致命扩散粒子非平衡定态的数量统计和最优历史
The number statistics and optimal history of non-equilibrium steady states of mortal diffusing particles
摘要：
假设一个位于$x=0$的点状稳定源将粒子注入一条半无限长的直线。粒子扩散并死亡。在很长一段时间内，一个非平衡的稳定状态开始出现，我们假设它涉及许多粒子。如果粒子是非相互作用的，它们的总数$N$在稳定状态下是泊松分布的，平均$\bar{N}$是从确定性反应扩散方程预测的。在这里，我们确定最有可能的密度历史，这个驱动系统的条件下观察一个给定的$N$。我们还考虑了两个典型的例子\emph{interacting}扩散粒子：（一）一个家庭的致命的扩散晶格气体与恒定的扩散率（如所示的简单的对称排斥过程与致命粒子），和（ii）随机游走，可以湮灭对。在这两个例子中，我们计算$N$的（非泊松）平稳分布的方差。
英文摘要：
Suppose that a point-like steady source at $x=0$ injects particles into a half-infinite line. The particles diffuse and die. At long times a non-equilibrium steady state sets in, and we assume that it involves many particles. If the particles are non-interacting, their total number $N$ in the steady state is Poisson-distributed with mean $\bar{N}$ predicted from a deterministic reaction-diffusion equation. Here we determine the most likely density history of this driven system conditional on observing a given $N$. We also consider two prototypical examples of \emph{interacting} diffusing particles: (i) a family of mortal diffusive lattice gases with constant diffusivity (as illustrated by the simple symmetric exclusion process with mortal particles), and (ii) random walkers that can annihilate in pairs. In both examples we calculate the variances of the (non-Poissonian) stationary distributions of $N$.
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