Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2012-01-02
Physics
Condensed Matter
Statistical Mechanics
15 pages RevTex, 4 figures
Scientific paper
Relaxation of the thermal Casimir or van der Waals force for a model dielectric medium is investigated. We start with a model of interacting polarization fields with a dynamics that leads to a frequency dependent dielectric constant of the Debye form. In the static limit the usual zero frequency Matsubara mode component of the Casimir force is recovered. We then consider the out of equilibrium relaxation of the van der Waals force to its equilibrium value when two initially uncorrelated dielectric bodies are brought into sudden proximity. It is found that the spatial dependence of the out of equilibrium force is the same as the equilibrium one but it has a time dependent amplitude, or Hamaker coefficient, which increases in time to its equilibrium value. The final relaxation to the equilibrium value is exponential in systems with a single or finite number of polarization field relaxation times. However, in systems, such as those described by the Havriliak-Negami dielectric constant, with a broad distribution of relaxation times, we observe a much slower power law decay to the equilibrium value.
Dean David S.
Démery Vincent
Parsegian Adrian V.
Podgornik Rudolf
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