Nonperturbative calculation of the London--van der Waals interaction potential

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Nonperturbative calculation of the London–van der Waals interaction potential

P. R. Berman, G. W. Ford, and P. W. Milonni

Phys. Rev. A 89, 022127 – Published 28 February 2014

Abstract

The so-called remarkable formula [G. W. Ford, J. T. Lewis, and R. F. O'Connell, Phys. Rev. Lett. 55, 2273 (1985)] for the Helmholtz free energy is applied to the problem of determining the interaction potential to all orders in the coupling strength of a pair of oscillator dipoles interacting through the familiar dipole-dipole interaction of electrodynamics. Simple, straightforward calculations lead to expressions for (1) the London short-range potential, (2) the Casimir-Polder long-range potential, and (3) the potential at high temperature. Explicit results are shown for both the temperature dependence of the interaction potential and its deviation from the weak-coupling limit. It is stressed that the interaction potential is a change in free energy, not the energy; in particular, in the high temperature case, the change of energy is zero.

Received 10 December 2013

DOI:https://doi.org/10.1103/PhysRevA.89.022127

Authors & Affiliations

P. R. Berman and G. W. Ford

Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA

P. W. Milonni

Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA and Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA

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Issue

Vol. 89, Iss. 2 — February 2014

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