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Journal of Physics Conference Series

Path integral of charged particle in black cavity

Hagen M. Kleinert

Published Apr 1, 2006• 1 citation
Publisher

Abstract

We solve the forward-backward path integral for a point particle in a bath of photons and derive from it a master equation for the density matrix with electromagnetic dissipation, as well as the associated Langevin equation. The path integral approach yields an alternative access to the Wigner-Weisskopf formula for the natural line width of an atomic state at zero temperature and, in addition, the temperature broadening caused by decoherence.

DOI
10.1088/1742-6596/35/1/003

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We solve the forward-backward path integral for a point particle in a bath of photons and derive from it a master equation for the density matrix with electromagnetic dissipation, as well as the associated Langevin equation. The path integral approach yields an alternative access to the Wigner-Weisskopf formula for the natural line width of an atomic state at zero temperature and, in addition, the temperature broadening caused by decoherence.
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The master equation for a linear open quantum system in a general environment is derived using a stochastic approach. This is an alternative derivation to that of Hu, Paz and Zhang, which was based on the direct computation of path integrals, or to that of Halliwell and Yu, based on the evolution of the Wigner function for a linear closed quantum system. We first show by using the influence functinal formalism that the reduced Wigner function for the open system coincides with a distribution function resulting from averaging both over the initial conditions and the stochastic source of a formal Langevin equation. The master equation for the reduced Wigner function can then be deduced as a Fokker-Planck equation obtained from the formal Langevin equation.