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Journal Articles Physical Review E Year : 2022

Exact time dependence of the cumulants of a tracer position in a dense lattice gas

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Abstract

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.
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Dates and versions

hal-03842911 , version 1 (07-11-2022)

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Alexis Poncet, Aurélien Grabsch, Olivier Bénichou, Pierre Illien. Exact time dependence of the cumulants of a tracer position in a dense lattice gas. Physical Review E , 2022, 105 (5), pp.054139. ⟨10.1103/PhysRevE.105.054139⟩. ⟨hal-03842911⟩
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