β Scribed by R.P. Feynman; F.L. Vernon Jr.
No coin nor oath required. For personal study only.
A formalism has been developed, using Feynman's space-time formulation of nonrelativistic quantum mechanics whereby the behavior of a system of interest, which is coupled to other external quantum systems, may be calculated in terms of its own variables only. It is shown that the effect of the external systems in such a formalism can always be included in a general class of functionals (influence functionals) of the coordinates of the system only. The proper- ties of influence functionals for general systems are examined. Then, specific forms of influence functionals representing the effect of definite and random classical forces, linear dissipative systems at finite temperatures, and combinations of these are analyzed in detail. The linear system analysis is first done for perfectly linear systems composed of combinations of harmonic oscillators, loss being introduced by continuous distributions of oscillators. Then approximately linear systems and restrictions necessary for the linear behavior are considered. Influence func- tionals for all linear systems are shown to have the same form in terms of their classical response functions. In addition, a fluctuation-dissipation theorem is derived relating temperature and dissipation of the linear system to a fluctuating classical potential acting on the system of interest which reduces to the Nyquist-Johnson relation for noise in the case of electric circuits. Sample calculations of transition probabilities for the spontaneous emission of an atom in free space and in a cavity are made. Finally, a theorem is proved showing that within the require- ments of linearity all sources of noise or quantum fluctuation introduced by maser-type amplification devices are accounted for by a classical calculation of the characteristics of the maser. c 1963 Academic Press
π SIMILAR VOLUMES
We study the global smooth solution and the global attractor for a dissipative nonlinear evolution system given by strongly coupled parabolic equations.
## Abstract To demonstrate its applicability for realistic open systems, we apply the dynamic mean field quantum dissipative theory to simulate the photoβinduced excitation and nonradiative decay of an embedded butadiene molecule. The Markovian approximation is adopted to further reduce the computa