2,421 research outputs found
Dissipative flow and vortex shedding in the Painlev\'e boundary layer of a Bose Einstein condensate
Raman et al. have found experimental evidence for a critical velocity under
which there is no dissipation when a detuned laser beam is moved in a
Bose-Einstein condensate. We analyze the origin of this critical velocity in
the low density region close to the boundary layer of the cloud. In the frame
of the laser beam, we do a blow up on this low density region which can be
described by a Painlev\'e equation and write the approximate equation satisfied
by the wave function in this region. We find that there is always a drag around
the laser beam. Though the beam passes through the surface of the cloud and the
sound velocity is small in the Painlev\'e boundary layer, the shedding of
vortices starts only when a threshold velocity is reached. This critical
velocity is lower than the critical velocity computed for the corresponding 2D
problem at the center of the cloud. At low velocity, there is a stationary
solution without vortex and the drag is small. At the onset of vortex shedding,
that is above the critical velocity, there is a drastic increase in drag.Comment: 4 pages, 4 figures (with 9 ps files
Deconstructing (2,0) proposals
C. P. is supported by the U.S. Department of Energy under
Grant No. DE-FG02-96ER40959. M. S. S. is supported by
an EURYI award of the European Science Foundatio
About Superluminal motions and Special Relativity: A Discussion of some recent Experiments, and the solution of the Causal Paradoxes
Some experiments, performed at Berkeley, Cologne, Florence, Vienna, Orsay,
Rennes, etc., led to the claim that something seems to travel with a group
velocity larger than the speed c of light in vacuum. Various other experimental
results seem to point in the same direction: For instance, localized wavelet-
type solutions to Maxwell equations have been found, both theoretically and
experimentally, that travel with superluminal speed. [Even muonic and
electronic neutrinos [it has been proposed] might be "tachyons", since their
square mass appears to be negative]. With regard to the first-mentioned
experiments, it was recently claimed by Guenter Nimtz that those results with
evanescent waves (or tunneling photons) imply superluminal signal and impulse
transmission, and therefore violate Einstein causality. In this note we want to
stress that, on the contrary, all such results do not place relativistic
causality in jeopardy, even if they referred to actual tachyonic motions: In
fact, Special Relativity can cope even with superluminal objects and waves. For
instance, it is possible (at least in microphysics) to solve also the known
causal paradoxes, devised for faster than light motion, although this is not
widely recognized yet. Here we show, in detail and rigorously, how to solve the
oldest causal paradox, originally proposed by Tolman, which is the kernel of
many further tachyon paradoxes (like J.Bell's, F.A.E.Pirani's, J.D.Edmonds' and
others'). The key to the solution is a careful application of tachyon
mechanics, as it unambiguously follows from special relativity. At Last, in one
of the two Appendices, we propose how to evaluate the group-velocity in the
case of evanescent waves. [PACS nos.: 03.30.+p; 03.50.De; 41.20.Jb; 73.40.Gk;
84.40.Az; 42.82.Et ]Comment: LaTeX file: 26 pages, with 5 Figures (and two Appendices). The
original version of this paper appeared in the Journal below
Approximate Analytic Solution for the Spatiotemporal Evolution of Wave Packets undergoing Arbitrary Dispersion
We apply expansion methods to obtain an approximate expression in terms of
elementary functions for the space and time dependence of wave packets in a
dispersive medium. The specific application to pulses in a cold plasma is
considered in detail, and the explicit analytic formula that results is
provided. When certain general initial conditions are satisfied, these
expressions describe the packet evolution quite well. We conclude by employing
the method to exhibit aspects of dispersive pulse propagation in a cold plasma,
and suggest how predicted and experimental effects may be compared to improve
the theoretical description of a medium's dispersive properties.Comment: 17 pages, 4 figures, RevTe
Sommerfeld's image method in the calculation of van der Waals forces
We show how the image method can be used together with a recent method
developed by C. Eberlein and R. Zietal to obtain the dispersive van der Waals
interaction between an atom and a perfectly conducting surface of arbitrary
shape. We discuss in detail the case of an atom and a semi- infinite conducting
plane. In order to employ the above procedure to this problem it is necessary
to use the ingenious image method introduced by Sommerfeld more than one
century ago, which is a generalization of the standard procedure. Finally, we
briefly discuss other interesting situations that can also be treated by the
joint use of Sommerfeld's image technique and Eberlein-Zietal method.Comment: To appear in the proceedings of Conference on Quantum Field Theory
under the Influence of External Conditions (QFEXT11
Generalized Quantum Dynamics as Pre-Quantum Mechanics
We address the issue of when generalized quantum dynamics, which is a
classical symplectic dynamics for noncommuting operator phase space variables
based on a graded total trace Hamiltonian , reduces to Heisenberg
picture complex quantum mechanics. We begin by showing that when , with a Weyl ordered operator Hamiltonian, then the generalized
quantum dynamics operator equations of motion agree with those obtained from
in the Heisenberg picture by using canonical commutation relations. The
remainder of the paper is devoted to a study of how an effective canonical
algebra can arise, without this condition simply being imposed by fiat on the
operator initial values. We first show that for any total trace Hamiltonian
which involves no noncommutative constants, there is a conserved
anti--self--adjoint operator with a structure which is closely
related to the canonical commutator algebra. We study the canonical
transformations of generalized quantum dynamics, and show that is a
canonical invariant, as is the operator phase space volume element. The latter
result is a generalization of Liouville's theorem, and permits the application
of statistical mechanical methods to determine the canonical ensemble governing
the equilibrium distribution of operator initial values. We give arguments
based on a Ward identity analogous to the equipartition theorem of classical
statistical mechanics, suggesting that statistical ensemble averages of Weyl
ordered polynomials in the operator phase space variables correspond to the
Wightman functions of a unitary complex quantum mechanics, with a conserved
operator Hamiltonian and with the standard canonical commutation relations
obeyed by Weyl ordered operator strings. Thus there is a well--defined sense inComment: 79 pages, no figures, plain te
Diffractive orbits in isospectral billiards
Isospectral domains are non-isometric regions of space for which the spectra
of the Laplace-Beltrami operator coincide. In the two-dimensional Euclidean
space, instances of such domains have been given. It has been proved for these
examples that the length spectrum, that is the set of the lengths of all
periodic trajectories, coincides as well. However there is no one-to-one
correspondence between the diffractive trajectories. It will be shown here how
the diffractive contributions to the Green functions match nevertheless in a
''one-to-three'' correspondence.Comment: 20 pages, 6 figure
Quantum mechanics in curved space-time
In this paper, the principles of the general relativity are used to formulate
quantum wave equations for spin-0 and spin-1/2 particles. More specifically,
the equations are worked in a Schwarzschild-like metric. As a test, the
hydrogen atom spectrum is calculated. A comparison of the calculated spectrum
with the numerical data of the deuterium energy levels shows a significant
improvement of the accord, and the deviations are almost five times smaller
then the ones obtained with the Dirac theory. The implications of the theory
considering the strong interactions are also discussed
Recovery of chaotic tunneling due to destruction of dynamical localization by external noise
Quantum tunneling in the presence of chaos is analyzed, focusing especially
on the interplay between quantum tunneling and dynamical localization. We
observed flooding of potentially existing tunneling amplitude by adding noise
to the chaotic sea to attenuate the destructive interference generating
dynamical localization. This phenomenon is related to the nature of complex
orbits describing tunneling between torus and chaotic regions. The tunneling
rate is found to obey a perturbative scaling with noise intensity when the
noise intensity is sufficiently small and then saturate in a large noise
intensity regime. A relation between the tunneling rate and the localization
length of the chaotic states is also demonstrated. It is shown that due to the
competition between dynamical tunneling and dynamical localization, the
tunneling rate is not a monotonically increasing function of Planck's constant.
The above results are obtained for a system with a sharp border between torus
and chaotic regions. The validity of the results for a system with a smoothed
border is also explained.Comment: 14 pages, 15 figure
Can multistate dark matter annihilation explain the high-energy cosmic ray lepton anomalies?
Multistate dark matter (DM) models with small mass splittings and couplings
to light hidden sector bosons have been proposed as an explanation for the
PAMELA/Fermi/H.E.S.S. high-energy lepton excesses. We investigate this proposal
over a wide range of DM density profiles, in the framework of concrete models
with doublet or triplet dark matter and a hidden SU(2) gauge sector that mixes
with standard model hypercharge. The gauge coupling is bounded from below by
the DM relic density, and the Sommerfeld enhancement factor is explicitly
computable for given values of the DM and gauge boson masses M, mu and the
(largest) dark matter mass splitting delta M_{12}. Sommerfeld enhancement is
stronger at the galactic center than near the Sun because of the radial
dependence of the DM velocity profile, which strengthens the inverse Compton
(IC) gamma ray constraints relative to usual assumptions. We find that the
PAMELA/Fermi/H.E.S.S. lepton excesses are marginally compatible with the model
predictions, and with CMB and Fermi gamma ray constraints, for M ~ 800 GeV, mu
~ 200 MeV, and a dark matter profile with noncuspy Einasto parameters alpha >
0.20, r_s ~ 30 kpc. We also find that the annihilating DM must provide only a
subdominant (< 0.4) component of the total DM mass density, since otherwise the
boost factor due to Sommerfeld enhancement is too large.Comment: 20 pages, 12 figures; v2: Corrected branching ratio for ground state
DM annihilations into leptons, leading to boost factors that are larger than
allowed. Added explicit results for doublet DM model. Some conclusions
changed; main conclusion of tension between inverse Compton constraints and
N-body simulations of halo profiles is unchange
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