9 research outputs found
Quantum energies with worldline numerics
We present new results for Casimir forces between rigid bodies which impose
Dirichlet boundary conditions on a fluctuating scalar field. As a universal
computational tool, we employ worldline numerics which builds on a combination
of the string-inspired worldline approach with Monte-Carlo techniques.
Worldline numerics is not only particularly powerful for inhomogeneous
background configurations such as involved Casimir geometries, it also provides
for an intuitive picture of quantum-fluctuation-induced phenomena. Results for
the Casimir geometries of a sphere above a plate and a new perpendicular-plates
configuration are presented.Comment: 8 pages, 2 figures, Submitted to the Proceedings of the Seventh
Workshop QFEXT'05 (Barcelona, September 5-9, 2005), Refs updated, version to
appear in JPhys
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
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
Divergences in the vacuum energy for frequency-dependent interactions
We propose a method for determining ultra-violet divergences in the vacuum
energy for systems whose spectrum of perturbations is defined through a
non-linear spectrum problem, i.e, when the fluctuation operator itself depends
on the frequency. The method is applied to the plasma shell model, which
describes some properties of the interaction of electromagnetic field with
fullerens. We formulate a scalar model, which simplifies the matrix structure,
but keeps the frequency dependence of the plasma shell, and calculate the
ultra-violet divergences in the case when the plasma sheet is slightly curved.
The divergent terms are expressed in terms of surface integrals of
corresponding invariants.Comment: 14 pages, revtex, v2: clarifications adde
Recent Developments in the Casimir Effect
In this talk I review various developments in the past year concerning
quantum vacuum energy, the Casimir effect. In particular, there has been
continuing controversy surrounding the temperature correction to the Lifshitz
formula for the Casimir force between real materials, be they metals or
semiconductors. Consensus has emerged as to how Casimir energy accelerates in a
weak gravitational field; quantum vacuum energy, including the divergent parts
which renormalize the masses of the Casimir plates, accelerates indeed
according to the equivalence principle. Significant development has been
forthcoming in applying the multiple scattering formalism to describe the
interaction between nontrivial objects. In weak coupling, closed-form
expressions for the Casimir force between the bodies, which for example reveal
significant discrepancies from the naive proximity force approximation, can be
achieved in many cases.Comment: 29 pages, 14 figures, uses jpconf.cls style. Invited opening talk at
"60 Years of the Casimir Effect," Brasilia, June 21-29, 200
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
Scalar Casimir densities for cylindrically symmetric Robin boundaries
Wightman function, the vacuum expectation values of the field square and the
energy-momentum tensor are investigated for a massive scalar field with general
curvature coupling parameter in the region between two coaxial cylindrical
boundaries. It is assumed that the field obeys general Robin boundary
conditions on bounding surfaces. The application of a variant of the
generalized Abel-Plana formula allows to extract from the expectation values
the contribution from single shells and to present the interference part in
terms of exponentially convergent integrals. The vacuum forces acting on the
boundaries are presented as the sum of self-action and interaction terms. The
first one contains well-known surface divergences and needs a further
renormalization. The interaction forces between the cylindrical boundaries are
finite and are attractive for special cases of Dirichlet and Neumann scalars.
For the general Robin case the interaction forces can be both attractive or
repulsive depending on the coefficients in the boundary conditions. The total
Casimir energy is evaluated by using the zeta function regularization
technique. It is shown that it contains a part which is located on bounding
surfaces. The formula for the interference part of the surface energy is
derived and the energy balance is discussed.Comment: 22 pages, 5 figure
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