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Quantum Langevin equation from forward--backward path integral

H. Kleinert·S. V. Shabanov
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Abstract

The quantum Langevin equation is derived from the Feynman-Veron forward--backward path integral representation for a density matrix of a quantum system in a thermal oscillator bath. We exhibit the mechanism by which the classical, $c$-valued noise in the Feynman-Vernon theory turns into an operator-valued quantum noise fulfilling characteristic commutation relation necessary for the unitarity of the time evolution in the quantum Langevin equation.

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H. Kleinert, S. V. Shabanov. 1995-03-02. Quantum Langevin equation from forward--backward path integral. https://doi.org/10.1016/0375-9601(95)00169-4

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