Abstract:
We study a gas of repulsively interacting bosons in an optical lattice and explore the physics beyond the lowest band Hubbard model. Utilizing a generalized Gutzwiller ansatz, we find how the lowest band physics is modified by the inclusion of the first excited bands. In contrast to the prediction of the lowest band Bose-Hubbard model, a reentrant behavior of superfluidity is envisaged as well as decreasing width of the Mott lobes at strong coupling.

Abstract:
We address the issue of determining an effective two-body interaction for mean-field calculations of energies of many-body systems. We show that the effective interaction is proportional to the phase shift, and demonstrate this result in the quasiclassical approximation when there is a trapping potential in addition to the short-range interaction between a pair of particles. We calculate numerically energy levels for the case of an interaction with a short-range square-well and a harmonic trapping potential and show that the numerical results agree well with the analytical expression. We derive a generalized Gross--Pitaevskii equation which includes effective range corrections and discuss the form of the electron--atom effective interaction to be used in calculations of Rydberg atoms and molecules.

Abstract:
We study the ground state of the rotating spinor condensate and show that for slow rotation the ground state of the ferromagnetic spinor condensate is a coreless vortex. While coreless vortex is not topologically stable, we show that there is an energetic threshold for the creation of a coreless vortex. This threshold corresponds to a critical rotation frequency that vanishes as the system size increases. Also, we demonstrate the dramatically different behavior of the spinor condensate with anti-ferromagnetic interactions. For anti-ferromagnetic spinor condensate the angular momentum as a function of rotation frequency exhibits the familiar staircase behavior, but in contrast to an ordinary condensate the first step is to the state with angular momentum 1/2 per particle.

Abstract:
We present a model of the vertical stratification and the spectra of an irradiated medium under the assumption of constant pressure. Such a solution has properties intermediate between constant density models and hydrostatic equilibrium models, and it may represent a flattened configuration of gas clumps accreting onto the central black hole. Such a medium develops a hot skin, thicker than hydrostatic models, but thinner than constant density models, under comparable irradiation. The range of theoretical values of the alpha_ox index is comparable to those from hydrostatic models and both are close to the observed values for Seyfert galaxies but lower than in quasars. The amount of X-ray Compton reflection is consistent with the observed range. The characteristic property of the model is a frequently multicomponent iron K alpha line.

Abstract:
We study the rotational properties of an attractively interacting Bose gas in a quadratic + quartic potential. The low-lying modes of both rotational ground state configurations, namely the vortex and the center of mass rotating states, are solved. The vortex excitation spectrum is positive for weak interactions but the lowest modes decrease rapidly to negative values when the interactions become stronger. The broken rotational symmetry involved in the center of mass rotating state induces the appearance of an extra zero-energy mode in the Bogoliubov spectrum. The excitations of the center of mass rotational state also demonstrate the coupling between the center of mass and relative motions.

Abstract:
Nayakshin & Kazanas (2002) have considered the time-dependent illumination of an accretion disc in Active Galactic Nuclei, in the lamppost model. We extend their study to the flare model, which postulates the release of a large X-ray flux above a small region of the accretion disc. A fundamental difference with the lamppost model is that the region of the disc below the flare is not illuminated before the onset of the flare. A few test models show that the spectrum which follows immediately the increase in continuum flux should display the characteristics of a highly illuminated but dense gas, i.e. very intense X-ray emission lines and ionization edges in the soft X-ray range. The behaviour of the iron line is different in the case of a "moderate" and a ``strong'' flare: for a moderate flare, the spectrum displays a neutral component of the Fe K$\alpha$ line at 6.4 keV, gradually leading to more highly ionized lines. For a strong flare, the lines are already emitted by FeXXV (around 6.7 keV) after the onset, and have an equivalent width of several hundreds of eV. We find that the observed correlations between $R$, $\Gamma$, and the X-ray flux, are well accounted by a combination of flares having not achieved pressure equilibrium, strongly suggesting that the observed spectrum is dominated by regions in non-pressure equilibrium, typical of the onset of the flares. Finally a flare being confined to a small region of the disc, the spectral lines should be narrow (except for a weak Compton broadening), Doppler shifted, and moving.

Abstract:
We present a study of the spin dynamics of magnetic defects induced by Li substitution of the plane Cu in the normal state of YBa$_2$Cu$_3$O$_{6+x}$. The fluctuations of the coupled Cu magnetic moments in the vicinity of Li are probed by near-neighbour $^{89}$Y {\it and} $^7$Li NMR spin lattice relaxation. The data indicates that the magnetic perturbation fluctuates as a single entity with a correlation time $\tau$ which scales with the local static susceptibility. This behaviour is reminiscent of the low $T$ Kondo state of magnetic impurities in conventional metals. Surprisingly it extends well above the ``Kondo'' temperature for the underdoped pseudogapped case.

Abstract:
We present the first Ga(4f) NMR study of the Cr susceptibility in the archetype of Kagome based frustrated antiferromagnets, SrCr$_{8}$Ga$_{4}$O$_{19}$. Our major finding is that the susceptibility of the frustrated lattice goes through a maximum around 50 K. Our data also supports the existence of paramagnetic ``clusters'' of spins, responsible for the Curie behavior observed in the macroscopic susceptibility at low T. These results set novel features for the constantly debated physics of geometrically frustrated magnets.

Abstract:
Different nanofabricated superconducting circuits based on Josephson junctions have already achieved a degree of quantum coherence sufficient to demonstrate coherent superpositions of their quantum states. These circuits are considered for implementing quantum bits, which are the building blocks for the recently proposed quantum computer designs. We report experiments in which the state of a quantum bit circuit, the quantronium, is efficiently manipulated using methods inspired from Nuclear Magnetic Resonance (NMR).

Abstract:
We measure the magnetic susceptibility nearby Li spinless impurities in the superconducting phase of the high Tc cuprate YBaCuO. The induced moment which was found to exist above Tc persists below Tc. In the underdoped regime, it retains its Curie law below Tc. In contrast, near optimal doping, the large Kondo screening observed above Tc (T_K=135 K) is strongly reduced below Tc as expected theoretically when the superconducting gap develops. This moment still extends essentially on its 4 near neighbour Cu, showing the persistence of AF correlations in the superconducting state. A direct comparison with recent STM results of Pan et al. is proposed.