Discrete Q- and P-symbols for spin s

Non-orthogonal bases of projectors on coherent states are introduced to expand Hermitean operators acting on the Hilbert space of a spin s. It is shown that the expectation values of a Hermitean operator (A) over cap in a family of (2s + 1)(2) spin-coherent states determine the operator unambiguously. In other words, knowing the Q-symbol of (A) over cap at (2s + 1)(2) points on the unit sphere is already sufficient in order to recover the operator. This provides a straightforward method to reconstruct the mixed state of a spin since its density matrix is explicitly parametrized in terms of expectation values. Furthermore, a discrete P-symbol emerges naturally which is related to a basis dual to the original one

Supersolutions

We develop classical globally supersymmetric theories. As much as possible, we treat various dimensions and various amounts of supersymmetry in a uniform manner. We discuss theories both in components and in superspace. Throughout we emphasize geometric aspects. The beginning chapters give a general discussion about supersymmetric field theories; then we move on to detailed computations of lagrangians, etc. in specific theories. An appendix details our sign conventions. This text will appear in a two-volume work "Quantum Fields and Strings: A Course for Mathematicians" to be published soon by the American Mathematical Society. Some of the cross-references may be found at http://www.math.ias.edu/~drm/QFT/Comment: 130 pages, AMSTe

Excellence of function fields of conics

For every generalized quadratic form or hermitian form over a division algebra, the anisotropic kernel of the form obtained by scalar extension to the function field of a smooth projective conic is defined over the field of constants. The proof does not require any hypothesis on the characteristic

Auctioning incentive contracts; application to welfare-to-work programs

This paper applies the theory of auctioning incentive contracts to welfare-to-work programs. In several countries, the government procures welfare-to-work projects to employment service providers. In doing so, the government trades off adverse selection (the winning provider is not the most efficient one) and moral hazard (the winning provider shirks in his effort to reintegrate unemployed people). We compare three simple auctions with the socially optimal mechanism and show that two of these auctions approximate the optimal mechanism if the number of providers is large. Using simulations, we observe that competition between three bidders is already sufficient for the outcome of these auctions to reach 95% of the optimal level of social welfare.

Many-Body Rate Limit on Photoassociation of a Bose-Einstein Condensate

We briefly report on zero-temperature photoassociation of a Bose-Einstein condensate, focusing on the many-body rate limit for atom-molecule conversion. An upgraded model that explicitly includes spontaneous radiative decay leads to an unanticipated shift in the position of the photoassociation resonance, which affects whether the rate (constant) maximizes or saturates, as well as the limiting value itself. A simple analytical model agrees with numerical experiments, but only for high density. Finally, an explicit comparison with the two-body unitary limit, set by the size of the condensate, finds that the many-body rate limit is generally more strict.Comment: 4 pages, 3 figures, 59 references. v2: discussion added; to appear in PR

The galactic antiproton spectrum at high energies: background expectation vs. exotic contributions

A new generation of upcoming space-based experiments will soon start to probe the spectrum of cosmic ray antiparticles with an unprecedented accuracy and, in particular, will open up a window to energies much higher than those accessible so far. It is thus timely to carefully investigate the expected antiparticle fluxes at high energies. Here, we perform such an analysis for the case of antiprotons. We consider both standard sources as the collision of other cosmic rays with interstellar matter, as well as exotic contributions from dark matter annihilations in the galactic halo. Up to energies well above 100 GeV, we find that the background flux in antiprotons is almost uniquely determined by the existing low-energy data on various cosmic ray species; for even higher energies, however, the uncertainties in the parameters of the underlying propagation model eventually become significant. We also show that if the dark matter is composed of particles with masses at the TeV scale, which is naturally expected in extra-dimensional models as well as in certain parameter regions of supersymmetric models, the annihilation flux can become comparable to - or even dominate - the antiproton background at the high energies considered here.Comment: 17 pages revtex4, 7 figures; minor changes (to match the published version