503 research outputs found
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
Geometry and material effects in Casimir physics - Scattering theory
We give a comprehensive presentation of methods for calculating the Casimir
force to arbitrary accuracy, for any number of objects, arbitrary shapes,
susceptibility functions, and separations. The technique is applicable to
objects immersed in media other than vacuum, to nonzero temperatures, and to
spatial arrangements in which one object is enclosed in another. Our method
combines each object's classical electromagnetic scattering amplitude with
universal translation matrices, which convert between the bases used to
calculate scattering for each object, but are otherwise independent of the
details of the individual objects. This approach, which combines methods of
statistical physics and scattering theory, is well suited to analyze many
diverse phenomena. We illustrate its power and versatility by a number of
examples, which show how the interplay of geometry and material properties
helps to understand and control Casimir forces. We also examine whether
electrodynamic Casimir forces can lead to stable levitation. Neglecting
permeabilities, we prove that any equilibrium position of objects subject to
such forces is unstable if the permittivities of all objects are higher or
lower than that of the enveloping medium; the former being the generic case for
ordinary materials in vacuum.Comment: 44 pages, 11 figures, to appear in upcoming Lecture Notes in Physics
volume in Casimir physic
Casimir forces between arbitrary compact objects: Scalar and electromagnetic field
We develop an exact method for computing the Casimir energy between arbitrary
compact objects, both with boundary conditions for a scalar field and
dielectrics or perfect conductors for the electromagnetic field. The energy is
obtained as an interaction between multipoles, generated by quantum source or
current fluctuations. The objects' shape and composition enter only through
their scattering matrices. The result is exact when all multipoles are
included, and converges rapidly. A low frequency expansion yields the energy as
a series in the ratio of the objects' size to their separation. As examples, we
obtain this series for two spheres with Robin boundary conditions for a scalar
field and dielectric spheres for the electromagnetic field. The full
interaction at all separations is obtained for spheres with Robin boundary
conditions and for perfectly conducting spheres.Comment: 24 pages, 3 figures, contribution to QFEXT07 proceeding
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
On the accuracy of the PFA: analogies between Casimir and electrostatic forces
We present an overview of the validity of the Proximity Force Approximation
(PFA) in the calculation of Casimir forces between perfect conductors for
different geometries, with particular emphasis for the configuration of a
cylinder in front of a plane. In all cases we compare the exact numerical
results with those of PFA, and with asymptotic expansions that include the next
to leading order corrections. We also discuss the similarities and differences
between the results for Casimir and electrostatic forces.Comment: 17 pages, 5 figures, Proceedings of the meeting "60 years of Casimir
effect", Brasilia, 200
Vacuum local and global electromagnetic self-energies for a point-like and an extended field source
We consider the electric and magnetic energy densities (or equivalently field
fluctuations) in the space around a point-like field source in its ground
state, after having subtracted the spatially uniform zero-point energy terms,
and discuss the problem of their singular behavior at the source's position. We
show that the assumption of a point-like source leads, for a simple Hamiltonian
model of the interaction of the source with the electromagnetic radiation
field, to a divergence of the renormalized electric and magnetic energy density
at the position of the source. We analyze in detail the mathematical structure
of such singularity in terms of a delta function and its derivatives. We also
show that an appropriate consideration of these singular terms solves an
apparent inconsistency between the total field energy and the space integral of
its density. Thus the finite field energy stored in these singular terms gives
an important contribution to the self-energy of the source. We then consider
the case of an extended source, smeared out over a finite volume and described
by an appropriate form factor. We show that in this case all divergences in
local quantities such as the electric and the magnetic energy density, as well
as any inconsistency between global and space-integrated local self-energies,
disappear.Comment: 8 pages. The final publication is available at link.springer.co
Casimir forces on a silicon micromechanical chip
Quantum fluctuations give rise to van der Waals and Casimir forces that
dominate the interaction between electrically neutral objects at sub-micron
separations. Under the trend of miniaturization, such quantum electrodynamical
effects are expected to play an important role in micro- and nano-mechanical
devices. Nevertheless, utilization of Casimir forces on the chip level remains
a major challenge because all experiments so far require an external object to
be manually positioned close to the mechanical element. Here, by integrating a
force-sensing micromechanical beam and an electrostatic actuator on a single
chip, we demonstrate the Casimir effect between two micromachined silicon
components on the same substrate. A high degree of parallelism between the two
near-planar interacting surfaces can be achieved because they are defined in a
single lithographic step. Apart from providing a compact platform for Casimir
force measurements, this scheme also opens the possibility of tailoring the
Casimir force using lithographically defined components of non-conventional
shapes
Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders
We analyze the Casimir force between two parallel infinite metal cylinders,
with nearby metal plates (sidewalls), using complementary methods for mutual
confirmation. The attractive force between cylinders is shown to have a
nonmonotonic dependence on the separation to the plates. This intrinsically
multi-body phenomenon, which occurs with either one or two sidewalls
(generalizing an earlier result for squares between two sidewalls), does not
follow from any simple two-body force description. We can, however, explain the
nonmonotonicity by considering the screening (enhancement) of the interactions
by the fluctuating charges (currents) on the two cylinders, and their images on
the nearby plate(s). Furthermore, we show that this effect also implies a
nonmonotonic dependence of the cylinder-plate force on the cylinder-cylinder
separation.Comment: 5 pages, 4 figure
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