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- W2011934323 abstract "An analytic expression valid at any temperature T is derived for the interaction energy $V(R)$ of two polarizable electric dipoles separated by distance R immersed in the thermal quantum field. The expression is a sum that reduces to the Casimir-Polder vacuum interaction integral for $mathrm{KR}ensuremath{ll}1$ and to the classical limit for $mathrm{KR}ensuremath{gg}1,$ where $Kensuremath{equiv}2ensuremath{pi}{k}_{B}T/ensuremath{Elzxh}c.$ For atomic dipoles with dominant absorption frequency ${ensuremath{omega}}_{0}{=k}_{0}c,$ this $V(R)$ and its logarithmic derivative are evaluated numerically and plotted vs R for several values of ${ensuremath{omega}}_{0}$ and T. Also, simple approximate expressions for $V(R)$ and their ranges of validity are derived. Both the numerical results and the simple approximate expressions scale with $mathrm{KR}$ for $Rensuremath{gtrsim}{R}_{2}{=110/k}_{0}$ and with ${k}_{0}R$ for $Rensuremath{lesssim}{R}_{3}=0.74/K.$ They also exhibit the London limit $ensuremath{propto}{R}^{ensuremath{-}6}$ for $Rensuremath{lesssim}{0.023/k}_{0},$ the Casimir-Polder limit $ensuremath{propto}{R}^{ensuremath{-}7}$ for ${R}_{2}ensuremath{lesssim}Rensuremath{lesssim}{R}_{3},$ if this range exists, and the classical limit $ensuremath{propto}{R}^{ensuremath{-}6}$ for $Rensuremath{gtrsim}7.4/K.$ If ${k}_{B}T/ensuremath{Elzxh}{ensuremath{omega}}_{0}ensuremath{gtrsim}{10}^{3},$ then ${R}_{2}ensuremath{gtrsim}{R}_{3},$ and true ${R}^{ensuremath{-}7}$ behavior does not occur. A physical analysis of these results and suggestions for crucial experiments are presented." @default.
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- W2011934323 date "1999-09-01" @default.
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- W2011934323 title "Casimir-Polder interaction at finite temperature" @default.
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- W2011934323 doi "https://doi.org/10.1103/physreva.60.2577" @default.
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