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

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    • 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

  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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