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

On the mutual polarization of two He-4 atoms

We propose a simple method based on the standard quantum-mechanical perturbation theory to calculate the mutual polarization of two atoms He^4.Comment: 9 pages, 1 table; the article is revised and the calculation is essentially refined; v4: final version, the Introduction is delete

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

Non-dipole angular anisotropy parameters of semi-filled shell atoms

We present the results of calculations of outer shell non-dipole angular anisotropy parameters for semi-filled shell atoms in the Hartree-Fock (HF) one-electron approximation and with account of inter-electron correlations in the frame of the Spin Polarized Random Phase Approximation with Exchange (SP RPAE). We demonstrate for the first time that this characteristic of photoionization process is essentially sensitive to the fact whether the photoelectron has the same or opposite spin orientation to that of the semi-filled shell.Comment: 15 pages, 8 figure

The Stern-Gerlach Experiment Revisited

The Stern-Gerlach-Experiment (SGE) of 1922 is a seminal benchmark experiment of quantum physics providing evidence for several fundamental properties of quantum systems. Based on today's knowledge we illustrate the different benchmark results of the SGE for the development of modern quantum physics and chemistry. The SGE provided the first direct experimental evidence for angular momentum quantization in the quantum world and thus also for the existence of directional quantization of all angular momenta in the process of measurement. It measured for the first time a ground state property of an atom, it produced for the first time a `spin-polarized' atomic beam, it almost revealed the electron spin. The SGE was the first fully successful molecular beam experiment with high momentum-resolution by beam measurements in vacuum. This technique provided a new kinematic microscope with which inner atomic or nuclear properties could be investigated. The original SGE is described together with early attempts by Einstein, Ehrenfest, Heisenberg, and others to understand directional quantization in the SGE. Heisenberg's and Einstein's proposals of an improved multi-stage SGE are presented. The first realization of these proposals by Stern, Phipps, Frisch and Segr\`e is described. The set-up suggested by Einstein can be considered an anticipation of a Rabi-apparatus. Recent theoretical work is mentioned in which the directional quantization process and possible interference effects of the two different spin states are investigated. In full agreement with the results of the new quantum theory directional quantization appears as a general and universal feature of quantum measurements. One experimental example for such directional quantization in scattering processes is shown. Last not least, the early history of the `almost' discovery of the electron spin in the SGE is revisited.Comment: 50pp, 17 fig

P/2010 A2 LINEAR II: dynamical dust modelling

P/2010 A2 is an object on an asteroidal orbit that was observed to have an extended tail or debris trail in January 2010. In this work, we fit the outburst of P/2010 A2 with a conical burst model, and verify previous suspicions that this was a one--time collisional event rather than an sustained cometary outburst, implying that P/2010 A2 is not a new Main Belt Comet driven by ice sublimation. We find that the best--fit cone opening angle is about 40 to 50 degrees, in agreement with numerical and laboratory simulations of cratering events. Mapping debris orbits to sky positions suggests that the distinctive arc features in the debris correspond to the same debris cone inferred from the extended dust. From the velocity of the debris, and from the presence of a velocity maximum at around 15 cm/s, we infer that the surface of A2 probably has a very low strength (<1 kPa), comparable to lunar regolith.Comment: 14 pages, 25 figures; accepted by Astronomy and Astrophysic

Semiclassical Description of Tunneling in Mixed Systems: The Case of the Annular Billiard

We study quantum-mechanical tunneling between symmetry-related pairs of regular phase space regions that are separated by a chaotic layer. We consider the annular billiard, and use scattering theory to relate the splitting of quasi-degenerate states quantized on the two regular regions to specific paths connecting them. The tunneling amplitudes involved are given a semiclassical interpretation by extending the billiard boundaries to complex space and generalizing specular reflection to complex rays. We give analytical expressions for the splittings, and show that the dominant contributions come from {\em chaos-assisted}\/ paths that tunnel into and out of the chaotic layer.Comment: 4 pages, uuencoded postscript file, replaces a corrupted versio

The fundamental solution and Strichartz estimates for the Schr\"odinger equation on flat euclidean cones

We study the Schr\"odinger equation on a flat euclidean cone $\mathbb{R}_+ \times \mathbb{S}^1_\rho$ of cross-sectional radius $\rho > 0$, developing asymptotics for the fundamental solution both in the regime near the cone point and at radial infinity. These asymptotic expansions remain uniform while approaching the intersection of the "geometric front", the part of the solution coming from formal application of the method of images, and the "diffractive front" emerging from the cone tip. As an application, we prove Strichartz estimates for the Schr\"odinger propagator on this class of cones.Comment: 21 pages, 4 figures. Minor typos corrected. To be published in Comm. Math. Phy

Shrunk loop theorem for the topology probabilities of closed Brownian (or Feynman) paths on the twice punctured plane

The shrunk loop theorem presented here is an integral identity which facilitates the calculation of the relative probability (or probability amplitude) of any given topology that a free, closed Brownian or Feynman path of a given 'duration' might have on the twice punctured plane (the plane with two marked points). The result is expressed as a scattering series of integrals of increasing dimensionality based on the maximally shrunk version of the path. Physically, this applies in different contexts: (i) the topology probability of a closed ideal polymer chain on a plane with two impassable points, (ii) the trace of the Schroedinger Green function, and thence spectral information, in the presence of two Aharonov-Bohm fluxes, (iii) the same with two branch points of a Riemann surface instead of fluxes. Our theorem starts with the Stovicek expansion for the Green function in the presence of two Aharonov-Bohm flux lines, which itself is based on the famous Sommerfeld one puncture point solution of 1896 (the one puncture case has much easier topology, just one winding number). Stovicek's expansion itself can supply the results at the expense of choosing a base point on the loop and then integrating it away. The shrunk loop theorem eliminates this extra two dimensional integration, distilling the topology from the geometry.Comment: 29 pages, 5 figures (accepted by J. Phys. A: Math. Gen.