2}}} $。与后者相反，即使在前一种情况下，粒子也不会遵守详细的余额。对于一般$α$，我们认为在$γ_1>γ_2$ case中稳态的方法是指数的，我们在数值上证明了...。
We investigate the run and tumble particle (RTP), also known as persistent Brownian motion, in one dimension. A telegraphic noise $σ(t)$ drives the particle which changes between $\pm 1$ values with some rates. Denoting the rate of flip from $1$ to $-1$ as $R_1$ and the converse rate as $R_2$, we consider the position and direction dependent rates of the form $R_1(x)=\left(\frac{\mid x \mid}{l}\right) ^α\left[γ_1~θ(x)+γ_2 ~θ(-x)\right]$ and $R_2(x)=\left(\frac{\mid x \mid}{l}\right) ^α\left[γ_2~θ(x)+γ_1 ~θ(-x)\right]$ with $α\geq 0$. For $γ_1 >γ_2$, we find that the particle exhibits a steady-state probability distriution even in an infinite line whose exact form depends on $α$. For $α=0$ and $1$, we solve the master equations exactly for arbitrary $γ_1$ and $γ_2$ at large $t$. From our explicit expression for time-dependent probability distribution $P(x,t)$ we find that it exponentially relaxes to the steady-state distribution for $γ_1 > γ_2$. On the other hand, for $γ_1<γ_2$, the large $t$ behaviour of $P(x,t)$ is drastically different than $γ_1=γ_2$ case where the distribution decays as $t^{-\frac{1}{2}}$. Contrary to the latter, detailed balance is not obeyed by the particle even at large $t$ in the former case. For general $α$, we argue that the approach to the steady state in $γ_1>γ_2$ case is exponential which we numerically demonstrate....
