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Radiophysics and Quantum Electronics

Nonequilibrium correlation functions of fluctuation forces in quantum theory of generalized Langevin equations

S. A. Dyagilev, V. B. Tsaregradskii

Published May 1, 1981• 0 citations
Publisher
DOI
10.1007/bf01033752

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In the spirit of the linear response theory, a simple derivation is given of a Langevin equation for collective modes of a macroscopic system. Unlike in the usual treatment, we separate a weak interaction of individual particles with collective modes which is allowed to depend on time. In nonequilibrium cases, we have shown that a damping constant of the collective modes can be expressed in terms of a time correlation function, in which its average is taken with respect to a nonequilibrium density matrix rather than a usual canonical density matrix. A microscopic expression for a Langevin random force is obtained in terms of fluctuations of a density matrix.
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A new derivation of the Langevin equation for a system in contact with a heat reservoir in equilibrium is given based on the concept of path probability inherent in the Feynman approach to quantum mechanics. The derived Langevin equation is a generalization of the Magalinski type, i.e., it is a second order differential equation and contains a shift term, a retarded damping term, a destruction term and a random force term in addition to the usual external potential force term. It is a semi-classical equation in the sense that it is a classical equation but contains a quantal response function of the Kubo formula type and the second moment of the random force is given by a quantal symmetrized correlation function. The fluctuation-dissipation theorem of the second kind is exactly valid between the response and the correlation functions.