1,273 research outputs found
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
String Picture of a Frustrated Quantum Magnet and Dimer Model
We map a geometrically frustrated Ising system with transversal field
generated quantum dynamics to a strongly anisotropic lattice of non-crossing
elastic strings. The combined effect of frustration, quantum and thermal spin
fluctuations is explained in terms of a competition between intrinsic lattice
pinning of strings and topological defects in the lattice. From this picture we
obtain analytic results for correlations and the phase diagram which agree
nicely with recent simulations.Comment: 4 pages, 2 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
Test of Replica Theory: Thermodynamics of 2D Model Systems with Quenched Disorder
We study the statistics of thermodynamic quantities in two related systems
with quenched disorder: A (1+1)-dimensional planar lattice of elastic lines in
a random potential and the 2-dimensional random bond dimer model. The first
system is examined by a replica-symmetric Bethe ansatz (RBA) while the latter
is studied numerically by a polynomial algorithm which circumvents slow glassy
dynamics. We establish a mapping of the two models which allows for a detailed
comparison of RBA predictions and simulations. Over a wide range of disorder
strength, the effective lattice stiffness and cumulants of various
thermodynamic quantities in both approaches are found to agree excellently. Our
comparison provides, for the first time, a detailed quantitative confirmation
of the replica approach and renders the planar line lattice a unique testing
ground for concepts in random systems.Comment: 16 pages, 14 figure
Carbon radio recombination lines from gigahertz to megahertz frequencies towards Orion A
Context. The combined use of carbon radio recombination lines (CRRLs) and the
158 m-[CII] line is a powerful tool for the study of the energetics and
physical conditions (e.g., temperature and density) of photodissociation
regions (PDRs). However, there are few observational studies that exploit this
synergy. Aims. Here we explore the relation between CRRLs and the 158
m-[CII] line in light of new observations and models. Methods. We present
new and existing observations of CRRLs in the frequency range 0.15--230 GHz
with ALMA, VLA, the GBT, Effelsberg 100m, and LOFAR towards Orion~A (M42). We
complement these observations with SOFIA observations of the 158 m-[CII]
line. We studied two PDRs: the foreground atomic gas, known as the Veil, and
the dense PDR between the HII region and the background molecular cloud.
Results. In the Veil we are able to determine the gas temperature and electron
density, which we use to measure the ionization parameter and the photoelectric
heating efficiency. In the dense PDR, we are able to identify a layered PDR
structure at the surface of the molecular cloud to the south of the Trapezium
cluster. There we find that the radio lines trace the colder portion of the
ionized carbon layer, the C/C/CO interface. By modeling the emission of
the ~m-[CII] line and CRRLs as arising from a PDR we derive a thermal
pressure K cm and a radiation field
close to the Trapezium. Conclusions. This work provides
additional observational support for the use of CRRLs and the 158 m-[CII]
line as complementary tools to study dense and diffuse PDRs, and highlights the
usefulness of CRRLs as probes of the C/C/CO interface.Comment: 18 pages, 16 figures, accepted for publication in A&
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
Multiple Scattering: Dispersion, Temperature Dependence, and Annular Pistons
We review various applications of the multiple scattering approach to the
calculation of Casimir forces between separate bodies, including dispersion,
wedge geometries, annular pistons, and temperature dependence. Exact results
are obtained in many cases.Comment: 15 pages, 12 figures, contributed to the Festschrift for Emilio
Elizald
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
Casimir energy and geometry : beyond the Proximity Force Approximation
We review the relation between Casimir effect and geometry, emphasizing
deviations from the commonly used Proximity Force Approximation (PFA). We use
to this aim the scattering formalism which is nowadays the best tool available
for accurate and reliable theory-experiment comparisons. We first recall the
main lines of this formalism when the mirrors can be considered to obey
specular reflection. We then discuss the more general case where non planar
mirrors give rise to non-specular reflection with wavevectors and field
polarisations mixed. The general formalism has already been fruitfully used for
evaluating the effect of roughness on the Casimir force as well as the lateral
Casimir force or Casimir torque appearing between corrugated surfaces. In this
short review, we focus our attention on the case of the lateral force which
should make possible in the future an experimental demonstration of the
nontrivial (i.e. beyond PFA) interplay of geometry and Casimir effect.Comment: corrected typos, added references, QFEXT'07 special issue in J. Phys.
Avalanches in mean-field models and the Barkhausen noise in spin-glasses
We obtain a general formula for the distribution of sizes of "static
avalanches", or shocks, in generic mean-field glasses with
replica-symmetry-breaking saddle points. For the Sherrington-Kirkpatrick (SK)
spin-glass it yields the density rho(S) of the sizes of magnetization jumps S
along the equilibrium magnetization curve at zero temperature. Continuous
replica-symmetry breaking allows for a power-law behavior rho(S) ~ 1/(S)^tau
with exponent tau=1 for SK, related to the criticality (marginal stability) of
the spin-glass phase. All scales of the ultrametric phase space are implicated
in jump events. Similar results are obtained for the sizes S of static jumps of
pinned elastic systems, or of shocks in Burgers turbulence in large dimension.
In all cases with a one-step solution, rho(S) ~ S exp(-A S^2). A simple
interpretation relating droplets to shocks, and a scaling theory for the
equilibrium analog of Barkhausen noise in finite-dimensional spin glasses are
discussed.Comment: 6 pages, 1 figur
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