Phases, many-body entropy measures and coherence of interacting bosons in optical lattices

Already a few bosons with contact interparticle interactions in small optical lattices feature a variety of quantum phases: superfluid, Mott-insulator and fermionized Tonks gases can be probed in such systems. To detect these phases -- pivotal for both experiment and theory -- as well as their many-body properties we analyze several distinct measures for the one-body and many-body Shannon information entropies. We exemplify the connection of these entropies with spatial correlations in the many-body state by contrasting them to the Glauber normalized correlation functions. To obtain the ground-state for lattices with commensurate filling (i.e. an integer number of particles per site) for the full range of repulsive interparticle interactions we utilize the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) in order to solve the many-boson Schr\"odinger equation. We demonstrate that all emergent phases -- the superfluid, the Mott insulator, and the fermionized gas can be characterized equivalently by our many-body entropy measures and by Glauber's normalized correlation functions. In contrast to our many-body entropy measures, single-particle entropy cannot capture these transitions.Comment: 11 pages, 7 figures, software available at http://ultracold.or

Superfluid-insulator transition in strongly disordered one-dimensional systems

We present an asymptotically exact renormalization-group theory of the superfluid-insulator transition in one-dimensional (1D) disordered systems, with emphasis on an accurate description of the interplay between the Giamarchi-Schulz (instanton-anti-instanton) and weak-link (scratched-XY) criticalities. Combining the theory with extensive quantum Monte Carlo simulations allows us to shed new light on the ground-state phase diagram of the 1D disordered Bose-Hubbard model at unit filling

Maximally inhomogeneous G\"{o}del-Farnsworth-Kerr generalizations

It is pointed out that physically meaningful aligned Petrov type D perfect fluid space-times with constant zero-order Riemann invariants are either the homogeneous solutions found by G\"{o}del (isotropic case) and Farnsworth and Kerr (anisotropic case), or new inhomogeneous generalizations of these with non-constant rotation. The construction of the line element and the local geometric properties for the latter are presented.Comment: 4 pages, conference proceeding of Spanish Relativity Meeting (ERE 2009, Bilbao

A new special class of Petrov type D vacuum space-times in dimension five

Using extensions of the Newman-Penrose and Geroch-Held-Penrose formalisms to five dimensions, we invariantly classify all Petrov type $D$ vacuum solutions for which the Riemann tensor is isotropic in a plane orthogonal to a pair of Weyl alligned null directionsComment: 4 pages, 1 table, no figures. Contribution to the proceedings of the Spanish Relativity Meeting 2010 held in Granada (Spain

Rotating solenoidal perfect fluids of Petrov type D

We prove that aligned Petrov type D perfect fluids for which the vorticity vector is not orthogonal to the plane of repeated principal null directions and for which the magnetic part of the Weyl tensor with respect to the fluid velocity has vanishing divergence, are necessarily purely electric or locally rotationally symmetric. The LRS metrics are presented explicitly.Comment: 6 pages, no figure

Complete classification of purely magnetic, non-rotating and non-accelerating perfect fluids

Recently the class of purely magnetic non-rotating dust spacetimes has been shown to be empty (Wylleman, Class. Quant. Grav. 23, 2727). It turns out that purely magnetic rotating dust models are subject to severe integrability conditions as well. One of the consequences of the present paper is that also rotating dust cannot be purely magnetic when it is of Petrov type D or when it has a vanishing spatial gradient of the energy density. For purely magnetic and non-rotating perfect fluids on the other hand, which have been fully classified earlier for Petrov type D (Lozanovski, Class. Quant. Grav. 19, 6377), the fluid is shown to be non-accelerating if and only if the spatial density gradient vanishes. Under these conditions, a new and algebraically general solution is found, which is unique up to a constant rescaling, which is spatially homogeneous of Bianchi type $VI_0$, has degenerate shear and is of Petrov type I($M^\infty)$ in the extended Arianrhod-McIntosh classification. The metric and the equation of state are explicitly constructed and properties of the model are briefly discussed. We finally situate it within the class of normal geodesic flows with degenerate shear tensor.Comment: 12 pages; introduction partly rewritten, notation made more clear, table of results adde

Expanding perfect fluid generalizations of the C-metric

We reexamine Petrov type D gravitational fields generated by a perfect fluid with spatially homogeneous energy density and in which the flow lines form a timelike non-shearing and non-rotating congruence. It is shown that the anisotropic such spacetimes, which comprise the vacuum C-metric as a limit case, can have \emph{non-zero} expansion, contrary to the conclusion in the original investigation by Barnes (Gen. Rel. Grav. 4, 105 (1973)). This class consists of cosmological models with generically one and at most two Killing vectors. We construct their line element and discuss some important properties. The methods used in this investigation incite to deduce testable criteria regarding shearfree normality and staticity op Petrov type $D$ spacetimes in general, which we add in an appendix.Comment: 16 pages, extended and amended versio