TY - JOUR

T1 - Isothermal Langevin dynamics in systems with power-law spatially dependent friction

AU - Regev, Shaked

AU - Grønbech-Jensen, Niels

AU - Farago, Oded

N1 - Publisher Copyright:
© 2016 American Physical Society.

PY - 2016/7/13

Y1 - 2016/7/13

N2 - We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially dependent diffusion coefficient of the form D(x)∼|x|c, at constant temperature. The particle's probability distribution function (PDF) is calculated both analytically, by solving Fick's diffusion equation, and from numerical simulations of the underdamped Langevin equation. At long times, the PDFs calculated by both approaches yield identical results, corresponding to subdiffusion for c<0 and superdiffusion for 01, the diffusion equation predicts that the particles accelerate. Here we show that this phenomenon, previously considered in several works as an illustration for the possible dramatic effects of spatially dependent thermal noise, is unphysical. We argue that in an isothermal medium, the motion cannot exceed the ballistic limit (x2∼t2). The ballistic limit is reached when the friction coefficient drops sufficiently fast at large distances from the origin and is correctly captured by Langevin's equation.

AB - We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially dependent diffusion coefficient of the form D(x)∼|x|c, at constant temperature. The particle's probability distribution function (PDF) is calculated both analytically, by solving Fick's diffusion equation, and from numerical simulations of the underdamped Langevin equation. At long times, the PDFs calculated by both approaches yield identical results, corresponding to subdiffusion for c<0 and superdiffusion for 01, the diffusion equation predicts that the particles accelerate. Here we show that this phenomenon, previously considered in several works as an illustration for the possible dramatic effects of spatially dependent thermal noise, is unphysical. We argue that in an isothermal medium, the motion cannot exceed the ballistic limit (x2∼t2). The ballistic limit is reached when the friction coefficient drops sufficiently fast at large distances from the origin and is correctly captured by Langevin's equation.

UR - http://www.scopus.com/inward/record.url?scp=84979266942&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.94.012116

DO - 10.1103/PhysRevE.94.012116

M3 - Article

C2 - 27575086

AN - SCOPUS:84979266942

VL - 94

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 1

M1 - 012116

ER -