Tracer particle diffusion in a system with hardcore interacting particles

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Tracer particle diffusion in a system with hardcore interacting particles. / Pigeon, Simon; Fogelmark, Karl; Söderberg, Bo; Mukhopadhyay, Gautam; Ambjörnsson, Tobias.

I: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, Nr. 12, 123209, 21.12.2017.

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

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TY - JOUR

T1 - Tracer particle diffusion in a system with hardcore interacting particles

AU - Pigeon, Simon

AU - Fogelmark, Karl

AU - Söderberg, Bo

AU - Mukhopadhyay, Gautam

AU - Ambjörnsson, Tobias

PY - 2017/12/21

Y1 - 2017/12/21

N2 - In this study, inspired by the work of Nakazato and Kitahara (1980 Prog. Theor. Phys. 64 2261), we consider the theoretical problem of tracer particle diffusion in an environment of diffusing hardcore interacting crowder particles. The tracer particle has a different diffusion constant from the crowder particles. Based on a transformation of the generating function, we provide an exact formal expansion for the tracer particle probability density, valid for any lattice in the thermodynamic limit. By applying this formal solution to dynamics on a regular Bravais lattice we provide a closed form approximation for the tracer particle diffusion constant which extends the Nakazato and Kitahara results to include also b.c.c. and f.c.c. lattices. Finally, we compare our analytical results to simulations in two and three dimensions.

AB - In this study, inspired by the work of Nakazato and Kitahara (1980 Prog. Theor. Phys. 64 2261), we consider the theoretical problem of tracer particle diffusion in an environment of diffusing hardcore interacting crowder particles. The tracer particle has a different diffusion constant from the crowder particles. Based on a transformation of the generating function, we provide an exact formal expansion for the tracer particle probability density, valid for any lattice in the thermodynamic limit. By applying this formal solution to dynamics on a regular Bravais lattice we provide a closed form approximation for the tracer particle diffusion constant which extends the Nakazato and Kitahara results to include also b.c.c. and f.c.c. lattices. Finally, we compare our analytical results to simulations in two and three dimensions.

KW - Brownian motion

KW - correlation functions

KW - diffusion

KW - stochastic particle dynamics

U2 - 10.1088/1742-5468/aa9db3

DO - 10.1088/1742-5468/aa9db3

M3 - Article

VL - 2017

JO - Journal of Statistical Mechanics: Theory and Experiment

T2 - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 12

M1 - 123209

ER -