Long-range correlations of the surface charge between two electrical media

Complete text of publication follows. We consider an interface between two semi-infinite media, characterized by different frequency dependent dielectric functions, which are in thermal equilibrium. The distinct electric properties of the media give rise to a surface charge density on the interface which is associated with the discontinuity of the normal component of the electric field. The surface charge density fluctuates in time around its mean value. The correlation of the surface charge fluctuations at two points on the interface, with times different by t and distances different by r, is described by the structure function S(t,r). At large distances r, S(t,r) exhibits a tail of type h(t)/r3 . This inverse-power law behavior is not a sign for a critical state of the system, but the result of the long-range character of electromagnetic forces combined with the asymmetry between the two media. In the sense of distributions, the 2D Fourier transform of 1/r3 is -2πq (q is the wave vector). Thus the structure function S(q,r) has a kink singularity at q=0, behaving like -2πh(t)q. This small-q behavior differs substantially from the standard q2 dependence of short-ranged structure functions. The prefactor function h(t) can be measured by scattering experiments. The form of h(t) depends on the considered 'physical model': One can use either classical or quantum mechanics, the electromagnetic interactions can be treated in either non-retarded (the speed of light is infinite) or retarded regimes. First we evaluate h(t) in the non-retarded regime. The classical universal form of the static h(0) is obtained by simple macroscopic arguments based on a combination of the linear response theory and the electrostatic method of images. Rytov's phenomenological theory of fluctuations of electromagnetic fields leads to a more complicated non-universal form of the quantum h(t). The consideration of retardation effects puts back the quantum form of h(t) to the classical one, in the region of very small values of the wave vector q. The obtained results are checked on the microscopic model of the jellium conductor in contact with vacuum.