Long Range Scattering and Modified Wave Operators for some Hartree Type Equations

We study the theory of scattering for a class of Hartree type equations with long range interactions in space dimension n > 2, including Hartree equations with potential V(x) = lambda |x|^{- gamma} with gamma < 1. For 1/2 < gamma < 1 we prove the existence of modified wave operators with no size restriction on the data and we determine the asymptotic behaviour in time of solutions in the range of the wave operators.Comment: TeX, 89 pages, available http://qcd.th.u-psud.f

Spin-3/2 Fermions in Twistor Formalism

Consistency conditions for the local existence of massless spin 3/2 fields has been explored that the field equations for massless helicity 3/2 are consistent iff the space-time is Ricci-flat and that in Minkowski space-time the space of conserved charges for the fields is its twistor space itself. After considering the twistorial methods to study such massless helicity 3/2 fields, we derive in flat space-time that the charges of spin-3/2 fields defined topologically by the first Chern number of their spin-lowered self-dual Maxwell fields, are given by their twistor space, and in curved space-time that the (anti-)self-duality of the space-time is the necessary condition. Since in N=1 supergravity torsions are the essential ingredients, we generalize our space-time to that with torsion (Einstein-Cartan theory) and have investigated the consistency of existence of spin 3/2 fields in it. A simple solution is found that the space-time has to be conformally (anti-)self-dual, left-(or right-)torsion-free. The integrability condition on $\alpha$-surface shows that the (anti-)self-dual Weyl spinor can be described only by the covariant derivative of the right-(left-)handed-torsion.Comment: 13 pages, Latex2e. The derivations and the conclusions are improve

Fluctuation-dissipation relations outside the linear response regime in a two-dimensional driven lattice gas along the direction transverse to the driving force

We performed numerical experiments on a two-dimensional driven lattice gas, which constitutes a simple stochastic nonequilibrium many-body model. In this model, focusing on the behavior along the direction transverse to the external driving force, we numerically measure transport coefficients and dynamical fluctuations outside the linear response regime far from equilibrium. Using these quantities, we find the validity of the Einstein relation, the Green-Kubo relation and the fluctuation-response relation.Comment: 4 pages, 5 figure

Depth/diameter relationships of fresh craters within Hesperia Planum, Mars

Meteorite impact craters represent important geological features for revealing the near-surface layers of a planetary surface. In the case of Mars, this characteristic was proposed as a useful method to study spatial variations of such attributes as the distribution of sub-surface volatiles, and heat flow. Using the Planetary Image Cartography System (PICS) software, a quantitative analysis was completed of the geometry of fresh impact craters in the Hesperia Planum region of Mars, where an uniform target material and optimum viewing geometry make possible an analysis of target effects over a large geographic region. Because of the morphologic similarity to the lunar maria, it is likely that Hesperia Planum comprises a series of flood lavas that partially infilled topographic depressions within the Martian highlands. Measurements of partially buried crater rims suggest that the lava flows within Hesperia Planum are between 200-400 m thick

Scattering and small data completeness for the critical nonlinear Schroediger equation

We prove Asymptotic Completeness of one dimensional NLS with long range nonlinearities. We also prove existence and expansion of asymptotic solutions with large data at infinity

Dirac spinor fields in the teleparallel gravity: comment on "Metric-affine approach to teleparallel gravity"

We show that the coupling of a Dirac spinor field with the gravitational field in the teleparallel equivalent of general relativity is consistent. For an arbitrary SO(3,1) connection there are two possibilities for the coupling of the spinor field with the gravitational field. The problems of consistency raised by Y. N. Obukhov and J. G. Pereira in the paper {\it Metric-affine approach to teleparallel gravity} [gr-qc/0212080] take place only in the framework of one particular coupling. By adopting an alternative coupling the consistency problem disappears.Comment: 8 pages, Latex file, no figures, to appear in the Phys. Rev. D as a Commen