1,499 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
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
Comment on ``Roughening Transition of Interfaces in Disordered Media''
Emig and Nattermann (Phys. Rev. Lett. 81, 1469 (1998)) have recently
investigated the competition between lattice pinning and impurity pinning using
a Renormalisation Group (RG) approach. For elastic objects of internal
dimensions , they find, at zero temperature, an interesting second
order phase transition between a flat phase for small disorder and a rough
phase for large disorder. These results contrast with those obtained using the
replica variational approach for the same problem, where a first order
transition between flat and rough phases was predicted. In this comment, we
show that these results can be reconciled by analysing the RG flow for an
arbitrary dimension for the displacement field.Comment: Submitted to Phys. Rev. Let
Ingredients of a Casimir analog computer
We present the basic ingredients of a technique to compute quantum Casimir
forces at micrometer scales using antenna measurements at tabletop, e.g.
centimeter, scales, forming a type of analog computer for the Casimir force.
This technique relies on a correspondence that we derive between the contour
integration of the Casimir force in the complex frequency plane and the
electromagnetic response of a physical dissipative medium in a finite, real
frequency bandwidth
Exact Solutions of a Model for Granular Avalanches
We present exact solutions of the non-linear {\sc bcre} model for granular
avalanches without diffusion. We assume a generic sandpile profile consisting
of two regions of constant but different slope. Our solution is constructed in
terms of characteristic curves from which several novel predictions for
experiments on avalanches are deduced: Analytical results are given for the
shock condition, shock coordinates, universal quantities at the shock, slope
relaxation at large times, velocities of the active region and of the sandpile
profile.Comment: 7 pages, 2 figure
Mode summation approach to Casimir effect between two objects
In this paper, we explore the TGTG formula from the perspective of mode
summation approach. Both scalar fields and electromagnetic fields are
considered. In this approach, one has to first solve the equation of motion to
find a wave basis for each object. The two T's in the TGTG formula are
T-matrices representing the Lippmann-Schwinger T-operators, one for each of the
objects. The two G's in the TGTG formula are the translation matrices, relating
the wave basis of an object to the wave basis of the other object. After
discussing the general theory, we apply the prescription to derive the explicit
formulas for the Casimir energies for the sphere-sphere, sphere-plane,
cylinder-cylinder and cylinder-plane interactions. First the T-matrices for a
plane, a sphere and a cylinder are derived for the following cases: the object
is imposed with general Robin boundary conditions; the object is
semitransparent; and the object is magnetodielectric. Then the operator
approach is used to derive the translation matrices. From these, the explicit
TGTG formula for each of the scenarios can be written down. Besides summarizing
all the TGTG formulas that have been derived so far, we also provide the TGTG
formulas for some scenarios that have not been considered before.Comment: 42 page
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
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&
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