标题： 周期TASEP中电流波动的尺度性质 显示英文标题

标题： Scaling Properties of Current Fluctuations in Periodic TASEP

摘要： 我们研究在大小为$N$的环上具有$p$个粒子的完全不对称简单排斥过程（TASEP）中的电流波动。 通过用参数$\gamma$对马尔可夫生成元进行变形，我们利用坐标贝特假设技术分析了控制电流统计的倾斜算子。 我们推导了标度累积生成函数（SCGF），即最大特征值以及以贝特根表示的谱隙的隐式表达式，利用卡西尼卵形线的几何结构。 在热力学极限下，固定粒子密度时，由$\gamma$的符号区分的区域之间出现动态相变。 对于正的变形参数$\gamma$，SCGF 表现出抛射标度，随着系统大小$N$线性增长。 对于负的$\gamma$，SCGF 收敛到一个普遍常数，突显出不同的波动区域。 相应地，控制松弛时间的谱隙表现出定性不同的有限尺寸标度：对于$\gamma>0$，它以$O(N^{-1})$的方式关闭，反映了缓慢的松弛，但对于$\gamma<0$，它呈指数下降，表明快速收敛。 这些结果为驱动相互作用粒子系统中的亚稳态和松弛动力学提供了见解。 显示英文摘要

摘要： We investigate current fluctuations in the totally asymmetric simple exclusion process (TASEP) on a ring of size $N$ with $p$ particles. By deforming the Markov generator with a parameter $\gamma$, we analyze the tilted operator governing current statistics using coordinate Bethe ansatz techniques. We derive implicit expressions for the scaled cumulant generating function (SCGF), i.e. the largest eigenvalue, and the spectral gap in terms of Bethe roots, exploiting the geometric structure of Cassini ovals. In the thermodynamic limit, at fixed particle density, a dynamical phase transition emerges between regimes distinguished by the sign of $\gamma$. For positive deformation $\gamma$, the SCGF exhibits ballistic scaling, growing linearly with system size $N$. For negative $\gamma$, the SCGF converges to a universal constant, highlighting distinct fluctuation regimes. Correspondingly, the spectral gap, controlling relaxation times, shows qualitatively different finite-size scaling: it closes as $O(N^{-1})$ for $\gamma>0$ reflecting slow relaxation, but it decreases exponentially for $\gamma<0$ indicating rapid convergence. These results provide insight into the metastability and relaxation dynamics in driven interacting particle systems.