1,303 research outputs found
Casimir forces beyond the proximity approximation
The proximity force approximation (PFA) relates the interaction between
closely spaced, smoothly curved objects to the force between parallel plates.
Precision experiments on Casimir forces necessitate, and spur research on,
corrections to the PFA. We use a derivative expansion for gently curved
surfaces to derive the leading curvature modifications to the PFA. Our methods
apply to any homogeneous and isotropic materials; here we present results for
Dirichlet and Neumann boundary conditions and for perfect conductors. A Pad\'e
extrapolation constrained by a multipole expansion at large distance and our
improved expansion at short distances, provides an accurate expression for the
sphere-plate Casimir force at all separations.Comment: 4 pages, 1 figur
Conformal Field Theory of Critical Casimir Interactions in 2D
Thermal fluctuations of a critical system induce long-ranged Casimir forces
between objects that couple to the underlying field. For two dimensional (2D)
conformal field theories (CFT) we derive an exact result for the Casimir
interaction between two objects of arbitrary shape, in terms of (1) the free
energy of a circular ring whose radii are determined by the mutual capacitance
of two conductors with the objects' shape; and (2) a purely geometric energy
that is proportional to conformal charge of the CFT, but otherwise
super-universal in that it depends only on the shapes and is independent of
boundary conditions and other details.Comment: 5 pages, 3 figure
Casimir force driven ratchets
We explore the non-linear dynamics of two parallel periodically patterned
metal surfaces that are coupled by the zero-point fluctuations of the
electromagnetic field between them. The resulting Casimir force generates for
asymmetric patterns with a time-periodically driven surface-to-surface distance
a ratchet effect, allowing for directed lateral motion of the surfaces in
sizeable parameter ranges. It is crucial to take into account inertia effects
and hence chaotic dynamics which are described by Langevin dynamics. Multiple
velocity reversals occur as a function of driving, mean surface distance, and
effective damping. These transport properties are shown to be stable against
weak ambient noise.Comment: 4 pages, 3 figure
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
Casimir force between sharp-shaped conductors
Casimir forces between conductors at the sub-micron scale cannot be ignored
in the design and operation of micro-electromechanical (MEM) devices. However,
these forces depend non-trivially on geometry, and existing formulae and
approximations cannot deal with realistic micro-machinery components with sharp
edges and tips. Here, we employ a novel approach to electromagnetic scattering,
appropriate to perfect conductors with sharp edges and tips, specifically to
wedges and cones. The interaction of these objects with a metal plate (and
among themselves) is then computed systematically by a multiple-scattering
series. For the wedge, we obtain analytical expressions for the interaction
with a plate, as functions of opening angle and tilt, which should provide a
particularly useful tool for the design of MEMs. Our result for the Casimir
interactions between conducting cones and plates applies directly to the force
on the tip of a scanning tunneling probe; the unexpectedly large temperature
dependence of the force in these configurations should attract immediate
experimental interest
Material Dependence of the Wire-Particle Casimir Interaction
We study the Casimir interaction between a metallic cylindrical wire and a
metallic spherical particle by employing the scattering formalism. At large
separations, we derive the asymptotic form of the interaction. In addition, we
find the interaction between a metallic wire and an isotropic atom, both in the
non-retarded and retarded limits. We identify the conditions under which the
asymptotic Casimir interaction does not depend on the material properties of
the metallic wire and the particle. Moreover, we compute the exact Casimir
interaction between the particle and the wire numerically. We show that there
is a complete agreement between the numerics and the asymptotic energies at
large separations. For short separations, our numerical results show good
agreement with the proximity force approximation
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
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