Brownian motion in a classical ideal gas:A microscopic approach to Langevin's equation

Lahiri, Rangan and Arvind, * and Sain, Anirban (2004) Brownian motion in a classical ideal gas:A microscopic approach to Langevin's equation. In: Pramana:Journal of Physics, 62 (5). pp. 1015-1028.

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Abstract

We present an insightful `derivation' of the Langevin equation and the fluctuation dissipation theorem in the specific context of a heavier particle moving through an ideal gas of much lighter particles. The Newton's law of motion (mxx = F) for the heavy particle reduces to a Langevin equation (valid on a coarser time-scale) with the assumption that the lighter gas particles follow a Boltzmann velocity distribution. Starting from the kinematics of the random collisions we show that (1) the average force (F) oc -x x and (2) the correlation function of the fluctuating force rl = F - (F) is related to the strength of the average force.

Item Type:	Journal Article
Publication:	Pramana:Journal of Physics
Publisher:	Indian Academy of Sciences
Additional Information:	Copyright of this article belongs to Indian academy of Sciences.
Keywords:	Brownian motion;Fluctuation dissipation theorem;Ideal gas
Department/Centre:	Division of Physical & Mathematical Sciences > Physics
Date Deposited:	01 Jul 2008
Last Modified:	20 Jan 2012 06:31
URI:	http://eprints.iisc.ac.in/id/eprint/11387

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