Journal of Statistical Physics

, Volume 46, Issue 5, pp 803–810

On the quantum langevin equation

  • G. W. Ford
  • M. Kac

DOI: 10.1007/BF01011142

Cite this article as:
Ford, G.W. & Kac, M. J Stat Phys (1987) 46: 803. doi:10.1007/BF01011142


The quantum Langevin equation is the Heisenberg equation of motion for the (operator) coordinate of a Brownian particle coupled to a heat bath. We give an elementary derivation of this equation for a simple coupled-oscillator model of the heat bath.

Key words

Langevin equationquantum stochastic processesBrownian motionheat bathcoupled oscillators

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • G. W. Ford
    • 1
  • M. Kac
    • 2
  1. 1.Department of PhysicsUniversity of Southern CaliforniaLos Angeles
  2. 2.Department of MathematicsUniversity of Southern CaliforniaLos Angeles
  3. 3.Department of PhysicsUniversity of MichiganAnn Arbor