1,233 research outputs found
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
Material dependence of Casimir forces: gradient expansion beyond proximity
A widely used method for estimating Casimir interactions [H. B. G. Casimir,
Proc. K. Ned. Akad. Wet. 51, 793 (1948)] between gently curved material
surfaces at short distances is the proximity force approximation (PFA). While
this approximation is asymptotically exact at vanishing separations,
quantifying corrections to PFA has been notoriously difficult. Here we use a
derivative expansion to compute the leading curvature correction to PFA for
metals (gold) and insulators (SiO) at room temperature. We derive an
explicit expression for the amplitude of the PFA correction to
the force gradient for axially symmetric surfaces. In the non-retarded limit,
the corrections to the Casimir free energy are found to scale logarithmically
with distance. For gold, has an unusually large temperature
dependence.Comment: 4 pages, 2 figure
Casimir interaction between a plate and a cylinder
We find the exact Casimir force between a plate and a cylinder, a geometry
intermediate between parallel plates, where the force is known exactly, and the
plate--sphere, where it is known at large separations. The force has an
unexpectedly weak decay \sim L/(H^3 \ln(H/R)) at large plate--cylinder
separations H (L and R are the cylinder length and radius), due to transverse
magnetic modes. Path integral quantization with a partial wave expansion
additionally gives a qualitative difference for the density of states of
electric and magnetic modes, and corrections at finite temperatures.Comment: 4 pages, 3 figure
The Casimir effect as scattering problem
We show that Casimir-force calculations for a finite number of
non-overlapping obstacles can be mapped onto quantum-mechanical billiard-type
problems which are characterized by the scattering of a fictitious point
particle off the very same obstacles. With the help of a modified Krein trace
formula the genuine/finite part of the Casimir energy is determined as the
energy-weighted integral over the log-determinant of the multi-scattering
matrix of the analog billiard problem. The formalism is self-regulating and
inherently shows that the Casimir energy is governed by the infrared end of the
multi-scattering phase shifts or spectrum of the fluctuating field. The
calculation is exact and in principle applicable for any separation(s) between
the obstacles. In practice, it is more suited for large- to medium-range
separations. We report especially about the Casimir energy of a fluctuating
massless scalar field between two spheres or a sphere and a plate under
Dirichlet and Neumann boundary conditions. But the formalism can easily be
extended to any number of spheres and/or planes in three or arbitrary
dimensions, with a variety of boundary conditions or non-overlapping
potentials/non-ideal reflectors.Comment: 14 pages, 2 figures, plenary talk at QFEXT07, Leipzig, September
2007, some typos correcte
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
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
Geothermal Casimir Phenomena
We present first worldline analytical and numerical results for the
nontrivial interplay between geometry and temperature dependencies of the
Casimir effect. We show that the temperature dependence of the Casimir force
can be significantly larger for open geometries (e.g., perpendicular plates)
than for closed geometries (e.g., parallel plates). For surface separations in
the experimentally relevant range, the thermal correction for the
perpendicular-plates configuration exhibits a stronger parameter dependence and
exceeds that for parallel plates by an order of magnitude at room temperature.
This effect can be attributed to the fact that the fluctuation spectrum for
closed geometries is gapped, inhibiting the thermal excitation of modes at low
temperatures. By contrast, open geometries support a thermal excitation of the
low-lying modes in the gapless spectrum already at low temperatures.Comment: 8 pages, 3 figures, contribution to QFEXT07 proceedings, v2:
discussion switched from Casimir energy to Casimir force, new analytical
results included, matches JPhysA versio
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
Non-equilibrium Casimir forces: Spheres and sphere-plate
We discuss non-equilibrium extensions of the Casimir force (due to
electromagnetic fluctuations), where the objects as well as the environment are
held at different temperatures. While the formalism we develop is quite
general, we focus on a sphere in front of a plate, as well as two spheres, when
the radius is small compared to separation and thermal wavelengths. In this
limit the forces can be expressed analytically in terms of the lowest order
multipoles, and corroborated with results obtained by diluting parallel plates
of vanishing thickness. Non-equilibrium forces are generally stronger than
their equilibrium counterpart, and may oscillate with separation (at a scale
set by material resonances). For both geometries we obtain stable points of
zero net force, while two spheres may have equal forces in magnitude and
direction resulting in a self-propelling state.Comment: 6 pages, 6 figure
- …