The heat kernel coefficients for the dielectric cylinder

We calculate the \hkks for the \elm field in the background of a dielectric cylinder with non equal speeds of light inside and outside. The coefficient $a_{2}$ whose vanishing makes the vacuum energy of a massless field unique, turns out to be zero in dilute order, i.e., in order (\ep-1)^{2}, and nonzero beyond. As a consequence, the vanishing of the vacuum energy in the presence of a dielectric cylinder found by Casimir-Polder summation must take place irrespectively of the methods by which it might be calculated.Comment: 14 pages, 1 figur

Frequency-dependent Drude damping in Casimir force calculations

The Casimir force is calculated between Au thin films that are described by a Drude model with a frequency dependent damping function. The model parameters are obtained from available experimental data for Au thin films. Two cases are considered; annealed and nonannealed films that have a different damping function. Compared with the calculations using a Drude model with a constant damping parameter, we observe changes in the Casimir force of a few percent. This behavior is only observed in films of no more than 300 $\AA$ thick.Comment: Proceedings of the meeting "60 years of Casimir effect", Brasilia, 200

New approach to the thermal Casimir force between real metals

The new approach to the theoretical description of the thermal Casimir force between real metals is presented. It uses the plasma-like dielectric permittivity that takes into account the interband transitions of core electrons. This permittivity precisely satisfies the Kramers-Kronig relations. The respective Casimir entropy is positive and vanishes at zero temperature in accordance with the Nernst heat theorem. The physical reasons why the Drude dielectric function, when substituted in the Lifshitz formula, is inconsistent with electrodynamics are elucidated. The proposed approach is the single one consistent with all measurements of the Casimir force performed up to date. The application of this approach to metal-type semiconductors is considered.Comment: 14 pages, 6 figures. Proceedings of QFEXT07, to appear in J. Phys.

Integral Equations for Heat Kernel in Compound Media

By making use of the potentials of the heat conduction equation the integral equations are derived which determine the heat kernel for the Laplace operator $-a^2\Delta$ in the case of compound media. In each of the media the parameter $a^2$ acquires a certain constant value. At the interface of the media the conditions are imposed which demand the continuity of the `temperature' and the `heat flows'. The integration in the equations is spread out only over the interface of the media. As a result the dimension of the initial problem is reduced by 1. The perturbation series for the integral equations derived are nothing else as the multiple scattering expansions for the relevant heat kernels. Thus a rigorous derivation of these expansions is given. In the one dimensional case the integral equations at hand are solved explicitly (Abel equations) and the exact expressions for the regarding heat kernels are obtained for diverse matching conditions. Derivation of the asymptotic expansion of the integrated heat kernel for a compound media is considered by making use of the perturbation series for the integral equations obtained. The method proposed is also applicable to the configurations when the same medium is divided, by a smooth compact surface, into internal and external regions, or when only the region inside (or outside) this surface is considered with appropriate boundary conditions.Comment: 26 pages, no figures, no tables, REVTeX4; two items are added into the Reference List; a new section is added, a version that will be published in J. Math. Phy

Vacuum energy in conical space with additional boundary conditions

Total vacuum energy of some quantized fields in conical space with additional boundary conditions is calculated. These conditions are imposed on a cylindrical surface which is coaxial with the symmetry axis of conical space. The explicit form of the matching conditions depends on the field under consideration. In the case of electromagnetic field, the perfectly conducting boundary conditions or isorefractive matching conditions are imposed on the cylindrical surface. For a massless scalar field, the semi-transparent conditions ($\delta$-potential) on the cylindrical shell are investigated. As a result, the total Casimir energy of electromagnetic field and scalar field, per a unit length along the symmetry axis, proves to be finite unlike the case of an infinitely thin cosmic string. In these studies the spectral zeta functions are widely used. It is shown briefly how to apply this technique for obtaining the asymptotics of the relevant thermodynamical functions in the high temperature limit.Comment: 29 pages, 2 figures, the title was changed for a more adequate one, the abstract was rewritten, a few typos and minor grammar mistakes were correcte

Casimir repulsion and metamaterials

We analyze the conditions for getting the Casimir repulsion between two nonequal plates. The force between plates with magnetic permeability defined by Drude or Lorentz models is calculated. The short and long distance limits of the force are derived. The Casimir set-up with the hypothetical perfect matching metamaterial is discussed. We put into question the possibility of getting repulsion within the design of metamaterials based on metallic inclusions.Comment: 12 pages, 5 figures, contributed to 8th Workshop on Quantum Field Theory Under the Influence of External Conditions (QFEXT07), Leipzig, Germany, 17-21 Sep 2007, v2, typos correcte

Normal and lateral Casimir force: Advances and prospects

We discuss recent experimental and theoretical results on the Casimir force between real material bodies made of different materials. Special attention is paid to calculations of the normal Casimir force acting perpendicular to the surface with the help of the Lifshitz theory taking into account the role of free charge carriers. Theoretical results for the thermal Casimir force acting between metallic, dielectric and semiconductor materials are presented and compared with available experimental data. Main attention is concentrated on the possibility to control the magnitude and sign of the Casimir force for applications in nanotechnology. In this respect we consider experiments on the optical modulation of the Casimir force between metal and semiconductor test bodies with laser light. Another option is the use of ferromagnetic materials, specifically, ferromagnetic dielectrics. Under some conditions this allows to get Casimir repulsion. The lateral Casimir force acting between sinusoidally corrugated surfaces can be considered as some kind of noncontact friction caused by zero-point oscillations of the electromagnetic field. Recent experiments and computations using the exact theory have demonstrated the role of diffraction-type effects in this phenomenon and the possibility to get asymmetric force profiles. Conclusion is made that the Casimir force may play important role in the operation of different devices on the nanoscale.Comment: 27 pages, 13 figures; Invited keynote lecture at the 2nd International Conference on Science of Friction, Ise-Shima, Mie, Japan, September 13-18, 2010; to appear in J. Phys.: Conf. Se

Casimir Force on Real Materials - the Slab and Cavity Geometry

We analyse the potential of the geometry of a slab in a planar cavity for the purpose of Casimir force experiments. The force and its dependence on temperature, material properties and finite slab thickness are investigated both analytically and numerically for slab and walls made of aluminium and teflon FEP respectively. We conclude that such a setup is ideal for measurements of the temperature dependence of the Casimir force. By numerical calculation it is shown that temperature effects are dramatically larger for dielectrics, suggesting that a dielectric such as teflon FEP whose properties vary little within a moderate temperature range, should be considered for experimental purposes. We finally discuss the subtle but fundamental matter of the various Green's two-point function approaches present in the literature and show how they are different formulations describing the same phenomenon.Comment: 24 pages, 11 figures; expanded discussion, one appendix added, 1 new figure and 10 new references. To appear in J. Phys. A: Math. Theo

Dispersion force for materials relevant for micro and nanodevices fabrication

The dispersion (van der Waals and Casimir) force between two semi-spaces are calculated using the Lifshitz theory for different materials relevant for micro and nanodevices fabrication, namely, gold, silicon, gallium arsenide, diamond and two types of diamond-like carbon (DLC), silicon carbide, silicon nitride and silicon dioxide. The calculations were performed using recent experimental optical data available in the literature, usually ranging from the far infrared up to the extreme ultraviolet bands of the electromagnetic spectrum. The results are presented in the form of a correction factor to the Casimir force predicted between perfect conductors, for the separation between the semi-spaces varying from 1 nanometre up to 1 micrometre. The relative importance of the contributions to the dispersion force of the optical properties in different spectral ranges is analyzed. The role of the temperature for semiconductors and insulators is also addressed. The results are meant to be useful for the estimation of the impact of the Casimir and van der Waals forces on the operational parameters of micro and nanodevices