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Brownian motion in a classical ideal gas: A microscopic approach to Langevin’s equation
Rangan Lahiri Arvind Anirban Sain
Volume 62 Issue 5 May 2004 pp 1015-1028
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https://www.ias.ac.in/article/fulltext/pram/062/05/1015-1028 -
Keywords
Brownian motion ;fluctuation dissipation theorem ;ideal gas -
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 (mx = 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〉 ∞ −x and (2) the correlation function of the fluctuating forceη = F — 〈F〉 is related to the strength of the average force.
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Author Affiliations
Rangan Lahiri1 Arvind2 3 Anirban Sain4 5
- Department of Physics, Indian Institute of Science, Bangalore - 560 012, India
- Department of Physics, Carnegie Mellon University, Pittsburgh, PA - 15213, USA
- Department of Physics, Guru Nanak Dev University, Amritsar - 143 005, India
- Department of Physics, University of Waterloo, Ontario, Canada - N2L3G1, Canada
- Department of Physics, Indian Institute of Technology, Powai, Mumbai - 400 076, India
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Dates
- Published
- May 2004
- Manuscript received
- 3 February 2003
- Manuscript revised
- 12 January 2004
- Accepted
- 17 January 2004
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Pramana – Journal of Physics
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