12 research outputs found
Casimir Energies: Temperature Dependence, Dispersion, and Anomalies
Assuming the conventional Casimir setting with two thick parallel perfectly
conducting plates of large extent with a homogeneous and isotropic medium
between them, we discuss the physical meaning of the electromagnetic field
energy when the intervening medium is weakly dispersive but
nondissipative. The presence of dispersion means that the energy density
contains terms of the form and
. We find that, as refers
thermodynamically to a non-closed physical system, it is {\it not} to be
identified with the internal thermodynamic energy following from the free
energy , or the electromagnetic energy , when the last-mentioned
quantities are calculated without such dispersive derivatives. To arrive at
this conclusion, we adopt a model in which the system is a capacitor, linked to
an external self-inductance such that stationary oscillations become
possible. Therewith the model system becomes a non-closed one. As an
introductory step, we review the meaning of the nondispersive energies,
and . As a final topic, we consider an anomaly connected with local surface
divergences encountered in Casimir energy calculations for higher spacetime
dimensions, , and discuss briefly its dispersive generalization. This kind
of application is essentially a generalization of the treatment of Alnes {\it
et al.} [J. Phys. A: Math. Theor. {\bf 40}, F315 (2007)] to the case of a
medium-filled cavity between two hyperplanes.Comment: 15 pages, no figures; slight revision of discussio
Casimir effect with rough metallic mirrors
We calculate the second order roughness correction to the Casimir energy for
two parallel metallic mirrors. Our results may also be applied to the
plane-sphere geometry used in most experiments. The metallic mirrors are
described by the plasma model, with arbitrary values for the plasma wavelength,
the mirror separation and the roughness correlation length, with the roughness
amplitude remaining the smallest length scale for perturbation theory to hold.
From the analysis of the intracavity field fluctuations, we obtain the
Casimir energy correction in terms of generalized reflection operators, which
account for diffraction and polarization coupling in the scattering by the
rough surfaces. We present simple analytical expressions for several limiting
cases, as well as numerical results that allow for a reliable calculation of
the roughness correction in real experiments. The correction is larger than the
result of the Proximity Force Approximation, which is obtained from our theory
as a limiting case (very smooth surfaces).Comment: 16 page
Casimir interaction between plane and spherical metallic surfaces
We give an exact series expansion of the Casimir force between plane and
spherical metallic surfaces in the non trivial situation where the sphere
radius , the plane-sphere distance and the plasma wavelength
have arbitrary relative values. We then present numerical
evaluation of this expansion for not too small values of . For metallic
nanospheres where and have comparable values, we interpret
our results in terms of a correlation between the effects of geometry beyond
the proximity force approximation (PFA) and of finite reflectivity due to
material properties. We also discuss the interest of our results for the
current Casimir experiments performed with spheres of large radius .Comment: 4 pages, new presentation (highlighting the novelty of the results)
and added references. To appear in Physical Review Letter
Thermal corrections to the Casimir effect
The Casimir effect, reflecting quantum vacuum fluctuations in the
electromagnetic field in a region with material boundaries, has been studied
both theoretically and experimentally since 1948. The forces between dielectric
and metallic surfaces both plane and curved have been measured at the 10 to 1
percent level in a variety of room-temperature experiments, and remarkable
agreement with the zero-temperature theory has been achieved. In fitting the
data various corrections due to surface roughness, patch potentials, curvature,
and temperature have been incorporated. It is the latter that is the subject of
the present article. We point out that, in fact, no temperature dependence has
yet been detected, and that the experimental situation is still too fluid to
permit conclusions about thermal corrections to the Casimir effect.
Theoretically, there are subtle issues concerning thermodynamics and
electrodynamics which have resulted in disparate predictions concerning the
nature of these corrections. However, a general consensus has seemed to emerge
that suggests that the temperature correction to the Casimir effect is
relatively large, and should be observable in future experiments involving
surfaces separated at the few micrometer scale.Comment: 21 pages, 9 eps figures, uses iopart.cls. Final version to be
published in New Journal of Physics, contains Conclusion and clarified
remark
Movement and Fluctuations of the Vacuum
Quantum fields possess zero-point or vacuum fluctuations which induce
mechanical effects, namely generalised Casimir forces, on any scatterer.
Symmetries of vacuum therefore raise fundamental questions when confronted
with the principle of relativity of motion in vacuum. The specific case of
uniformly accelerated motion is particularly interesting, in connection with
the much debated question of the appearance of vacuum in accelerated frames.
The choice of Rindler representation, commonly used in General Relativity,
transforms vacuum fluctuations into thermal fluctuations, raising difficulties
of interpretation. In contrast, the conformal representation of uniformly
accelerated frames fits the symmetry properties of field propagation and
quantum vacuum and thus leads to extend the principle of relativity of motion
to uniform accelerations.
Mirrors moving in vacuum with a non uniform acceleration are known to
radiate. The associated radiation reaction force is directly connected to
fluctuating forces felt by motionless mirrors through fluctuation-dissipation
relations. Scatterers in vacuum undergo a quantum Brownian motion which
describes irreducible quantum fluctuations. Vacuum fluctuations impose ultimate
limitations on measurements of position in space-time, and thus challenge the
very concept of space-time localisation within a quantum framework.
For test masses greater than Planck mass, the ultimate limit in localisation
is determined by gravitational vacuum fluctuations. Not only positions in
space-time, but also geodesic distances, behave as quantum variables,
reflecting the necessary quantum nature of an underlying geometry.Comment: 17 pages, to appear in Reports on Progress in Physic