Casimir stress in an inhomogeneous medium

The Casimir effect in an inhomogeneous dielectric is investigated using Lifshitz's theory of electromagnetic vacuum energy. A permittivity function that depends continuously on one Cartesian coordinate is chosen, bounded on each side by homogeneous dielectrics. The result for the Casimir stress is infinite everywhere inside the inhomogeneous region, a divergence that does not occur for piece-wise homogeneous dielectrics with planar boundaries. A Casimir force per unit volume can be extracted from the infinite stress but it diverges on the boundaries between the inhomogeneous medium and the homogeneous dielectrics. An alternative regularization of the vacuum stress is considered that removes the contribution of the inhomogeneity over small distances, where macroscopic electromagnetism is invalid. The alternative regularization yields a finite Casimir stress inside the inhomogeneous region, but the stress and force per unit volume diverge on the boundaries with the homogeneous dielectrics. The case of inhomogeneous dielectrics with planar boundaries thus falls outside the current understanding of the Casimir effect.Comment: 17 page

Effect of high-K dielectrics on charge transport in graphene

The effect of various dielectrics on charge mobility in single layer graphene is investigated. By calculating the remote optical phonon scattering arising from the polar substrates, and combining it with their effect on Coulombic impurity scattering, a comprehensive picture of the effect of dielectrics on charge transport in graphene emerges. It is found that though high-$\kappa$ dielectrics can strongly reduce Coulombic scattering by dielectric screening, scattering from surface phonon modes arising from them wash out this advantage. By comparing the room-temperature transport properties with narrow-bandgap III-V semiconductors, strategies to improve the mobility in single layer graphene are outlined.Comment: 6 pages, 4 Figure

Measured current drainage through holes in various dielectrics up to 2 kilovolts in a dilute plasma

The electron current drained from a plasma through approximately 0.05 cm diameter holes in eight possible space applicable dielectrics placed on a probe biased at voltages up to 2000 V dc have been determined both theoretically and experimentally. The dielectrics tested were Parylene C and N, Teflon FEP type C, Teflon TFE, Nomex, quartz 7940 Corning Glass, Mylar A, and Kapton H polymide film. A Laplace field was used to predict an upper limit for the drainage current. The measured current was less than the computed current for quartz, Teflon FEP, and the 0.0123 cm thick sample of Parylene N for all voltages tested. The drainage current through the other dielectrics became equal to or greater than the computed current at a voltage below 2000 V. The magnitudes of the currents were between 0.1 and 10 microamperes for most of the dielectrics

The issue of photons in dielectrics: Hamiltonian viewpoint

The definition of the photon in the vacuum of general relativity provided by Kermack et al. and by Synge is extended to nondispersive, nonhomogeneous, isotropic dielectrics in arbitrary motion by Hamiltonian methods that rely on Gordon's effective metric. By these methods the old dilemma, whether the momentum-energy vector of the photon in dielectrics is timelike or spacelike in character, is shown to reappear under a novel guise.Comment: 12 pages, one figure; text to appear in Nuovo Cimento

The issue of photons in dielectrics: Hamiltonian viewpoint

The definition of the photon in the vacuum of general relativity provided by Kermack et al. and by Synge is extended to nondispersive, nonhomogeneous, isotropic dielectrics in arbitrary motion by Hamiltonian methods that rely on Gordon's effective metric. By these methods the old dilemma, whether the momentum-energy vector of the photon in dielectrics is timelike or spacelike in character, is shown to reappear under a novel guise.Comment: 12 pages, one figure; text to appear in Nuovo Cimento

Nonlinear graphene plasmonics: amplitude equation

Using perturbation expansion of Maxwell equations, the amplitude equation is derived for nonlinear TM and TE surface plasmon waves supported by graphene. The equation describes interplay between in-plane beam diffraction and nonlinerity due to light intensity induced corrections to graphene conductivity and susceptibility of dielectrics. For strongly localized TM plasmons, graphene is found to bring the superior contribution to the overall nonlinearity. In contrast, nonlinear response of the substrate and cladding dielectrics can become dominant for weakly localized TE plasmons.Comment: published in Phys. Rev.

Thermal quantum field theory and the Casimir interaction between dielectrics

The Casimir and van der Waals interaction between two dissimilar thick dielectric plates is reconsidered on the basis of thermal quantum field theory in Matsubara formulation. We briefly review two main derivations of the Lifshitz formula in the framework of thermal quantum field theory without use of the fluctuation-dissipation theorem. A set of special conditions is formulated under which these derivations remain valid in the presence of dissipation. The low-temperature behavior of the Casimir and van der Waals interactions between dissimilar dielectrics is found analytically from the Lifshitz theory for both an idealized model of dilute dielectrics and for real dielectrics with finite static dielectric permittivities. The free energy, pressure and entropy of the Casimir and van der Waals interactions at low temperatures demonstrate the same universal dependence on the temperature as was previously discovered for ideal metals. The entropy vanishes when temperature goes to zero proving the validity of the Nernst heat theorem. This solves the long-standing problem on the consistency of the Lifshitz theory with thermodynamics in the case of dielectric plates. The obtained asymptotic expressions are compared with numerical computations for both dissimilar and similar real dielectrics and found to be in excellent agreement. The role of the zero-frequency term in Matsubara sum is investigated in the case of dielectric plates. It is shown that the inclusion of conductivity in the model of dielectric response leads to the violation of the Nernst heat theorem. The applications of this result to the topical problems of noncontact atomic friction and the Casimir interaction between real metals are discussed.Comment: 39 pages, 4 figures, to appear in Phys. Rev.