论文标题
示踪剂位置在密集的晶格气中的累积物的确切时间依赖性
Exact time dependence of the cumulants of a tracer position in a dense lattice gas
论文作者
论文摘要
我们开发了一种一般方法，以计算示踪剂粒子在硬核颗粒的致密晶格气体中的累积物的确切时间依赖性。更确切地说，我们计算与标记粒子在任意时间的位置相关的累积生成函数，以及在晶格上空缺的密度下的领先顺序。特别是，我们的方法可以访问示踪剂位置累积物的短时动力学 - 这种制度很少有结果。通过证明它超出了对称的1D随机步行的情况，并涵盖了（i）有偏见的示踪剂的重要情况，证明了我们方法的普遍性； （ii）梳状结构； （iii）$ d $维度情况。
We develop a general method to calculate the exact time dependence of the cumulants of the position of a tracer particle in a dense lattice gas of hardcore particles. More precisely, we calculate the cumulant generating function associated with the position of a tagged particle at arbitrary time, and at leading order in the density of vacancies on the lattice. In particular, our approach gives access to the short-time dynamics of the cumulants of the tracer position -- a regime in which few results are known. The generality of our approach is demonstrated by showing that it goes beyond the case of a symmetric 1D random walk, and covers the important situations of (i) a biased tracer; (ii) comb-like structures; and (iii) $d$-dimensional situations.
