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Extra resources for Advances in Chemical Physics: Memory Function Approahes to Stochastic Problems in Condensed Matter, Volume 62
50). We then obtain which is the Laplace transform of where Let us write Eq. 49) explicitly for A and come back from the quantumlike P. GRIGOLINI 18 to the classical formalism. 55c) The symbol ( )eq denotes averaging over the equilibrium distribution p,(A,b) [seeEq. 5)]. 57) Let us substitute Eq. 56) into Eq. 54) and assume A, = 0 while identifying A with the variable velocity u. 58) b=-yu+f(t) that is, the standard Langevin equation. This makes it clear why the hierarchy equations of Eq. 49) for k = 0,1,2,...
The dynamics of our sys- P. GRIGOLINI AND F. 2’) iL of Eq. 2) denotes a rigorous Liouvillian operator such as that of Section 11. Po drives both a and b, but it does not have any interaction term between sets a and b, that is, Yo= Ya+ 2Zb (3 -4) This property is satisfied by the system illustrated in Section I1 and every other system explored with the same method in the present volume. As pointed out in Chapter I, we have to apply the Zwanzig projection method to the interaction picture. For clarity let us rewrite the corresponding result (see Chapter I): where Q ~ 1 - p Throughout this chapter we shall use the projection operator P defined as BASIC DESCRIPTION OF RULES LEADING TO ADIABATIC ELIMINATION 45 which reduces to Eq.
Bhttiker and R. Landauer, in Nonlinear Phenomena at Phase Transition and Instabilities, T. , NATO AS1 Series, Plenum, New York, 1981; R. Landauer, J. Appl. , 33,2209 (1962); R. Landauer, in Electrical Transport and Optical Properties of Inhomogeneour Media, J. C. Garland and D. B. , American Institute of Physics, New York, Sec. 9; R. Landauer and J. A. Swanson, Phys. , 121, 1668 (1961); R. Landauer and J. W. F. , B. G. Teubner, Stuttgart, 1973. 17. A. Adelman. A h . Chem. , XLIV, 143 (1980). 18.
Advances in Chemical Physics: Memory Function Approahes to Stochastic Problems in Condensed Matter, Volume 62