Taxes in a simple wealth distribution model by inelastically scattering particles

In this work we use an inelastic scattering process of particles to propose a model able to reproduce the salient features of the wealth distribution in an economy by including taxes to each trading process and redistributing that collected among the population according to a given criterion. Additionally, we show that different optimal levels of taxes may exist depending on the redistribution criterion.Comment: 7 pages, 7 figure

Dyson-Schwinger Equations and the Quark-Gluon Plasma

We review applications of Dyson-Schwinger equations at nonzero temperature, T, and chemical potential, mu, touching topics such as: deconfinement and chiral symmetry restoration; the behaviour of bulk thermodynamic quantities; the (T,mu)-dependence of hadron properties; and the possibility of diquark condensation.Comment: 13 pages, 1 figure, LaTeX, sprocl.sty, epsfig.sty. Summary of presentations by the authors at the Workshop "Understanding Deconfinement in QCD", ECT*, Trento, 1-13/March, 199

Bose condensation in flat bands

We derive effective Hamiltonians for lattice bosons with strong geometrical frustration of the kinetic energy by projecting the interactions on the flat lowest Bloch band. Specifically, we consider the Bose Hubbard model on the one dimensional sawtooth lattice and the two dimensional kagome lattice. Starting from a strictly local interaction the projection gives rise to effective long-range terms stabilizing a supersolid phase at densities above nu_c=1/9 of the kagome lattice. In the sawtooth lattice on the other hand we show that the solid order, which exists at the magic filling nu_c=1/4, is unstable to further doping. The universal low-energy properties at filling 1/4+delta nu are described by the well known commensurate-incommensurate transition. We support the analytic results by detailed numerical calculations using the Density Matrix Renormalization Group and exact diagonalization. Finally, we discuss possible realizations of the models using ultracold atoms as well as frustrated quantum magnets in high magnetic fields. We compute the momentum distribution and the noise correlations, that can be extracted from time of flight experiments or neutron scattering, and point to signatures of the unique supersolid phase of the kagome lattice.Comment: 18 pages, 13 figure

A Semi-analytic Study of Axial Perturbations of Ultra Compact Stars

Compact object perturbations, at linear order, often lead in solving one or more coupled wave equations. The study of these equations was typically done by numerical or semi-analytical methods. The WKB method and the associated Bohr-Sommerfeld rule have been proved extremely useful tools in the study of black-hole perturbations and the estimation of the related quasi-normal modes. Here we present an extension of the aforementioned semi-analytic methods in the study of perturbations of ultra-compact stars and gravastars.Comment: Accepted for publication in CQG, 13 pages, 3 figures, 5 table

Unnested islands of period-doublings in an injected semiconductor laser

We present a theoretical study of unnested period-doubling islands in three-dimensional rate equations modeling a semiconductor laser subject to external optical injection. In this phenomenon successive curves of period doublings are not arranged in nicely nested islands, but intersect each other. This overall structure is globally organized by several codimension-2 bifurcations. As a consequence, the chaotic region existing inside an unnested island of period doublings can be entered not only via a period-doubling cascade but also via the breakup of a torus, and even via the sudden appearance of a chaotic attractor. In order to fully understand these different chaotic transitions we reveal underlying global bifurcations and we show how they are connected to codimension-2 bifurcation points. Unnested islands of period doublings appear to be generic and hence must be expected in a large class of dynamical systems

Reply to "Comment on 'Z2-slave-spin theory for strongly correlated fermions' "

We show that the physical subspace in the Z2-slave-spin theory is conserved under the time evolution of the system. Thus, when restricted to the physical subspace, this representation gives a complete and consistent description of the original problem. In addition, we review two known examples from the existing literature in which the projection onto the physical subspace can be relaxed: (i) the non-interacting limit in any dimension at half filling and (ii) the interacting model in the infinite dimensional limit at half filling. In both cases, physical observables are correctly obtained without explicit treatment of the constraints which define the physical subspace. In these examples, correct results are obtained, despite the fact that unphysical states enter the solution.Comment: Reply to http://link.aps.org/doi/10.1103/PhysRevB.87.03710

ISO_q(3) and ISO_q(2,1)

We prove the embedding of ISO_q(3) \hook ISU^{ex}_{\sqrt{q}}(2) and ISO_q(2,1) \hook ISL^{ex}_q(2,R) as $^*$-algebras and give a Hilbert space representation of $ISU^{ex}_{\sqrt{q}}(2)$Comment: 10 pages, 12 figures, Late