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

Some Remarks about Variable Mass Systems

We comment about the general argument given to obtain the rocket equation as it is exposed in standard textbooks. In our opinion, it can induce students to a wrong answer when solving variable mass problems.Comment: 2 page

Radiative damping: a case study

We are interested in the motion of a classical charge coupled to the Maxwell self-field and subject to a uniform external magnetic field, B. This is a physically relevant, but difficult dynamical problem, to which contributions range over more than one hundred years. Specifically, we will study the Sommerfeld-Page approximation which assumes an extended charge distribution at small velocities. The memory equation is then linear and many details become available. We discuss how the friction equation arises in the limit of "small" B and contrast this result with the standard Taylor expansion resulting in a second order equation for the velocity of the charge.Comment: 4 figure

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

Small Disks and Semiclassical Resonances

We study the effect on quantum spectra of the existence of small circular disks in a billiard system. In the limit where the disk radii vanish there is no effect, however this limit is approached very slowly so that even very small radii have comparatively large effects. We include diffractive orbits which scatter off the small disks in the periodic orbit expansion. This situation is formally similar to edge diffraction except that the disk radii introduce a length scale in the problem such that for wave lengths smaller than the order of the disk radius we recover the usual semi-classical approximation; however, for wave lengths larger than the order of the disk radius there is a qualitatively different behaviour. We test the theory by successfully estimating the positions of scattering resonances in geometries consisting of three and four small disks.Comment: Final published version - some changes in the discussion and the labels on one figure are correcte

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

Boundary conditions at spatial infinity for fields in Casimir calculations

The importance of imposing proper boundary conditions for fields at spatial infinity in the Casimir calculations is elucidated.Comment: 8 pages, 1 figure, submitted to the Proceedings of The Seventh Workshop QFEXT'05 (Barcelona, September 5-9, 2005

Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. III. On the determination of radiation

We discuss the issue of radiation extraction in asymptotically flat space-times within the framework of conformal methods for numerical relativity. Our aim is to show that there exists a well defined and accurate extraction procedure which mimics the physical measurement process. It operates entirely intrisically within \scri^+ so that there is no further approximation necessary apart from the basic assumption that the arena be an asymptotically flat space-time. We define the notion of a detector at infinity by idealising local observers in Minkowski space. A detailed discussion is presented for Maxwell fields and the generalisation to linearised and full gravity is performed by way of the similar structure of the asymptotic fields.Comment: LaTeX2e,13 pages,2 figure

Resolution of the Klein Paradox

We present a resolution of the Klein paradox within the framework of one-particle relativistic quantum mechanics. Not only reflection becomes total but the vacuum remains neutral as well. This is accomplished by replacing the pair production process with virtual negative energy "incidence" within the barrier in a similar manner to what is done with image charges in electrostatic and virtual sources in optics.Comment: 9 pages, 8 figure

Gamma-ray signatures of annihilation to charged leptons in dark matter substructure

Due to their higher concentrations and small internal velocities, Milky Way subhalos can be at least as important as the smooth halo in accounting for the GeV positron excess via dark matter annihilation. After showing how this can be achieved in various scenarios, including in Sommerfeld models, we demonstrate that, in this case, the diffuse inverse-Compton emission resulting from electrons and positrons produced in substructure leads to a nearly-isotropic signal close to the level of the isotropic GeV gamma-ray background seen by Fermi. Moreover, we show that HESS cosmic-ray electron measurements can be used to constrain multi-TeV internal bremsstrahlung gamma rays arising from annihilation to charged leptons.Comment: 8 pages, 4 figures; minor updates to match published versio