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.

On Possible Measurement of Gravitational Interaction Parameters on Board a Satellite

The recently suggested SEE (Satellite Energy Exchange) method of measuring the gravitational constant $G$, possible equivalence principle violation (measured by the E\"{o}tv\"{o}s parameter $\eta$) and the hypothetic 5th force parameters $\alpha$ and $\lambda$ on board a drag-free Earth's satellite is discussed and further developed. Various particle trajectories near a heavy ball are numerically simulated. Some basic sources of error are analysed. The $G$ measurement procedure is modelled by noise insertion to a ``true'' trajectory. It is concluded that the present knowledge of $G, \alpha$ (for $\lambda \geq 1$ m) and $\eta$ can be improved by at least two orders of magnitude.Comment: (only two misprints on title page) 7 page

Derived categories of Burniat surfaces and exceptional collections

We construct an exceptional collection $\Upsilon$ of maximal possible length 6 on any of the Burniat surfaces with $K_X^2=6$, a 4-dimensional family of surfaces of general type with $p_g=q=0$. We also calculate the DG algebra of endomorphisms of this collection and show that the subcategory generated by this collection is the same for all Burniat surfaces. The semiorthogonal complement $\mathcal A$ of $\Upsilon$ is an "almost phantom" category: it has trivial Hochschild homology, and K_0(\mathcal A)=\bZ_2^6.Comment: 15 pages, 1 figure; further remarks expande

APSIS - an Artificial Planetary System in Space to probe extra-dimensional gravity and MOND

A proposal is made to test Newton's inverse-square law using the perihelion shift of test masses (planets) in free fall within a spacecraft located at the Earth-Sun L2 point. Such an Artificial Planetary System In Space (APSIS) will operate in a drag-free environment with controlled experimental conditions and minimal interference from terrestrial sources of contamination. We demonstrate that such a space experiment can probe the presence of a "hidden" fifth dimension on the scale of a micron, if the perihelion shift of a "planet" can be measured to sub-arc-second accuracy. Some suggestions for spacecraft design are made.Comment: 17 pages, revtex, references added. To appear in Special issue of IJMP

Complete moduli of cubic threefolds and their intermediate Jacobians

The intermediate Jacobian map, which associates to a smooth cubic threefold its intermediate Jacobian, does not extend to the GIT compactification of the space of cubic threefolds, not even as a map to the Satake compactification of the moduli space of principally polarized abelian fivefolds. A much better "wonderful" compactification of the space of cubic threefolds was constructed by the first and fourth authors --- it has a modular interpretation, and divisorial normal crossing boundary. We prove that the intermediate Jacobian map extends to a morphism from the wonderful compactification to the second Voronoi toroidal compactification of the moduli of principally polarized abelian fivefolds --- the first and fourth author previously showed that it extends to the Satake compactification. Since the second Voronoi compactification has a modular interpretation, our extended intermediate Jacobian map encodes all of the geometric information about the degenerations of intermediate Jacobians, and allows for the study of the geometry of cubic threefolds via degeneration techniques. As one application we give a complete classification of all degenerations of intermediate Jacobians of cubic threefolds of torus rank 1 and 2.Comment: 56 pages; v2: multiple updates and clarification in response to detailed referee's comment

EXAFS Characterization of Dendrimer‐Derived Pt/γ‐Al\u3csub\u3e2\u3c/sub\u3eO\u3csub\u3e3\u3c/sub\u3e

The various steps involved in the preparation of a Pt/γ‐Al2O3 material using hydroxyl‐terminated generation four (G4OH) PAMAM dendrimers as templates were monitored by EXAFS. The results indicate that Cl ligands in the Pt precursors (H2PtCl6 and K2PtCl4) were partially replaced by aquo ligands upon hydrolysis to form [PtCl3(H2O)3]+ and [PtCl2(H2O)2] species. After interaction of such species with G4OH, Cl ligands from the first coordination shell of Pt were further replaced by nitrogen atoms from the dendrimer interior, indicating the complexation of Pt with the dendrimer. This process was accompanied by a transfer of the electron density from the dendrimer to Pt, indicating that the former plays the role of a ligand. Following treatment of the H2PtCl6/G4OH and K2PtCl4/G4OH composites with NaBH4, no substantial changes were detecteded in the electronic or coordination environment of Pt, and no formation of metal nanoparticles was observed. However, when the reduction treatment was performed with H2, the formation of extremely small Pt clusters incorporating no more than 4 Pt atoms was observed. These Pt species remained strongly bonded to the dendrimer and their nuclearity depends on the length of the H2 treatment. Formation of Pt nanoparticles with an average diameter of approximately 10 Å was finally observed after the deposition of H2PtCl6/G4OH on γ‐Al2O3 and drying, suggesting that their formation may be related to the collapse of the dendrimer structure. The Pt nanoparticles formed appear to have high mobility, since subsequent thermal treatment in O2/H2 led to further sintering