Brownian motion in a classical ideal gas: A microscopic approach to Langevin’s equation
Rangan Lahiri Arvind Anirban Sain
Click here to view fulltext PDF
Permanent link:
https://www.ias.ac.in/article/fulltext/pram/062/05/1015-1028
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.
Rangan Lahiri1 Arvind2 3 Anirban Sain4 5
Volume 97, 2023
All articles
Continuous Article Publishing mode
Click here for Editorial Note on CAP Mode
© 2022-2023 Indian Academy of Sciences, Bengaluru.