Abstract
The behavior of a system in contact with a heat bath can be described either by a Langevin equation or by an equation for its density matrix. As both descriptions inevitably involve approximations, it is not evident that their results coincide. It is shown here by explicit calculation that they do. The main complication is that in the Langevin equation the random force is multiplied by a nonconstant factor, which itself feels the fluctuations. In an alternative formulation of the Langevin approach this complication is avoided.
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It is a pleasure to dedicate this work to Matthieu Ernst on the occasion of his 60th birthday.
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van Kampen, N.G., Oppenheim, I. Langevin and master equation in quantum mechanics. J Stat Phys 87, 1325–1334 (1997). https://doi.org/10.1007/BF02181287
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DOI: https://doi.org/10.1007/BF02181287