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Master Equation for Quantum Brownian Motion Derived by Stochastic Methods

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Abstract

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 functional 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.

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Authors and Affiliations

  1. Departamento de Física, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires, Argentina

    Esteban Calzetta

  2. Departament de Física Fonamental, Universitat de Barcelona, Barcelona, Spain

    Albert Roura & Enric Verdaguer

  3. Institut de Física d'Altes Energies (IFAE), Barcelona, Spain

    Enric Verdaguer

Authors
  1. Esteban Calzetta
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  2. Albert Roura
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  3. Enric Verdaguer
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Calzetta, E., Roura, A. & Verdaguer, E. Master Equation for Quantum Brownian Motion Derived by Stochastic Methods. International Journal of Theoretical Physics 40, 2317–2332 (2001). https://doi.org/10.1023/A:1012946523088

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