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SUMMARY:Isothermal Langevin dynamics in systems with power-law spatially d
ependent friction
DTSTART;VALUE=DATE-TIME:20170905T073000Z
DTEND;VALUE=DATE-TIME:20170905T080000Z
DTSTAMP;VALUE=DATE-TIME:20230206T020400Z
UID:indico-contribution-64@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Oded Farago (Ben Gurion University)\n\nWe study the
dynamics of Brownian particles in a heterogeneous one-dimensional medium w
ith a spatially-dependent diffusion coefficient of the form $D(x)\\sim|x|^
c$\, at constant temperature. The particle’s probability distribution fu
nction (PDF) is calculated both analytically\, by solving Fick’s diffusi
on equation\, and from numerical simulations of the underdamped Langevin e
quation. At large times\, the PDFs calculated by both approaches yield ide
ntical results\, corresponding to subdiffusion for $c < 0$\, and superdiff
usion for $0 < c < 1$. For $c > 1$\, 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 tha
t in an isothermal medium\, the motion cannot exceed the ballistic limit (
$\\langle x2\\rangle∼ t^2$). The ballistic limit is reached when the fri
ction coefficient drops sufficiently fast at large distances from the orig
in\, and is correctly captured by Langevin’s equation.\n\n$ $\n\n[1] S.
Regev\, N. Gronbech-Jensen\, and O. Farago\, Phys Rev. E **94**\, 012116 (
2016).\n\nhttps://zakopane.if.uj.edu.pl/event/4/contributions/64/
LOCATION:30
RELATED-TO:indico-event-4@zakopane.if.uj.edu.pl
URL:https://zakopane.if.uj.edu.pl/event/4/contributions/64/
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