Journal of Statistical Physics

, Volume 46, Issue 5–6, pp 803–810

On the quantum langevin equation

  • G. W. Ford
  • M. Kac
Articles

Abstract

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 equation quantum stochastic processes Brownian motion heat bath coupled oscillators 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. W. Ford, M. Kac, and P. Mazur,J. Math. Phys. 6:504 (1965).Google Scholar
  2. 2.
    A. O. Caldeira and A. J. Leggett,Phys. Rev. Lett. 46:211 (1981).Google Scholar
  3. 3.
    V. B. Magalinskij,Sov. Phys. JETP 36:1381 (1959).Google Scholar
  4. 4.
    L. D. Landau and E. M. Lifshitz,Statistical Physics, 2nd ed. (Addison-Wesley, Reading, Massachusetts, 1969).Google Scholar
  5. 5.
    R. Benguria and M. Kac,Phys. Rev. Lett. 46:1 (1981).Google Scholar
  6. 6.
    H. Maassen,J. Stat. Phys. 34:239 (1984).Google Scholar

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

Personalised recommendations