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The Theory of a General Quantum System Interacting with a Linear Dissipative System

Feynman, R. P. and Vernon, F. L., Jr. (2000) The Theory of a General Quantum System Interacting with a Linear Dissipative System. Annals of Physics, 281 (1-2). pp. 547-607. ISSN 0003-4916. doi:10.1006/aphy.2000.6017.

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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 properties 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 functionals 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 requirements 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.

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Additional Information:Copyright © 2000 Academic Press. All rights reserved. Received 5 April 1963. Reprinted from Volume 24, pages 118–173. This report is based on a portion of a thesis submitted by F. L. Vernon, Jr. in partial fulfilment of the requirements for the degree of Doctor of Philosophy at the California Institute of Technology, 1959.
Issue or Number:1-2
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:51301
Deposited By: Joy Painter
Deposited On:05 Nov 2014 20:45
Last Modified:10 Nov 2021 19:08

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