Gutzwiller approach to the Bose-Hubbard model with random local impurities

Recently it has been suggested that fermions whose hopping amplitude is quenched to extremely low values provide a convenient source of local disorder for lattice bosonic systems realized in current experiment on ultracold atoms. Here we investigate the phase diagram of such systems, which provide the experimental realization of a Bose-Hubbard model whose local potentials are randomly extracted from a binary distribution. Adopting a site-dependent Gutzwiller description of the state of the system, we address one- and two-dimensional lattices and obtain results agreeing with previous findings, as far as the compressibility of the system is concerned. We discuss the expected peaks in the experimental excitation spectrum of the system, related to the incompressible phases, and the superfluid character of the {\it partially compressible phases} characterizing the phase diagram of systems with binary disorder. In our investigation we make use of several analytical results whose derivation is described in the appendices, and whose validity is not limited to the system under concern.Comment: 12 pages, 5 figures. Some adjustments made to the manuscript and to figures. A few relevant observations added throughout the manuscript. Bibliography made more compact (collapsed some items

Limits to the presence of transiting circumbinary planets in CoRoT data

The CoRoT mission during its flight-phase 2007-2012 delivered the light-curves for over 2000 eclipsing binaries. Data from the Kepler mission have proven the existence of several transiting circumbinary planets. Albeit light-curves from CoRoT have typically lower precision and shorter coverage, CoRoT's number of targets is similar to Kepler, and some of the known circumbinary planets could potentially be detected in CoRoT data as well. The aim of this work has been a revision of the entire CoRoT data-set for the presence of circumbinary planets, and the derivation of limits to the abundances of such planets. We developed a code which removes the light curve of the eclipsing binaries and searches for quasi-periodic transit-like features in a light curve after removal of binary eclipses and instrumental features. The code needs little information on the sample systems and can be used for other space missions as well, like Kepler, K2, TESS and PLATO. The code is broad in the requirements leading to detections, but was tuned to deliver an amount of detections that is manageable in a subsequent, mainly visual, revision about their nature. In the CoRoT sample we identified three planet candidates whose transits would have arisen from a single pass across the central binary. No candidates remained however with transit events from multiple planetary orbits. We calculated the upper limits for the number of Jupiter, Saturn and Neptune sized planets in co-planar orbits for different orbital period ranges. We found that there are much less giant planets in short-periodic orbits around close binary systems than around single stars.Comment: Accepted for publication in A&A, 11 pages, 4 figures and 4 tables. Updated to fix error in acknowledgemen

Irreducible Lie-Yamaguti algebras

Lie-Yamaguti algebras (or generalized Lie triple systems) are binary-ternary algebras intimately related to reductive homogeneous spaces. The Lie-Yamaguti algebras which are irreducible as modules over their Lie inner derivation algebra are the algebraic counterpart of the isotropy irreducible homogeneous spaces. These systems will be shown to split into three disjoint types: adjoint type, non-simple type and generic type. The systems of the first two types will be classified and most of them will be shown to be related to a Generalized Tits Construction of Lie algebras.Comment: 25 page

Differential Calculi on Associative Algebras and Integrable Systems

After an introduction to some aspects of bidifferential calculus on associative algebras, we focus on the notion of a "symmetry" of a generalized zero curvature equation and derive Backlund and (forward, backward and binary) Darboux transformations from it. We also recall a matrix version of the binary Darboux transformation and, inspired by the so-called Cauchy matrix approach, present an infinite system of equations solved by it. Finally, we sketch recent work on a deformation of the matrix binary Darboux transformation in bidifferential calculus, leading to a treatment of integrable equations with sources.Comment: 19 pages, to appear in "Algebraic Structures and Applications", S. Silvestrov et al (eds.), Springer Proceedings in Mathematics & Statistics, 202