Gravity and Geometric Phases

The behavior of a quantum test particle satisfying the Klein-Gordon equation in a certain class of 4 dimensional stationary space-times is examined. In a space-time of a spinning cosmic string, the wave function of a particle in a box is shown to acquire a geometric phase when the box is transported around a closed path surrounding the string. When interpreted as an Aharonov-Anandan geometric phase, the effect is shown to be related to the Aharonov-Bohm effect.Comment: 11 pages, latex fil

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.

Thermal correction to the Casimir force, radiative heat transfer, and an experiment

The low-temperature asymptotic expressions for the Casimir interaction between two real metals described by Leontovich surface impedance are obtained in the framework of thermal quantum field theory. It is shown that the Casimir entropy computed using the impedance of infrared optics vanishes in the limit of zero temperature. By contrast, the Casimir entropy computed using the impedance of the Drude model attains at zero temperature a positive value which depends on the parameters of a system, i.e., the Nernst heat theorem is violated. Thus, the impedance of infrared optics withstands the thermodynamic test, whereas the impedance of the Drude model does not. We also perform a phenomenological analysis of the thermal Casimir force and of the radiative heat transfer through a vacuum gap between real metal plates. The characterization of a metal by means of the Leontovich impedance of the Drude model is shown to be inconsistent with experiment at separations of a few hundred nanometers. A modification of the impedance of infrared optics is suggested taking into account relaxation processes. The power of radiative heat transfer predicted from this impedance is several times less than previous predictions due to different contributions from the transverse electric evanescent waves. The physical meaning of low frequencies in the Lifshitz formula is discussed. It is concluded that new measurements of radiative heat transfer are required to find out the adequate description of a metal in the theory of electromagnetic fluctuations.Comment: 19 pages, 4 figures. svjour.cls is used, to appear in Eur. Phys. J.

Gravitational field around a time-like current-carrying screwed cosmic string in scalar-tensor theories

In this paper we obtain the space-time generated by a time-like current-carrying superconducting screwed cosmic string(TCSCS). This gravitational field is obtained in a modified scalar-tensor theory in the sense that torsion is taken into account. We show that this solution is comptible with a torsion field generated by the scalar field $\phi$. The analysis of gravitational effects of a TCSCS shows up that the torsion effects that appear in the physical frame of Jordan-Fierz can be described in a geometric form given by contorsion term plus a symmetric part which contains the scalar gradient. As an important application of this solution, we consider the linear perturbation method developed by Zel'dovich, investigate the accretion of cold dark matter due to the formation of wakes when a TCSCS moves with speed $v$ and discuss the role played by torsion. Our results are compared with those obtained for cosmic strings in the framework of scalar-tensor theories without taking torsion into account.Comment: 21 pages, no figures, Revised Version, presented at the "XXIV- Encontro Nacional de Fisica de Particulas e Campos ", Caxambu, MG, Brazil, to appear in Phys. Rev.

Lateral projection as a possible explanation of the nontrivial boundary dependence of the Casimir force

We find the lateral projection of the Casimir force for a configuration of a sphere above a corrugated plate. This force tends to change the sphere position in the direction of a nearest corrugation maximum. The probability distribution describing different positions of a sphere above a corrugated plate is suggested which is fitted well with experimental data demonstrating the nontrivial boundary dependence of the Casimir force.Comment: 5 pages, 1 figur

Electromagnetic Casimir densities induced by a conducting cylindrical shell in the cosmic string spacetime

We investigate the renormalized vacuum expectation values of the field square and the energy-momentum tensor for the electromagnetic field inside and outside of a conducting cylindrical shell in the cosmic string spacetime. By using the generalized Abel-Plana formula, the vacuum expectation values are presented in the form of the sum of boundary-free and boundary-induced parts. The asymptotic behavior of the vacuum expectation values of the field square, energy density and stresses are investigated in various limiting cases.Comment: 14 pages, 2 figures, discussion and references added, accepted for publication in Phys. Lett.

Improved tests of extra-dimensional physics and thermal quantum field theory from new Casimir force measurements

We report new constraints on extra-dimensional models and other physics beyond the Standard Model based on measurements of the Casimir force between two dissimilar metals for separations in the range 0.2--1.2 $\mu$m. The Casimir force between an Au-coated sphere and a Cu-coated plate of a microelectromechanical torsional oscillator was measured statically with an absolute error of 0.3 pN. In addition, the Casimir pressure between two parallel plates was determined dynamically with an absolute error of $\approx 0.6$ mPa. Within the limits of experimental and theoretical errors, the results are in agreement with a theory that takes into account the finite conductivity and roughness of the two metals. The level of agreement between experiment and theory was then used to set limits on the predictions of extra-dimensional physics and thermal quantum field theory. It is shown that two theoretical approaches to the thermal Casimir force which predict effects linear in temperture are ruled out by these experiments. Finally, constraints on Yukawa corrections to Newton's law of gravity are strengthened by more than an order of magnitude in the range 56 nm to 330 nm.Comment: Revtex 4, 35 pages, 14 figures in .gif format, accepted for publication in Phys. Rev.

Higher order conductivity corrections to the Casimir force

The finite conductivity corrections to the Casimir force in two configurations are calculated in the third and fourth orders in relative penetration depth of electromagnetic zero oscillations into the metal. The obtained analytical perturbation results are compared with recent computations. Applications to the modern experiments are discussed.Comment: 15 pages, 4 figure

Holonomy Transformation in the FRW Metric

In this work we investigate loop variables in Friedman-Robertson-Walker spacetime. We analyze the parallel transport of vectors and spinors in several paths in this spacetime in order to classify its global properties. The band holonomy invariance is analysed in this background.Comment: 8 page