Work

Dimensional crossover via confinement in the lattice Lorentz gas

Year: 2024

Type: preprint

Abstract: We consider a lattice model in which a tracer particle moves in the presence of randomly distributed immobile obstacles. The crowding effect due to the obstacles interplays with the quasi-confinement imposed by wrapping the lattice onto a cylinder. We compute the velocity autocorrelation function and show that already in equilibrium the system exhibits a dimensional crossover from two- to one-dimensional as time progresses. A pulling force is switched on and we characterize analytically the stationary state in terms of the stationary velocity and diffusion coefficient. Stochastic simulations are used to discuss the range of validity of the analytic results. Our calculation, exact to first order in the obstacle density, holds for arbitrarily large forces and confinement size.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2409.04289

Authors: Squarcini, A., Tinti, A., Illien, P., Bénichou, O., Franosch, T.

Institutions: Universität Innsbruck, Sapienza University of Rome, Centre National de la Recherche Scientifique, Sorbonne Université, PHENIX laboratory, Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre-et-Marie-Curie

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Austrian Science Fund, Université Pierre et Marie Curie

Awards: G4495373907, Colloidal Monolayers in Periodic Laser Fields, G9000192918

OpenAlex ID: W4403587647

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