Path integral approach to quantum Brownian motion

A. O. Caldeira, A. J. Leggett

Research output: Contribution to journalArticlepeer-review


We apply the influence-functional method of Feynman and Vernon to the study of Brownian motion at arbitrary temperature. By choosing a specific model for the dissipative interaction of the system of interest with its environment, we are able to evaluate the influence functional in closed form and express it in terms of a few parameters such as the phenomenological viscosity coefficient. We show that in the limit h→0 the results obtained from the influence functional formalism reduce to the classical Fokker-Planck equation. In the case of a simple harmonic oscillator with arbitrarily strong damping and at arbitrary temperature, we obtain an explicit expression for the time evolution of the complete density matrix ρ{variant}(x, x′, t) when the system starts in a particular kind of pure state. We compare our results with those of other approaches to the problem of dissipation in quantum mechanics.

Original languageEnglish (US)
Pages (from-to)587-616
Number of pages30
JournalPhysica A: Statistical Mechanics and its Applications
Issue number3
StatePublished - Sep 1983
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics


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