Coupledoscillator theory of dispersion and CasimirPolder interactions
We address the question of the applicability of the argument theorem (of complex variable theory) to the calculation of two distinct energies: (i) the firstorder dispersion interaction energy of two separated oscillators, when one of the oscillators is excited initially and (ii) the CasimirPolder interaction of a groundstate quantum oscillator near a perfectly conducting plane. We show that the argument theorem can be used to obtain the generally accepted equation for the firstorder dispersion interaction energy, which is oscillatory and varies as the inverse power of the separation r of the oscillators for separations much greater than an optical wavelength. However, for such separations, the interaction energy cannot be transformed into an integral over the positive imaginary axis. If the argument theorem is used incorrectly to relate the interaction energy to an integral over the positive imaginary axis, the interaction energy is nonoscillatory and varies as r{sup −4}, a result found by several authors. Rather remarkably, this incorrect expression for the dispersion energy actually corresponds to the nonperturbative CasimirPolder energy for a groundstate quantum oscillator near a perfectly conducting wall, as we show using the socalled “remarkable formula” for the free energy of an oscillator coupled to a heat bathmore »
 Authors:

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 Physics Department, University of Michigan, 450 Church Street, Ann Arbor, Michigan 481091040 (United States)
 Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
 (United States)
 Publication Date:
 OSTI Identifier:
 22310725
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 16; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DISPERSIONS; FREE ENERGY; GROUND STATES; OSCILLATORS; STATISTICAL MECHANICS