The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics

We discuss methods to analyze a quantum Gibbs family in the ultra-cold regime where the norm closure of the Gibbs family fails due to discontinuities of the maximum-entropy inference. The current discussion of maximum-entropy inference and irreducible correlation in the area of quantum phase transitions is a major motivation for this research. We extend a representation of the irreducible correlation from finite temperatures to absolute zero.Comment: 8 pages, 3 figures, 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, 21-26 September 2014, Ch\^ateau du Clos Luc\'e, Amboise, Franc

LBV (Candidate) Nebulae: Bipolarity and Outflows

The most massive evolved stars (above 50 M_sun) undergo a phase of extreme mass loss in which their evolution is reversed from a redward to a blueward motion in the HRD. In this phase the stars are known as Luminous Blue Variables (LBVs) and they are located in the HRD close to the Humphreys-Davidson limit. It is far from understood what causes the strong mass loss or what triggers the so-called giant eruptions, active events in which in a short time a large amount of mass is ejected. Here I will present results from a larger project devoted to better understand LBVs through studying the LBV nebulae. These nebulae are formed as a consequence of the strong mass loss. The analysis concentrates on the morphology and kinematics of these nebulae. Of special concern was the frequently observed bipolar nature of the LBV nebulae. Bipolarity seems to be a general feature and strongly constrains models of the LBV phase and especially of the formation of the nebulae. In addition we found outflows from LBV nebulae, the first evidence for ongoing instabilities in the nebulae.Comment: 2 pages, to appear in : K.A. van der Hucht, A. Herrero & C. Esteban (eds.), A Massive Star Odyssey, from Main Sequence to Supernova, Proc. IAU Symp. No. 212 (San Francisco: ASP

A variation principle for ground spaces

The ground spaces of a vector space of hermitian matrices, partially ordered by inclusion, form a lattice constructible from top to bottom in terms of intersections of maximal ground spaces. In this paper we characterize the lattice elements and the maximal lattice elements within the set of all subspaces using constraints on operator cones. Our results contribute to the geometry of quantum marginals, as their lattices of exposed faces are isomorphic to the lattices of ground spaces of local Hamiltonians.Comment: 18 pages, 2 figures, version v3 has an improved exposition, v4 has a new non-commutative example and catches a glimpse of three qubit