Valery N. Marachevsky

Casimir interaction of dielectric gratings.

We derive an exact solution for the Casimir force between two arbitrary periodic dielectric gratings and illustrate our method by applying it to two nanostructured silicon gratings. We also reproduce the Casimir force gradient measured recently [H. B. Chan, Y. Bao, J. Zou, R. A. Cirelli, F. Klemens, W. M. Mansfield, and C. S. Pai, Phys. Rev. Lett. 101, 030401 (2008)10.1103/PhysRevLett.101.030401] between a silicon grating and a gold sphere taking into account the material dependence of the force. We find good agreement between our theoretical results and the measured values both in absolute force values and the ratios between the exact force and proximity force approximation predictions.

Perfect magnetic conductor Casimir piston in d+1 dimensions

Perfect magnetic conductor (PMC) boundary conditions are dual to the more familiar perfect electric conductor (PEC) conditions and can be viewed as the electromagnetic analog of the boundary conditions in the bag model for hadrons in QCD. Recent advances and requirements in communication technologies have attracted great interest in PMCs, and Casimir experiments involving structures that approximate PMCs may be carried out in the not-too-distant future. In this paper, we make a study of the zero-temperature PMC Casimir piston in d+1 dimensions. The PMC Casimir energy is explicitly evaluated by summing over p+1-dimensional Dirichlet energies where p ranges from 2 to d inclusively. We derive two exact d-dimensional expressions for the Casimir force on the piston and find that the force is negative (attractive) in all dimensions. Both expressions are applied to the case of 2+1 and 3+1 dimensions. A spin-off from our work is a contribution to the PEC literature: we obtain a useful alternative expression for the PEC Casimir piston in 3+1 dimensions and also evaluate the Casimir force per unit area on an infinite strip, a geometry of experimental interest.

Compact dimensions and the Casimir effect: the Proca connection

We study the Casimir effect in the presence of an extra dimension compactified on a circle of radius R (M4 × S1 spacetime). Our starting point is the Kaluza Klein decomposition of the 5D Maxwell action into a massless sector containing the 4D Maxwell action and an extra massless scalar field and a Proca sector containing 4D gauge fields with masses mn = n/R where n is a positive integer. An important point is that, in the presence of perfectly conducting parallel plates, the three degrees of freedom do not yield three discrete (non-penetrating) modes but two discrete modes and one continuum (penetrating) mode. The massless sector reproduces Casimirs original result and the Proca sector yields the corrections. The contribution from the Proca continuum mode is obtained within the framework of Lifshitz theory for plane parallel dielectrics whereas the discrete modes are calculated via 5D formulas for the piston geometry. An interesting manifestation of the extra compact dimension is that the Casimir force between perfectly conducting plates depends on the thicknesses of the slabs.

CASIMIR SURFACE FORCE ON A DILUTE DIELECTRIC BALL

The Casimir surface force density F on a dielectric dilute spherical ball of radius a, surrounded by a vacuum, is calculated at zero temperature. We treat (n − 1) (n being the refractive index) as a small parameter. The dispersive properties of the material are taken into account by adopting a simple dispersion relation, involving a sharp high frequency cutoff at ! = !0. For a nondispersive medium there appears (after regularization) a finite, physical, force F nondisp which is repulsive. By means of a uniform asymptotic expansion of the RiccatiBessel functions we calculate F nondisp up to the fourth order in 1/�. For a dispersive medium the main part of the force F disp is also repulsive. The dominant term in F disp is proportional to (n −1) 2 ! 3 /a , and will under usual physical conditions outweigh F nondisp by several orders of magnitude.

The Casimir effect: medium and geometry

Theory of the Casimir effect is presented in several examples. Casimir–Polder-type formulas, Lifshitz theory and theory of the Casimir effect for two gratings separated by a vacuum slit are derived. Equations for the electromagnetic field in the presence of a medium and dispersion are discussed. The Casimir effect for systems with a layer of 2 + 1 fermions is studied.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowkers 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.

Probing Atom-Surface Interactions by Diffraction of Bose-Einstein Condensates

In this article we analyze the Casimir-Polder interaction of atoms with a solid grating and an additional repulsive interaction between the atoms and the grating in the presence of an external laser source. The combined potential landscape above the solid body is probed locally by diffraction of Bose-Einstein condensates. Measured diffraction efficiencies reveal information about the shape of the Casimir-Polder interaction and allow us to discern between models based on a pairwise-summation (Hamaker) approach and Lifshitz theory.

Casimir Energy and Dilute Dielectric Ball

General formalism of quantum field theory and addition theorem for Bessel functions are applied to derive formula for CasimirPolder energy of interaction between a polarizable particle and a dilute dielectric ball. The equivalence of dipole-dipole interaction and Casimir energy for dilute homogeneous dielectrics is shown. A novel method is used to derive Casimir energy of a dilute dielectric ball without divergences in calculations. Physically realistic model of a dilute ball is discussed. Different approaches to the calculation of Casimir energy of a dielectric ball are reviewed. PACS numbers: 03.70.+k, 11.10.Gh, 12.20.-m, 12.20.Ds, 42.50.Lc ∗E-mail: root@VM1485.spb.edu

Theory of the Casimir effect in one-dimensional periodic dielectric systems

We derive an exact theory of the Casimir interaction between two arbitrary dielectric gratings with coinciding periods d. We then express the Casimir energy for two dielectric gratings or periodic dielectrics with coinciding periods in terms of Rayleigh coefficients.

CASIMIR ENERGY AND REALISTIC MODEL OF DILUTE DIELECTRIC BALL

The Casimir energy of a dilute homogeneous nonmagnetic dielectric ball at zero temperature is derived analytically for the first time for an arbitrary physically possible frequency dispersion of dielectric permittivity e(iω). A microscopic model of dielectrics is considered, divergences are absent in calculations because an average interatomic distance λ is a physical cutoff in the theory. This fact has been overlooked earlier, which led to divergences in various macroscopic approaches to the Casimir energy of connected dielectrics.The Casimir energy of a dilute homogeneous nonmagnetic dielectric ball at zero temperature is derived analytically for the first time for an arbitrary physically possible frequency dispersion of dielectric permittivity ε(iω). A microscopic model of dielectrics is considered, divergences are absent in calculations because an average interatomic distance λ is a physical cut-off in the theory. This fact has been overlooked before, which led to divergences in various macroscopic approaches to the Casimir energy of connected dielectrics. PACS numbers: 12.20.-m, 12.38.Bx, 34.20.Gj, 31.15.-p keywords: dipole interaction, Casimir energy, dilute dielectrics ∗E-mail: root@VM1485.spb.edu

New geometries in the Casimir effect: Dielectric gratings

An exact solution for the Casimir force between two arbitrary dielectric gratings with the same period d is presented. The Casimir energy for two dielectric gratings or periodic dielectrics is expressed in terms of Rayleigh coefficients. The theory is applied to calculate the Casimir force in several cases of interest.