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IBM Journal of Research and Development  
Volume 32, Number 1, Page 127 (1988)
Basic Concepts in Quantum and Stochastic T...
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Quantum noise and quantum Langevin equations

by C. W. Gardiner
The quantum Langevin equation of Ford, Kac, and Mazur is rederived and shown to be equivalent to an adjoint equation. This latter can be handled by means of van Kampen's cumulant expansion to yield derivations of the quaiclassical Langevin equation, stochastic electrodynamics, quantum optical, and quantum Brownian motion master equations (under appropriate conditions). The result of Benguria and Kac—that the quantum Langevin equation yields the Boltzmann distribution over energy levels in thermodynamic equilibrium—is also verified.
Related Subjects: Quantum theory and effects