Physics – Quantum Physics
Scientific paper
2007-09-26
Phys. Rev. E 77, 011114 (2008)
Physics
Quantum Physics
34 pages, 0 figures. New version includes restructured intro and minor typos corrected
Scientific paper
10.1103/PhysRevE.77.011114
We present an entirely microscopic calculation of the Casimir force $f(d)$ between two metallic plates in the limit of large separation $d$. The models of metals consist of mobile quantum charges in thermal equilibrium with the photon field at positive temperature $T$. Fluctuations of all degrees of freedom, matter and field, are treated according to the principles of quantum electrodynamics and statistical physics without recourse to approximations or intermediate assumptions. Our main result is the correctness of the asymptotic universal formula $ f(d) \sim -\frac{\zeta(3) \kB T}{8\pi d^3}$, $d\to\infty$. This supports the fact that, in the framework of Lifshitz' theory of electromagnetic fluctuations, transverse electric modes do not contribute in this regime. Moreover the microscopic origin of universality is seen to rely on perfect screening sum rules that hold in great generality for conducting media.
Buenzli Pascal R.
Martin Ph. A.
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