Charge and Current Sum Rules in Quantum Media Coupled to Radiation II |
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Authors: | Ladislav??amaj Bernard?Jancovici |
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Institution: | 1.Institute of Physics,Slovak Academy of Sciences,Bratislava,Slovakia;2.Laboratoire de Physique Théorique,Université de Paris-Sud,Orsay Cedex,France |
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Abstract: | This paper is a continuation of the previous study (Šamaj in J. Stat. Phys. 137:1–17, 2009), where a sequence of sum rules for the equilibrium charge and current density correlation functions in an infinite (bulk)
quantum media coupled to the radiation was derived by using Rytov’s fluctuational electrodynamics. Here, we extend the previous
results to inhomogeneous situations, in particular to the three-dimensional interface geometry of two joint semi-infinite
media. The sum rules derived for the charge-charge density correlations represent a generalization of the previous ones, related
to the interface dipole moment and to the long-ranged tail of the surface charge density correlation function along the interface
of a conductor in contact with an inert (not fluctuating) dielectric wall, to two fluctuating semi-infinite media of any kind.
The charge-current and current-current sum rules obtained here are, to our knowledge, new. The current-current sum rules indicate
a breaking of the directional invariance of the diagonal current-current correlations by the interface. The sum rules are
expressed explicitly in the classical high-temperature limit (the static case) and for the jellium model (the time-dependent
case). |
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