8 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
Casimir effect for curved geometries: PFA validity limits
We compute Casimir interaction energies for the sphere-plate and
cylinder-plate configuration induced by scalar-field fluctuations with
Dirichlet boundary conditions. Based on a high-precision calculation using
worldline numerics, we quantitatively determine the validity bounds of the
proximity force approximation (PFA) on which the comparison between all
corresponding experiments and theory are based. We observe the quantitative
failure of the PFA on the 1% level for a curvature parameter a/R > 0.00755.
Even qualitatively, the PFA fails to predict reliably the correct sign of
genuine Casimir curvature effects. We conclude that data analysis of future
experiments aiming at a precision of 0.1% must no longer be based on the PFA.Comment: 4 pages, 4 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
Casimir interaction between normal or superfluid grains in the Fermi sea
We report on a new force that acts on cavities (literally empty regions of
space) when they are immersed in a background of non-interacting fermionic
matter fields. The interaction follows from the obstructions to the (quantum
mechanical) motions of the fermions caused by the presence of bubbles or other
(heavy) particles in the Fermi sea, as, for example, nuclei in the neutron sea
in the inner crust of a neutron star or superfluid grains in a normal Fermi
liquid. The effect resembles the traditional Casimir interaction between
metallic mirrors in the vacuum. However, the fluctuating electromagnetic fields
are replaced by fermionic matter fields. We show that the fermionic Casimir
problem for a system of spherical cavities can be solved exactly, since the
calculation can be mapped onto a quantum mechanical billiard problem of a
point-particle scattered off a finite number of non-overlapping spheres or
disks. Finally we generalize the map method to other Casimir systems,
especially to the case of a fluctuating scalar field between two spheres or a
sphere and a plate under Dirichlet boundary conditions.Comment: 8 pages, 2 figures, submitted to the Proceedings of QFEXT'05,
Barcelona, Sept. 5-9, 200
Worldline Monte Carlo for fermion models at large N_f
Strongly-coupled fermionic systems can support a variety of low-energy
phenomena, giving rise to collective condensation, symmetry breaking and a rich
phase structure. We explore the potential of worldline Monte Carlo methods for
analyzing the effective action of fermionic systems at large flavor number N_f,
using the Gross-Neveu model as an example. Since the worldline Monte Carlo
approach does not require a discretized spacetime, fermion doubling problems
are absent, and chiral symmetry can manifestly be maintained. As a particular
advantage, fluctuations in general inhomogeneous condensates can conveniently
be dealt with analytically or numerically, while the renormalization can always
be uniquely performed analytically. We also critically examine the limitations
of a straightforward implementation of the algorithms, identifying potential
convergence problems in the presence of fermionic zero modes as well as in the
high-density region.Comment: 40 pages, 13 figure
Casimir forces and non-Newtonian gravitation
The search for non-relativistic deviations from Newtonian gravitation can
lead to new phenomena signalling the unification of gravity with the other
fundamental interactions. Various recent theoretical frameworks indicate a
possible window for non-Newtonian forces with gravitational coupling strength
in the micrometre range. The major expected background in the same range is
attributable to the Casimir force or variants of it if dielectric materials,
rather than conducting ones, are considered. Here we review the measurements of
the Casimir force performed so far in the micrometre range and how they
determine constraints on non-Newtonian gravitation, also discussing the
dominant sources of false signals. We also propose a geometry-independent
parameterization of all data in terms of the measurement of the constant c. Any
Casimir force measurement should lead, once all corrections are taken into
account, to a determination of the constant c which, in order to assess the
accuracy of the measurement, can be compared with its more precise value known
through microscopic measurements. Although the last decade of experiments has
resulted in solid demonstrations of the Casimir force, the situation is not
conclusive with respect to being able to discover new physics. Future
experiments and novel phenomenological analysis will be necessary to discover
non-Newtonian forces or to push the window for their possible existence into
regions of the parameter space which theoretically appear unnatural.Comment: Also available at http://www.iop.org/EJ/abstract/1367-2630/8/10/23
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