Quantum Langevin equation from forward--backward path integral
H. Kleinert, S. V. Shabanov
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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