1,112 research outputs found
First analytic correction beyond PFA for the electromagnetic field in sphere-plane geometry
We consider the vacuum energy for a configuration of a sphere in front of a
plane, both obeying conductor boundary condition, at small separation. For the
separation becoming small we derive the first next-to-leading order of the
asymptotic expansion in the separation-to-radius ratio \ep. This correction
is of order \ep. In opposite to the scalar cases it contains also
contributions proportional to logarithms in first and second order, \ep \ln
\ep and \ep (\ln \ep)^2. We compare this result with the available findings
of numerical and experimental approaches.Comment: 20 pages, 1 figur
Three-body Casimir effects and non-monotonic forces
Casimir interactions are not pair-wise additive. This property leads to
collective effects that we study for a pair of objects near a conducting wall.
We employ a scattering approach to compute the interaction in terms of
fluctuating multipoles. The wall can lead to a non-monotonic force between the
objects. For two atoms with anisotropic electric and magnetic dipole
polarizabilities we demonstrate that this non-monotonic effect results from a
competition between two- and three body interactions. By including higher order
multipoles we obtain the force between two macroscopic metallic spheres for a
wide range of sphere separations and distances to the wall.Comment: 4 pages, 4 figure
Casimir Forces: An Exact Approach for Periodically Deformed Objects
A novel approach for calculating Casimir forces between periodically deformed
objects is developed. This approach allows, for the first time, a rigorous
non-perturbative treatment of the Casimir effect for disconnected objects
beyond Casimir's original two-plate configuration. The approach takes into
account the collective nature of fluctuation induced forces, going beyond the
commonly used pairwise summation of two-body van der Waals forces. As an
application of the method, we exactly calculate the Casimir force due to scalar
field fluctuations between a flat and a rectangular corrugated plate. In the
latter case, the force is found to be always attractive.Comment: 4 pages, 3 figure
Mode summation approach to Casimir effect between two objects
In this paper, we explore the TGTG formula from the perspective of mode
summation approach. Both scalar fields and electromagnetic fields are
considered. In this approach, one has to first solve the equation of motion to
find a wave basis for each object. The two T's in the TGTG formula are
T-matrices representing the Lippmann-Schwinger T-operators, one for each of the
objects. The two G's in the TGTG formula are the translation matrices, relating
the wave basis of an object to the wave basis of the other object. After
discussing the general theory, we apply the prescription to derive the explicit
formulas for the Casimir energies for the sphere-sphere, sphere-plane,
cylinder-cylinder and cylinder-plane interactions. First the T-matrices for a
plane, a sphere and a cylinder are derived for the following cases: the object
is imposed with general Robin boundary conditions; the object is
semitransparent; and the object is magnetodielectric. Then the operator
approach is used to derive the translation matrices. From these, the explicit
TGTG formula for each of the scenarios can be written down. Besides summarizing
all the TGTG formulas that have been derived so far, we also provide the TGTG
formulas for some scenarios that have not been considered before.Comment: 42 page
Casimir interactions of an object inside a spherical metal shell
We investigate the electromagnetic Casimir interactions of an object
contained within an otherwise empty, perfectly conducting spherical shell. For
a small object we present analytical calculations of the force, which is
directed away from the center of the cavity, and the torque, which tends to
align the object opposite to the preferred alignment outside the cavity. For a
perfectly conducting sphere as the interior object, we compute the corrections
to the proximity force approximation (PFA) numerically. In both cases the
results for the interior configuration match smoothly onto those for the
corresponding exterior configuration.Comment: 4 pages, 3 figure
Quantum and thermal Casimir interaction between a sphere and a plate: Comparison of Drude and plasma models
We calculate the Casimir interaction between a sphere and a plate, both
described by the plasma model, the Drude model, or generalizations of the two
models. We compare the results at both zero and finite temperatures. At
asymptotically large separations we obtain analytical results for the
interaction that reveal a non-universal, i.e., material dependent interaction
for the plasma model. The latter result contains the asymptotic interaction for
Drude metals and perfect reflectors as different but universal limiting cases.
This observation is related to the screening of a static magnetic field by a
London superconductor. For small separations we find corrections to the
proximity force approximation (PFA) that support correlations between geometry
and material properties that are not captured by the Lifshitz theory. Our
results at finite temperatures reveal for Drude metals a non-monotonic
temperature dependence of the Casimir free energy and a negative entropy over a
sizeable range of separations.Comment: 11 pages, 5 figure
Casimir potential of a compact object enclosed by a spherical cavity
We study the electromagnetic Casimir interaction of a compact object
contained inside a closed cavity of another compact object. We express the
interaction energy in terms of the objects' scattering matrices and translation
matrices that relate the coordinate systems appropriate to each object. When
the enclosing object is an otherwise empty metallic spherical shell, much
larger than the internal object, and the two are sufficiently separated, the
Casimir force can be expressed in terms of the static electric and magnetic
multipole polarizabilities of the internal object, which is analogous to the
Casimir-Polder result. Although it is not a simple power law, the dependence of
the force on the separation of the object from the containing sphere is a
universal function of its displacement from the center of the sphere,
independent of other details of the object's electromagnetic response.
Furthermore, we compute the exact Casimir force between two metallic spheres
contained one inside the other at arbitrary separations. Finally, we combine
our results with earlier work on the Casimir force between two spheres to
obtain data on the leading order correction to the Proximity Force
Approximation for two metallic spheres both outside and within one another.Comment: 12 pages, 6 figure
Fluctuation induced quantum interactions between compact objects and a plane mirror
The interaction of compact objects with an infinitely extended mirror plane
due to quantum fluctuations of a scalar or electromagnetic field that scatters
off the objects is studied. The mirror plane is assumed to obey either
Dirichlet or Neumann boundary conditions or to be perfectly reflecting. Using
the method of images, we generalize a recently developed approach for compact
objects in unbounded space [1,2] to show that the Casimir interaction between
the objects and the mirror plane can be accurately obtained over a wide range
of separations in terms of charge and current fluctuations of the objects and
their images. Our general result for the interaction depends only on the
scattering matrices of the compact objects. It applies to scalar fields with
arbitrary boundary conditions and to the electromagnetic field coupled to
dielectric objects. For the experimentally important electromagnetic Casimir
interaction between a perfectly conducting sphere and a plane mirror we present
the first results that apply at all separations. We obtain both an asymptotic
large distance expansion and the two lowest order correction terms to the
proximity force approximation. The asymptotic Casimir-Polder potential for an
atom and a mirror is generalized to describe the interaction between a
dielectric sphere and a mirror, involving higher order multipole
polarizabilities that are important at sub-asymptotic distances.Comment: 19 pages, 7 figure
Exact results for classical Casimir interactions: Dirichlet and Drude model in the sphere-sphere and sphere-plane geometry
Analytic expressions that describe Casimir interactions over the entire range
of separations have been limited to planar surfaces. Here we derive analytic
expressions for the classical or high-temperature limit of Casimir interactions
between two spheres (interior and exterior configurations), including the
sphere-plane geometry as a special case, using bispherical coordinates. We
consider both Dirichlet boundary conditions and metallic boundary conditions
described by the Drude model. At short distances, closed-form expansions are
derived from the exact result, displaying an intricate structure of deviations
from the commonly employed proximity force approximation.Comment: 5 pages, 2 figure
Dynamics of granular avalanches caused by local perturbations
Surface flow of granular material is investigated within a continuum approach
in two dimensions. The dynamics is described by a non-linear coupling between
the two `states' of the granular material: a mobile layer and a static bed.
Following previous studies, we use mass and momentum conservation to derive
St-Venant like equations for the evolution of the thickness R of the mobile
layer and the profile Z of the static bed. This approach allows the rheology in
the flowing layer to be specified independently, and we consider in details the
two following models: a constant plug flow and a linear velocity profile. We
study and compare these models for non-stationary avalanches triggered by a
localized amount of mobile grains on a static bed of constant slope. We solve
analytically the non-linear dynamical equations by the method of
characteristics. This enables us to investigate the temporal evolution of the
avalanche size, amplitude and shape as a function of model parameters and
initial conditions. In particular, we can compute their large time behavior as
well as the condition for the formation of shocks.Comment: 25 pages, 12 figure
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