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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.

    • Author Affiliations

       

      Rangan Lahiri1 Arvind2 3 Anirban Sain4 5

      1. Department of Physics, Indian Institute of Science, Bangalore - 560 012, India
      2. Department of Physics, Carnegie Mellon University, Pittsburgh, PA - 15213, USA
      3. Department of Physics, Guru Nanak Dev University, Amritsar - 143 005, India
      4. Department of Physics, University of Waterloo, Ontario, Canada - N2L3G1, Canada
      5. Department of Physics, Indian Institute of Technology, Powai, Mumbai - 400 076, India

    • Dates

       
      Published
      May 2004
      Manuscript received
      3 February 2003
      Manuscript revised
      12 January 2004
      Accepted
      17 January 2004

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