A generating functional approach to the Hubbard model

The method of generating functional is generalized to the case of strongly correlated systems, and applied to the Hubbard model. For the electronic Green's function constructed for Hubbard operators, an equation using variational derivatives with respect to the fluctuating fields has been derived and its multiplicative form has been determined. Corrections for the electronic self-energy are calculated up to the second order with respect to the parameter W/U (W width of the band), and a mean field type approximation was formulated, including both charge and spin static fluctuations. The equations for the Bose-like Green's functions have been derived, describing the collective modes: the magnons and doublons. The properties of the poles of the doublon Green's functions depend on electronic filling. The investigation of the special case n=1 demonstrates that the doublon Green's function has a soft mode at the wave vector Q=(pi,pi,...), indicating possible instability of the uniform paramagnetic phase relatively to the two sublattices charge ordering. However this instability should compete with an instability to antiferromagnetic ordering.Comment: 31 pages, 7 figures, to be published in Eur. Phys. J.

Saturn's aurora in the January 2004 events

International audienceDifferences in the solar wind interaction with the magnetosphere of Saturn relative to the Earth result from the decrease in the solar wind plasma density and magnetic field strength with distance from the Sun, and from the change in the average angle of the IMF at Saturn's orbit. Other reasons are related to Saturn's rapid rotation and internal magnetospheric plasma sources. Moreover, the IMF structure observed by Cassini in 2003?2004 during the approach to Saturn is consistent with corotating interaction regions (CIRs) existing during the declining phase of the solar cycle. Two cases on 16 and 26 January 2004 are considered when disturbances in the solar wind passed Cassini and then Saturn. After the solar wind shock encountered the kronian magnetosphere, the auroral oval became brighter (especially at dawn) with a reduced radius. In these cases the auroral power was anti-correlated with the radius of the oval. Possible mechanisms responsible for such unexpected behavior are presented and discussed in detail

A few notes about the strigol´niki heresy

RésuméQuelques notes à propos de l’hérésie des « strigol´niki ».En mettant l’Église en accusation, les strigol´niki ne faisaient qu’exprimer les états d’âme du peuple chrétien, qui craignait que les sacrements administrés par des clercs indignes se révélassent inefficaces. La volée de critiques adressée au clergé témoigne à sa manière du succès de la catéchisation et du degré de dévouement à leur sacerdoce qu’on exigeait désormais des pasteurs. Il semble que le noyau de l’hérésie, autour duquel sont venues s’agglutiner des pratiques traditionnelles de piété et des croyances populaires, ait été la protestation contre la simonie entendue au sens large, c’est-à-dire comme toute espèce de transgression liée à l’ordination des prêtres. Les strigol´niki ont, semble-t-il, partagé ces caractéristiques, ainsi qu’une dévotion particulière pour l’Évangile, avec les Patarini de Milan.AbstractWhile accusing the Church, the strigol´niki actually expressed the mood of the flock, who feared that sacraments administered by unworthy clerics might be ineffective. The stream of criticism addressed to clerics testifies to the success of catechization and to the higher level of dedication required from the pastors. It seems that the heretic nucleus around which elements of traditional forms of piety and national belief conglomerated was protest against simony, broadly understood as any kind of infringement pertaining to the ordainment of priests. Alongside with especial reverence for the Gospel, these features of the strigol´niki movement appear similar to the Milanese Patarini’s

Rate of steady-state reconnection in an incompressible plasma

The reconnection rate is obtained for the simplest case of 2D symmetric reconnection in an incompressible plasma. In the short note (Erkaev et al., Phys. Rev. Lett.,84, 1455 (2000)), the reconnection rate is found by matching the outer Petschek solution and the inner diffusion region solution. Here the details of the numerical simulation of the diffusion region are presented and the asymptotic procedure which is used for deriving the reconnection rate is described. The reconnection rate is obtained as a decreasing function of the diffusion region length. For a sufficiently large diffusion region scale, the reconnection rate becomes close to that obtained in the Sweet-Parker solution with the inverse square root dependence on the magnetic Reynolds number, determined for the global size of the current sheet. On the other hand, for a small diffusion region length scale, the reconnection rate turns out to be very similar to that obtained in the Petschek model with a logarithmic dependence on the magnetic Reynolds number. This means that the Petschek regime seems to be possible only in the case of a strongly localized conductivity corresponding to a small scale of the diffusion region.Comment: 11 pages, 3 figure

Energetic Particles Dynamics in Mercury's Magnetosphere

We investigate the drift paths of energetic particles in Mercury's magnetosphere by tracing their motion through a model magnetic field. Test particle simulations solving the full Lorentz force show a quasi-trapped energetic particle population that gradient and curvature drift around the planet via "Shabansky" orbits, passing though high latitudes in the compressed dayside by equatorial latitudes on the nightside. Due to their large gyroradii, energetic H+ and Na+ ions will typically collide with the planet or the magnetopause and will not be able to complete a full drift orbit. These simulations provide direct comparison for recent spacecraft measurements from MESSENGER. Mercury's offset dipole results in an asymmetric loss cone and therefore an asymmetry in particle precipitation with more particles precipitating in the southern hemisphere. Since the planet lacks an atmosphere, precipitating particles will collide directly with the surface of the planet. The incident charged particles can kick up neutrals from the surface and have implications for the formation of the exosphere and weathering of the surfac