Viscous Brane Cosmology with a Brane-Bulk Energy Interchange Term

We assume a flat brane located at y=0, surrounded by an AdS space, and consider the 5D Einstein equations when the energy flux component of the energy-momentum tensor is related to the Hubble parameter through a constant Q. We calculate the metric tensor, as well as the Hubble parameter on the brane, when Q is small. As a special case, if the brane is tensionless, the influence from Q on the Hubble parameter is absent. We also consider the emission of gravitons from the brane, by means of the Boltzmann equation. Comparing the energy conservation equation derived herefrom with the energy conservation equation for a viscous fluid on the brane, we find that the entropy change for the fluid in the emission process has to be negative. This peculiar effect is related to the fluid on the brane being a non-closed thermodynamic system. The negative entropy property for non-closed systems is encountered in other areas in physics also, in particular, in connection with the Casimir effect at finite temperature.Comment: 12 pages, latex, no figure

Violation of the Nernst heat theorem in the theory of thermal Casimir force between Drude metals

We give a rigorous analytical derivation of low-temperature behavior of the Casimir entropy in the framework of the Lifshitz formula combined with the Drude dielectric function. An earlier result that the Casimir entropy at zero temperature is not equal to zero and depends on the parameters of the system is confirmed, i.e. the third law of thermodynamics (the Nernst heat theorem) is violated. We illustrate the resolution of this thermodynamical puzzle in the context of the surface impedance approach by several calculations of the thermal Casimir force and entropy for both real metals and dielectrics. Different representations for the impedances, which are equivalent for real photons, are discussed. Finally, we argue in favor of the Leontovich boundary condition which leads to results for the thermal Casimir force that are consistent with thermodynamics.Comment: 24 pages, 3 figures, accepted for publication in Phys. Rev.

Surface-impedance approach solves problems with the thermal Casimir force between real metals

The surface impedance approach to the description of the thermal Casimir effect in the case of real metals is elaborated starting from the free energy of oscillators. The Lifshitz formula expressed in terms of the dielectric permittivity depending only on frequency is shown to be inapplicable in the frequency region where a real current may arise leading to Joule heating of the metal. The standard concept of a fluctuating electromagnetic field on such frequencies meets difficulties when used as a model for the zero-point oscillations or thermal photons in the thermal equilibrium inside metals. Instead, the surface impedance permits not to consider the electromagnetic oscillations inside the metal but taking the realistic material properties into account by means of the effective boundary condition. An independent derivation of the Lifshitz-type formulas for the Casimir free energy and force between two metal plates is presented within the impedance approach. It is shown that they are free of the contradictions with thermodynamics which are specific to the usual Lifshitz formula for dielectrics in combination with the Drude model. We demonstrate that in the impedance approach the zero-frequency contribution is uniquely fixed by the form of impedance function and does not need any of the ad hoc prescriptions intensively discussed in the recent literature. As an example, the computations of the Casimir free energy between two gold plates are performed at different separations and temperatures. It is argued that the surface impedance approach lays a reliable framework for the future measurements of the thermal Casimir force.Comment: 21 pages, 3 figures, to appear in Phys. Rev.

Effects of Spatial Dispersion on the Casimir Force between Graphene Sheets

The Casimir force between graphene sheets is investigated with emphasis on the effect from spatial dispersion using a combination of factors, such as a nonzero chemical potential and an induced energy gap. We distinguish between two regimes for the interaction - T=0 $K$ and $T\neq 0$ $K$. It is found that the quantum mechanical interaction (T=0 $K$) retains its distance dependence regardless of the inclusion of dispersion. The spatial dispersion from the finite temperature Casimir force is found to contribute for the most part from $n=0$ Matsubara term. These effects become important as graphene is tailored to become a poor conductor by inducing a band gap.Comment: 6 pages, 9 figures. Submitted to EP

Electromagnetic field correlations near a surface with a nonlocal optical response

The coherence length of the thermal electromagnetic field near a planar surface has a minimum value related to the nonlocal dielectric response of the material. We perform two model calculations of the electric energy density and the field's degree of spatial coherence. Above a polar crystal, the lattice constant gives the minimum coherence length. It also gives the upper limit to the near field energy density, cutting off its $1/z^3$ divergence. Near an electron plasma described by the semiclassical Lindhard dielectric function, the corresponding length scale is fixed by plasma screening to the Thomas-Fermi length. The electron mean free path, however, sets a larger scale where significant deviations from the local description are visible.Comment: 15 pages, 7 figure files (.eps), \documentclass[global]{svjour}, accepted in special issue "Optics on the Nanoscale" (Applied Physics B, eds. V. Shalaev and F. Tr\"ager

The effects of heavy doping on the electronic states in semiconductors

The physics of semiconductors is reviewed. Topics included in the discussion are energy of the dopant system (kinetic energy in a many-valley semiconductor, exchange energy in an ellipsoidal Fermi volume, energy in a polar semiconductor), self energy shifts, band-gap narrowing, and piezo experiments. 31 refs., 27 figs