ABSTRACT
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) approximately -zeta(3)kBT/8pid3, d-->infinity. This supports the fact that, in the framework of the 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.
ABSTRACT
We study interatomic forces in a fluid consisting of a mixture of free charges and neutral atoms in the framework of the quantum many-body problem at nonzero temperature and nonzero density. Of central interest is the interplay between van der Waals forces and screening effects due to free charges. The analysis is carried out in a partially recombined hydrogen plasma in the Saha regime. The effective potentials in the medium between two atoms, or an atom and a charge, or two charges, are determined from the large-distance behavior of equilibrium proton-proton correlations. We show, in a proper low-temperature and low-density scaling limit, that those potentials all decay as r(-6) at large distance r, while the corresponding amplitudes are calculated exactly. In particular, the presence of free charges only causes a partial (nonexponential) screening of the atomic potential, and it does not modify its typical r(-6) decay. That potential reduces to the standard van der Waals form for two atoms in vacuum when the temperature is driven to zero. The analysis is based on first principles: it does not assume preformed atoms and takes into account in a coherent way all effects, quantum mechanical binding, ionization, and collective screening, which originate from the Coulomb potential. Our method relies on the path integral representation of the quantum Coulomb gas.
