• Rangan Lahiri

      Articles written in Pramana – Journal of Physics

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

      Rangan Lahiri Arvind Anirban Sain

      More Details Abstract Fulltext PDF

      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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