论文标题
Q-Boson零范围过程中的当前统计数据
Current statistics in the q-boson zero range process
论文作者
论文摘要
我们通过TQ连接的精确扰动溶液在Q-Boson零范围过程中获得了粒子电流的前两个累积物的精确公式。结果表示为双重轮廓积分的无限总和。我们对获得的表达式的大型系统尺寸限制$ n \ to \ infty $进行渐近分析。对于$ | q | \ neq1 $，第二个累积的领先条款重现了Kardar-Parisi-Zhang通用类中预期的$ n^{3/2} $缩放。缩放$ q \ asymp \ exp（-α/\ sqrt {n}）\ to1 $对应于Kardar-Parisi-Zhang和Edwards-Wilkinson普遍性类之间的交叉。在此缩放下，总和会收敛到一个积分，从而导致了先前针对不对称的简单排除过程得出的交叉缩放函数，并猜想为通用。
We obtain exact formulas of the first two cumulants of particle current in the q-boson zero range process via exact perturbative solution of the TQ-relation. The result is represented as an infinite sum of double contour integrals. We perform the asymptotic analysis of the large system size limit $N\to\infty$ of the expressions obtained. For $|q|\neq1$ the leading terms of the second cumulant reproduce the $N^{3/2}$ scaling expected for models in the Kardar-Parisi-Zhang universality class. The scaling $q\asymp\exp(-α/\sqrt{N})\to1$ corresponds to the the crossover between the Kardar-Parisi-Zhang and Edwards-Wilkinson universality classes. Under this scaling the sum converges to an integral, resulting in the crossover scaling function derived previously for the asymmetric simple exclusion process and conjectured to be universal.
