Exact Anomalous Current Fluctuations in a Deterministic Interacting Model
Exact Anomalous Current Fluctuations in a Deterministic Interacting Model
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DOI：
10.1103/physrevlett.128.160601
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发表时间：
2022-04-22
影响因子：
8.6
通讯作者：
Prosen, Tomaz
中科院分区：
文献类型：
--
作者：
Krajnik, Ziga;Schmidt, Johannes;Prosen, Tomaz
我们解析地计算了经典带电粒子相互作用自动机中电荷转移的全计数统计量。推导了矩生成函数相对于稳态平衡态的封闭表达式，利用渐近分析方法推导了连续时间尺度范围内电荷电流波动的结构。该解决方案显示出几个非正统的特征。最突出的是，在典型波动的时间尺度上，无偏置的稳态系综中积分电荷电流的概率分布明显是非高斯分布，尽管动态电荷磁化率具有扩散行为。虽然诱导电荷不平衡足以恢复高斯波动，但我们发现较高的累积量随时间以不同指数无限增长，意味着奇异尺度累积量。我们将这种现象与矩生成函数缺乏正则性条件和动力临界点的起始联系起来。实际上，无论电荷偏置如何，标度累积量生成函数都不能代表标度累积量的忠实生成函数，然而相关的勒让德对偶产生了正确的大偏差率函数。我们的发现暗示了确定性多体系统中新型的动态普适性类。
We analytically compute the full counting statistics of charge transfer in a classical automaton of interacting charged particles. Deriving a closed-form expression for the moment generating function with respect to a stationary equilibrium state, we employ asymptotic analysis to infer the structure of charge current fluctuations for a continuous range of timescales. The solution exhibits several unorthodox features. Most prominently, on the timescale of typical fluctuations the probability distribution of the integrated charge current in a stationary ensemble without bias is distinctly non-Gaussian despite diffusive behavior of dynamical charge susceptibility. While inducing a charge imbalance is enough to recover Gaussian fluctuations, we find that higher cumulants grow indefinitely in time with different exponents, implying singular scaled cumulants. We associate this phenomenon with the lack of a regularity condition on moment generating functions and the onset of a dynamical critical point. In effect, the scaled cumulant generating function does not, irrespectively of charge bias, represent a faithful generating function of the scaled cumulants, yet the associated Legendre dual yields the correct large-deviation rate function. Our findings hint at novel types of dynamical universality classes in deterministic many-body systems.