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arXiv:cond-mat/0011420

Common Origin of Quantum Regression and Quantum Fluctuation Dissipation Theorems

P. Shiktorov, Evgenij Starikov, Viktor Gružinskis, Lino Reggiani, Luca Varani, J. C. Vaissière

Published Nov 24, 2000• 0 citations
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Abstract

It is shown that the quantum fluctuation dissipation theorem can be considered as a mathematical formulation in the spectral representation of Onsager hypothesis on the regression of fluctuations in physical systems. It is shown that the quantum fluctuation dissipation theorem can be generalized to an arbitrary stationary state.
DOI
10.48550/arxiv.cond-mat/0011420

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In the attempt to derive the regression theorem from the fluctuation dissipation theorem several authors claim the violation of the former theorem in the quantum case. Here we pose the question: does it exisist a quantum fluctuation dissipation theorem (QFDT) in its conventional interpretation ? It is shown that the relation usually called as the QFDT is the condition of detailed macroscopic energetic balance. Following this interpretation the existing conflict between the two theorems in the quantum case is removed.
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Some 93 years ago, Onsager postulated his so-called regression hypothesis, which relates the time-dependent relaxation of a close-to-equilibrium system to its temporal correlations at thermal equilibrium. As far as quantum systems are concerned, it is long-known that this hypothesis cannot be quantitatively correct. Here, the authors analytically derive a suitably adjusted version of Onsager's original formula, provide a wide variety of numerical illustrations, and compare it with some pertinent previous works.