论文标题
排除过程中的当前和活动波动：后果和开放问题
Mapping current and activity fluctuations in exclusion processes: consequences and open questions
论文作者
论文摘要
考虑到不对称的简单排除过程（ASEP）中的活动和电流的较大偏差，我们表明，关节缩放累积累积生成活性功能与两个具有不同参数的ASEP的电流之间存在非平凡的对应关系。通过在源模型的变形马尔可夫矩阵上应用相似性转换来获得此映射，以获得目标模型的变形马尔可夫矩阵。我们首先得出了周期性边界条件的对应关系，并以扩散缩放极限（对应于弱的不对称简单排除过程或Wasep）中显示了映射是如何用宏观波动理论（MFT）的语言表达的。作为一个有趣的特定情况，我们将ASEP中电流的较大偏差映射到SSEP中的大量活动偏差，从而在SSEP中揭示了Kardar-Parisi-Zhang的范围。在大活动中，粒子构型表现出超均匀性[Jack等，PRL 114 060601（2015）]。利用量子自旋链理论的结果，我们通过评估半填充时结构因子的小波数渐近行为来表征过度均匀的状态。相反，我们从MFT中提出了在任何固定的总磁化强度（在热力学极限下）中旋转链中相关函数的猜想。此外，我们将映射概括为带有边界储层的两个开放式ASEP的情况，并将其应用于MFT形式主义的WASEP极限。该映射还使我们能够在由活动条件调节的WASEP中找到对称性的动力学相变（DPT），这是根据由电流调节的dpt的先验知识。
Considering the large deviations of activity and current in the Asymmetric Simple Exclusion Process (ASEP), we show that there exists a non-trivial correspondence between the joint scaled cumulant generating functions of activity and current of two ASEPs with different parameters. This mapping is obtained by applying a similarity transform on the deformed Markov matrix of the source model in order to obtain the deformed Markov matrix of the target model. We first derive this correspondence for periodic boundary conditions, and show in the diffusive scaling limit (corresponding to the Weakly Asymmetric Simple Exclusion Processes, or WASEP) how the mapping is expressed in the language of Macroscopic Fluctuation Theory (MFT). As an interesting specific case, we map the large deviations of current in the ASEP to the large deviations of activity in the SSEP, thereby uncovering a regime of Kardar-Parisi-Zhang in the distribution of activity in the SSEP. At large activity, particle configurations exhibit hyperuniformity [Jack et al., PRL 114 060601 (2015)]. Using results from quantum spin chain theory, we characterize the hyperuniform regime by evaluating the small wavenumber asymptotic behavior of the structure factor at half-filling. Conversely, we formulate from the MFT results a conjecture for a correlation function in spin chains at any fixed total magnetization (in the thermodynamic limit). In addition, we generalize the mapping to the case of two open ASEPs with boundary reservoirs, and we apply it in the WASEP limit in the MFT formalism. This mapping also allows us to find a symmetry-breaking dynamical phase transition (DPT) in the WASEP conditioned by activity, from the prior knowledge of a DPT in the WASEP conditioned by the current.
