TITLE

Correlation functions in finite memory-time reservoir theory

AUTHOR(S)

Arnoldus, Henk F.; George, Thomas F.

PUB. DATE

November 1987

SOURCE

Journal of Mathematical Physics;Nov87, Vol. 28 Issue 11, p2731

SOURCE TYPE

Academic Journal

DOC. TYPE

Article

ABSTRACT

Interaction of a small system S with a large reservoir R amounts to thermal relaxation of the reduced system density operator ?[SUBs] (t). The presence of the reservoir enters the equation of motion for ?[SUBs] (t) through the reservoir correlation functions f[SUBkl] (t) (defined in the text), which decay to zero for t ? 8 on a time scale t[SUBc]. Commonly, this t[SUBc] is much smaller than the inverse relaxation constants for the time evolution of ?s (t). Then a series of approximations can be made, which lead to a Markovian equation of motion for ?s (t). In this paper the assumption of a small reservoir correlation time is removed. The equation of motion for ?s (t) is solved, and it appears that the memory effect, due to t[SUBc] ?0, can be incorporated in a frequency dependence of the relaxation operator &Gammasim; (?). Subsequently, (unequal-time) quantum correlation functions of two system operators are considered, where explicit expressions for (the Laplace transform of) the correlation functions are obtained. They involve again the relaxation operator &Gammasim; (?), which accounts for the time regression. Additionally it is found that an initial-correlation operator &Gammasim;(?) arises, as a consequence of the fact that the equal-time correlation functions do not factorize as ?s (t) times the reservoir density operator. It is pointed out that the frequency dependence of &Gammasim;(?) and the occurrence of a nonzero &Gammasim;(?) both arise as a result of t[SUBc] ? 0, and should therefore be treated on an equal footing. Explicit evaluation of &Gammasim;(?) and &Gammasim;(?) shows that their matrix elements can be expressed entirely in &fsim;[SUBkl] (?), just as in the Markov approximation. Hence no essential complications appear if one should go beyond the limits of a small reservoir correlation time t[SUBc].

ACCESSION #

9849001

Tags: EQUATIONS of motion;  CORRELATION (Statistics)

 

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