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


Vernon, Frank Lee (1959) The Theory of a General Quantum System Interacting with a Linear Dissipative System. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/JNJ1-QZ83.


A formalism has been developed, using Feynman's space-time formulation of non-relativistic 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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Electrical Engineering and Physics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Minor Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Feynman, Richard Phillips
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1959
Record Number:CaltechETD:etd-02242006-154616
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:737
Deposited By: Imported from ETD-db
Deposited On:02 Mar 2006
Last Modified:19 Oct 2023 21:11

Thesis Files

PDF (Vernon_fl_1959.pdf) - Final Version
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