9,342 research outputs found
Critical free energy and Casimir forces in rectangular geometries
We study the critical behavior of the free energy and the thermodynamic
Casimir force in a block geometry in
dimensions with aspect ratio above, at, and below on
the basis of the O symmetric lattice model with periodic boundary
conditions (b.c.). We consider a simple-cubic lattice with isotropic
short-range interactions. Exact results are derived in the large - limit
describing the geometric crossover from film () over cubic to
cylindrical () geometries. For , three perturbation
approaches are presented that cover both the central finite-size regime near
for and the region outside the central
finite-size regime well above and below for arbitrary . At bulk
of isotropic systems with periodic b.c., we predict the critical Casimir
force in the vertical direction to be negative (attractive) for a slab
(), and zero for a cube
. We also present extrapolations to the cylinder limit
() and to the film limit () for and . Our
analytic results for finite-size scaling functions in the minimal
renormalization scheme at fixed dimension agree well with Monte Carlo
data for the three-dimensional Ising model by Hasenbusch for and by
Vasilyev et al. for above, at, and below .Comment: 23 pages, 14 figure
Stringent limitations on reductive perturbation studies of nonplanar acoustic solitons in plasmas
More than fifty years ago, the Korteweg-de Vries equation was shown to describe not only solitary surface waves on shallow water, but also nonlinear ion-acoustic waves. Because of the algorithmic ease of using reductive perturbation theory, intensive research followed on a wide range of wave types. Soon, the formalism was extended to nonplanar modes by introducing a stretching designed to accommodate spherically and cylindrically symmetric ion-acoustic waves. Over the last two decades many authors followed this approach, but almost all have ignored the severe restrictions in parameter space imposed by the Ansatz. In addition, for other steps in the formalism, the justification is often not spelled out, leading to effects that are physically undesirable or ambiguous. Hence, there is a need to critically assess this approach to nonplanar modes and to use it with the utmost care, respecting the restrictions on its validity. Only inward propagation may be meaningfully studied and respect for weak nonlinearities of at most 1/10 implies that one cannot get closer to the axis or centre of symmetry than about 30 Debye lengths. Thus, one is in a regime where the modes are quasi-planar and not particularly interesting. Most papers disregard these constraints and hence reach questionable conclusions
Exact results for classical Casimir interactions: Dirichlet and Drude model in the sphere-sphere and sphere-plane geometry
Analytic expressions that describe Casimir interactions over the entire range
of separations have been limited to planar surfaces. Here we derive analytic
expressions for the classical or high-temperature limit of Casimir interactions
between two spheres (interior and exterior configurations), including the
sphere-plane geometry as a special case, using bispherical coordinates. We
consider both Dirichlet boundary conditions and metallic boundary conditions
described by the Drude model. At short distances, closed-form expansions are
derived from the exact result, displaying an intricate structure of deviations
from the commonly employed proximity force approximation.Comment: 5 pages, 2 figure
A proposal of a UCN experiment to check an earthquake waves model
Elastic waves with transverse polarization inside incidence plane can create
longitudinal surface wave (LSW) after reflection from a free surface. At a
critical incidence angle this LSW accumulates energy density, which can be
orders of magnitude higher than energy density of the incident transverse wave.
A specially arranged vessel for storage of ultracold neutrons (UCN) can be used
to verify this effect.Comment: 8 pages 3 figures added a paragraph on vibrations along surface at
critical angl
Arrival time distribution for a driven system containing quenched dichotomous disorder
We study the arrival time distribution of overdamped particles driven by a
constant force in a piecewise linear random potential which generates the
dichotomous random force. Our approach is based on the path integral
representation of the probability density of the arrival time. We explicitly
calculate the path integral for a special case of dichotomous disorder and use
the corresponding characteristic function to derive prominent properties of the
arrival time probability density. Specifically, we establish the scaling
properties of the central moments, analyze the behavior of the probability
density for short, long, and intermediate distances. In order to quantify the
deviation of the arrival time distribution from a Gaussian shape, we evaluate
the skewness and the kurtosis.Comment: 18 pages, 5 figure
Acoustic waves: should they be propagated forward in time, or forward in space?
The evolution of acoustic waves can be evaluated in two ways: either as a
temporal, or a spatial propagation. Propagating in space provides the
considerable advantage of being able to handle dispersion and propagation
across interfaces with remarkable efficiency; but propagating in time is more
physical and gives correctly behaved reflections and scattering without effort.
Which should be chosen in a given situation, and what compromises might have to
be made? Here the natural behaviors of each choice of propagation are compared
and contrasted for an ordinary second order wave equation, the time-dependent
diffusion wave equation, an elastic rod wave equation, and the Stokes'/ van
Wijngaarden's equations, each case illuminating a characteristic feature of the
technique. Either choice of propagation axis enables a partitioning the wave
equation that gives rise to a directional factorization based on a natural
"reference" dispersion relation. The resulting exact coupled bidirectional
equations then reduce to a single unidirectional first-order wave equation
using a simple "slow evolution" assumption that minimizes effect of subsequent
approximations, while allowing a direct term-to-term comparison between exact
and approximate theories.Comment: 12 pages, v2 correcte
Quasi-point separation of variables for the Henon-Heiles system and a system with quartic potential
We examine the problem of integrability of two-dimensional Hamiltonian
systems by means of separation of variables. The systematic approach to
construction of the special non-pure coordinate separation of variables for
certain natural two-dimensional Hamiltonians is presented. The relations with
SUSY quantum mechanics are discussed.Comment: 11 pages, Late
Steplike electric conduction in a classical two-dimensional electron system through a narrow constriction in a microchannel
Using molecular dynamics simulation, we investigate transport properties of a
classical two-dimensional electron system confined in a microchannel with a
narrow constriction. As a function of the confinement strength of the
constriction, the calculated conductance in the simulations exhibits steplike
increases as reported in a recent experiment [D. G. Rees et al., Phys. Rev.
Lett. 106, 026803 (2011)]. It is confirmed that the number of the steps
corresponds to the number of stream lines of electrons through the
constriction. We verify that density fluctuation plays a major role in
smoothing the steps in the conductance.Comment: 11 pages, 9 figure
Self-consistent multi-mode lasing theory for complex or random lasing media
A semiclassical theory of single and multi-mode lasing is derived for open
complex or random media using a self-consistent linear response formulation.
Unlike standard approaches which use closed cavity solutions to describe the
lasing modes, we introduce an appropriate discrete basis of functions which
describe also the intensity and angular emission pattern outside the cavity.
This constant flux (CF) basis is dictated by the Green function which arises
when formulating the steady state Maxwell-Bloch equations as a self-consistent
linear response problem. This basis is similar to the quasi-bound state basis
which is familiar in resonator theory and it obeys biorthogonality relations
with a set of dual functions. Within a single-pole approximation for the Green
function the lasing modes are proportional to these CF states and their
intensities and lasing frequencies are determined by a set of non-linear
equations. When a near threshold approximation is made to these equations a
generalized version of the Haken-Sauermann equations for multi-mode lasing is
obtained, appropriate for open cavities. Illustrative results from these
equations are given for single and few mode lasing states, for the case of
dielectric cavity lasers. The standard near threshold approximation is found to
be unreliable. Applications to wave-chaotic cavities and random lasers are
discussed.Comment: 18 pages, 9 figure
Angular distribution studies on the two-photon ionization of hydrogen-like ions: Relativistic description
The angular distribution of the emitted electrons, following the two-photon
ionization of the hydrogen-like ions, is studied within the framework of second
order perturbation theory and the Dirac equation. Using a density matrix
approach, we have investigated the effects which arise from the polarization of
the incoming light as well as from the higher multipoles in the expansion of
the electron--photon interaction. For medium- and high-Z ions, in particular,
the non-dipole contributions give rise to a significant change in the angular
distribution of the emitted electrons, if compared with the electric-dipole
approximation. This includes a strong forward emission while, in dipole
approxmation, the electron emission always occurs symmetric with respect to the
plane which is perpendicular to the photon beam. Detailed computations for the
dependence of the photoelectron angular distributions on the polarization of
the incident light are carried out for the ionization of H, Xe, and
U (hydrogen-like) ions.Comment: 16 pages, 4 figures, published in J Phys
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