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arXiv:cond-mat/0606506 · Journal of Physics Condensed Matter

The status of the quantum dissipation–fluctuation relation and the Langevin equation

John C Taylor

Published Feb 23, 2007• 8 citations
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Abstract

I examine the arguments which have been given for quantum fluctuation–dissipation theorems. I distinguish between a weak form of the theorem, which is true under rather general conditions, and a strong form which requires a Langevin equation for its statement. I argue that the latter has not been reliably derived in general.
DOI
10.1088/0953-8984/19/10/106223

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The quantum fluctuation dissipation theorem (QFDT) in the Callen–Welton [ Phys. Rev.83 (1951) 34] form is critically revisited. We show that the role of the system eigenvalues is in general not correctly accounted for by the accepted form of the QFDT. As a consequence, a series of quantum results claimed in the literature, like the presence of zero point fluctuations, the violation of the quantum regression hypothesis, the non-white spectrum of the Langevin force, etc. emerge as a consequence of an incorrect application of the theorem. In this context the case of the single harmonic oscillator is illustrated as a typical example where the accepted form of the QFDT is proven to fail.
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