69 research outputs found
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
Drude model and Lifshitz formula
Since nearly 10 years, it is known that inserting the permittivity of the
Drude model into the Lifshitz formula for free energy causes a violation of the
third law of thermodynamics. In this paper we show that the standard Matsubara
formulation for free energy contains a contribution that is non-perturbative in
the relaxation parameter. We argue that the correct formula must have a
perturbative expansion and conclude that the standard Matsubara formulation
with the permittivity of the Drude model inserted is not correct. We trace the
non-perturbative contribution in the complex frequency plane, where it shows up
as a self-intersection or a bifurcation of the integration path.Comment: accepted for publication in EPJ
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.
Temperature correction to the Casimir force in cryogenic range and anomalous skin effect
Temperature correction to the Casimir force is considered for real metals at
low temperatures. With the temperature decrease the mean free path for
electrons becomes larger than the field penetration depth. In this condition
description of metals with the impedance of anomalous skin effect is shown to
be more appropriate than with the permittivity. The effect is crucial for the
temperature correction. It is demonstrated that in the zero frequency limit the
reflection coefficients should coincide with those of ideal metal if we demand
the entropy to be zero at T=0. All the other prescriptions discussed in the
literature for the term in the Lifshitz formula give negative entropy. It
is shown that the temperature correction in the region of anomalous skin effect
is not suppressed as it happens in the plasma model. This correction will be
important in the future cryogenic measurements of the Casimir force.Comment: 12 pages, 2 figures, to be published 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.
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 . 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 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.
Effects of Anomalous Magnetic Moment in the Quantum Motion of Neutral Particle in Magnetic and Electric Fields Produced by a Linear Source in a Conical Spacetime
In this paper we analyse the effect of the anomalous magnetic moment on the
non-relativistic quantum motion of a neutral particle in magnetic and electric
fields produced by linear sources of constant current and charge density,
respectively.Comment: 17 pages, no figur
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.
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