Some Hamiltonian Models of Friction

Mathematical results on some models describing the motion of a tracer particle through a Bose-Einstein condensate are described. In the limit of a very dense, very weakly interacting Bose gas and for a very large particle mass, the dynamics of the coupled system is determined by classical non-linear Hamiltonian equations of motion. The particle's motion exhibits deceleration corresponding to friction (with memory) caused by the emission of Cerenkov radiation of gapless modes into the gas. Precise results are stated and outlines of proofs are presented. Some technical details are deferred to forthcoming papers.Comment: 19 Pages, 1 figur

Status of Spin Physics - Experimental Summary

The current status of spin physics experiments, based on talks presented at the Third Circum-Pan-Pacific Symposium on High Energy Spin Physics held in Beijing, 2001, is summarized in this article. Highlights of recent experimental results at SLAC, JLab, and DESY, as well as future plans at these facilities and at RHIC-spin are discussed.Comment: 18 pages, 7 figures, Invited talk presented at the Third Circum-Pan-Pacific Symposium on High Energy Spin Physics held in Beijing, October, 200

Equivariant wave maps exterior to a ball

We consider the exterior Cauchy-Dirichlet problem for equivariant wave maps from 3+1 dimensional Minkowski spacetime into the three-sphere. Using mixed analytical and numerical methods we show that, for a given topological degree of the map, all solutions starting from smooth finite energy initial data converge to the unique static solution (harmonic map). The asymptotics of this relaxation process is described in detail. We hope that our model will provide an attractive mathematical setting for gaining insight into dissipation-by-dispersion phenomena, in particular the soliton resolution conjecture.Comment: 16 pages, 9 figure

Diffractive jets production in pp-collisions

We consider the exclusive diffractive dissociation of a proton into three jets with large transverse momenta in the double-logarithmic approximation of perturbative QCD. This process is sensitive to the proton unintegrated gluon distribution at small x and to the proton light-cone distribution amplitudes. According to our estimates, an observation of such processes in the early runs at LHC is feasible for jet transverse momenta of the order of 5 GeV.Comment: Presented at International Workshop on Diffraction in High-Energy Physics, La Londe-les-Maures, France, September 9 - 14, 200

Theory of Nonlinear Dispersive Waves and Selection of the Ground State

A theory of time dependent nonlinear dispersive equations of the Schroedinger / Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear Master equations (NLME), governing the evolution of the mode powers, and by a novel multi-time scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include BEC large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, ``selection of the ground state'', and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et. al. in nonlinear optical waveguides

The GDH Sum Rule and Related Integrals

The spin structure of the nucleon resonance region is analyzed on the basis of our phenomenological model MAID. Predictions are given for the Gerasimov-Drell-Hearn sum rule as well as generalized integrals over spin structure functions. The dependence of these integrals on momentum transfer is studied and rigorous relationships between various definitions of generalized Gerasimov-Drell-Hearn integrals and spin polarizabilities are derived. These results are compared to the predictions of chiral perturbation theory and phenomenological models.Comment: 15 pages LaTeX including 5 figure

QCD radiative and power corrections and Generalized GDH sum rules

We extend the earlier suggested QCD-motivated model for the $Q^2$-dependence of the generalized Gerasimov-Drell-Hearn (GDH) sum rule which assumes the smooth dependence of the structure function $g_T$, while the sharp dependence is due to the $g_2$ contribution and is described by the elastic part of the Burkhardt-Cottingham sum rule. The model successfully predicts the low crossing point for the proton GDH integral, but is at variance with the recent very accurate JLAB data. We show that, at this level of accuracy, one should include the previously neglected radiative and power QCD corrections, as boundary values for the model. We stress that the GDH integral, when measured with such a high accuracy achieved by the recent JLAB data, is very sensitive to QCD power corrections. We estimate the value of these power corrections from the JLAB data at $Q^2 \sim 1 {GeV}^2$. The inclusion of all QCD corrections leads to a good description of proton, neutron and deuteron data at all $Q^2$.Comment: 10 pages, 4 figures (to be published in Physical Review D

gamma* -> rhoT impact factor with twist three accuracy

We evaluate the impact factor of the transition gamma* -> rhoT taking into account the twist 3 contributions. We show that a gauge invariant expression is obtained with the help of QCD equations of motion. Our results are free of end-point singularities. This opens the way to a consistent treatment of factorization for exclusive processes with a transversally polarized vector meson.Comment: 4 pages, 1 figure; To appear in the proceedings of Diffraction 2008: International Workshop on Diffraction in High-Energy Physics, La Londe-les-Maures, France, September 9-14, 200