亚松弛时间尺度环上的TASEP
TASEP on a ring in sub-relaxation time scale
摘要：
在粒子数为$O(L)$的$L$大小的环上的KPZ普适性类中的相互作用粒子系统预期在所谓的弛豫时间尺度$t=O(L^{3/2})$上从KPZ动力学变为平衡动力学。特别是系统的大小，预计在亚弛豫时间尺度$t\ll L^{3/2}$的颗粒波动的影响很小。我们证明了这确实是完全不对称的简单排它过程（TASEP）与两种类型的初始条件的情况下。对于平坦的初始条件，我们证明了粒子涨落是由Airy $_1$过程给出的，就像在具有平坦初始条件的无限TASEP中一样。另一方面，具有阶跃初始条件的环上的TASEP等价于具有一定冲击初始条件的周期TASEP。对于相同初始条件的无限TASEP，我们计算了激波附近和远离激波处的涨落，并证明了周期TASEP在亚弛豫时间尺度上具有相同的涨落.
英文摘要：
Interacting particle systems in the KPZ universality class on a ring of size $L$ with $O(L)$ number of particles are expected to change from KPZ dynamics to equilibrium dynamics at the so-called relaxation time scale $t=O(L^{3/2})$. In particular the system size is expected to have little effect to the particle fluctuations in the sub-relaxation time scale $t\ll L^{3/2}$. We prove that this is indeed the case for the totally asymmetric simple exclusion process (TASEP) with two types of initial conditions. For flat initial condition, we show that the particle fluctuations are given by the Airy$_1$ process as in the infinite TASEP with flat initial condition. On the other hand, the TASEP on a ring with step initial condition is equivalent to the periodic TASEP with a certain shock initial condition. We compute the fluctuations explicitly both away from and near the shocks for the infinite TASEP with same initial condition, and then show that the periodic TASEP has same fluctuations in the sub-relaxation time scale.
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