论文标题
随机幂律重置下的对称排除过程
Symmetric Exclusion Process under Stochastic Power-law Resetting
论文作者
论文摘要
我们研究了在非马克维亚随机重置的存在下，对称排除过程的行为，在该重置的情况下，该系统的配置被重置为带有指数$α$的幂律等待时间的阶梯状轮廓。我们发现，重置的重置导致电流的丰富行为以及密度曲线。我们表明，对于任何有限系统，对于$α<1 $，密度曲线最终变为均匀，而对于$α> 1 $，最终达到了最终的非平凡的固定轮廓。我们还发现，在热力学系统大小的限制下，在较晚时，平均扩散电流会增长$ \ sim t^θ$，$θ= 1/2 $，对于$α\ le 1/2 $，$θ=α$，$ 1/2 <α\ le 1 $ 1 $ and $θ= 1 $ for $ a> $α> $ 1 $。我们还通过基于轨迹的扰动方法来分析地表征短期制度中扩散电流的分布。使用数值模拟，我们表明，在长期制度中，扩散电流分布遵循具有$α-$依赖性缩放函数的缩放形式。我们还使用更新方法来表征总电流的行为。我们发现，平均总电流还会增长代数$ \ sim t^ϕ $，其中$ ϕ = 1/2 $ for $α\ le 1 $，$ ϕ = 3/2-α$，$ 1 <α\ le 3/2 $，而对于$α> $α> 3/2 $，我们的平均总电流达到了平均值，我们可以准确地计算出静止值。总电流的差异还显示了代数增长，指数$δ= 1 $，对于$α\ le 1 $，$δ= 2-α$，$ 1 <α\ le 2 $，而其接近$α> 2 $的恒定值。目前的总分布仍然是$α<1 $的非平稳分布，而对于$α> 1 $，它达到了非平凡且强烈的非高斯固定分布，我们还使用续订方法对其进行计算。
We study the behaviour of a symmetric exclusion process in the presence of non-Markovian stochastic resetting, where the configuration of the system is reset to a step-like profile at power-law waiting times with an exponent $α$. We find that the power-law resetting leads to a rich behaviour for the currents, as well as density profile. We show that, for any finite system, for $α<1$, the density profile eventually becomes uniform while for $α>1$, an eventual non-trivial stationary profile is reached. We also find that, in the limit of thermodynamic system size, at late times, the average diffusive current grows $\sim t^θ$ with $θ= 1/2$ for $α\le 1/2$, $θ= α$ for $1/2 < α\le 1$ and $θ=1$ for $α> 1$. We also analytically characterize the distribution of the diffusive current in the short-time regime using a trajectory-based perturbative approach. Using numerical simulations, we show that in the long-time regime, the diffusive current distribution follows a scaling form with an $α-$dependent scaling function. We also characterise the behaviour of the total current using renewal approach. We find that the average total current also grows algebraically $\sim t^ϕ$ where $ϕ= 1/2$ for $α\le 1$, $ϕ=3/2-α$ for $1 < α\le 3/2$, while for $α> 3/2$ the average total current reaches a stationary value, which we compute exactly. The variance of the total current also shows an algebraic growth with an exponent $Δ=1$ for $α\le 1$, and $Δ=2-α$ for $1 < α\le 2$, whereas it approaches a constant value for $α>2$. The total current distribution remains non-stationary for $α<1$, while, for $α>1$, it reaches a non-trivial and strongly non-Gaussian stationary distribution, which we also compute using the renewal approach.
