Self trapping in the two-dimensional Bose-Hubbard model

We study the expansion of harmonically trapped bosons in a two-dimensional lattice after suddenly turning off the confining potential. We show that, in the presence of multiple occupancies per lattice site and strong interactions, the system exhibits a clear dynamical separation into slowly and rapidly expanding clouds. We discuss how this effect can be understood within a simple picture by invoking doublons and Bose enhancement. This picture is corroborated by an analysis of the momentum distribution function in the regions with slowly and rapidly expanding bosons.Comment: 7 pages, 8 figures, as publishe

Extracting the Mott gap from energy measurements in trapped atomic gases

We show that the measure of the so-called {\it release-energy}, which is an experimentally accessible quantity, makes it possible to assess the value of the Mott gap in the presence of the confinement potential that is unavoidable in the actual experimental setup. Indeed, the curve of the release-energy as a function of the total number of particles shows kinks that are directly related to the existence of excitation gaps. Calculations are presented within the Gutzwiller approach, but the final results go beyond this simple approximation and represent a genuine feature of the real system. In the case of harmonic confinement, the Mott gaps may be renormalized with respect to the uniform case. On the other hand, in the case of the recently proposed off-diagonal confinement, our results show an almost perfect agreement with the homogeneous case.Comment: 4 pages and 5 figure

The Central Bank in Colombia

Abstract: In the last decade the issue of the optimal degree of central bank independence has been at the center of attention of academics and policymakers in many countries. The direction of institutional reform has almost universally been toward making central banks more independent from political pressure. The motivation of this move is linked to an increased emphasis on price stability as the main or only goal of monetary policy after two decades of exceptionally high inflation rates. Colombia has made an effort in reforming a complex set of monetary institutions, which for over two decades delivered a persistent, moderate rate of inflation. The central bank reform -along with the elimination of many indexation practices, the liberalization of financial activity and the reduction of trade and capital account barriers- delivered substantial progress. This paper argues that a reduced set of "second generation" reforms aimed at correcting limitations that were maintained may further deepen these accomplishments. We propose to make the board of the bank smaller and to remove any members of the executive from it. An appropriate timing of appointments should also create stability in the board. Lengthening the appointment tenure of the governor and board members, together with a staggering of terms, reduces the risk that every new executive brings about an entire new board, or at least a new majority in the board of the bank. The central bank should also have a clear mandate that sets inflation control as its overarching goal. This is important because the recent involvement of the Constitutional Court in the matter of the relative precedence of inflation control over other goals raises much confusion. Finally, we conclude that the central bank is the institution better suited to supervise the financial sector. While arguments pro and against using the central bank as the financial regulator certainly exist, on balance we conclude that for a middle-income country this is the best solution.Bancos Centrales, Política Monetaria, Independencia de la Banca Central, Instituciones Financieras, Economía Institucional, Reformas Institucionales

Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model

We investigate the interaction-induced superfluid-to-Mott insulator transition in the one-dimensional Bose-Hubbard model (BHM) for fillings $n=1$, $n=2$, and $n=3$ by studying the single-particle gap, the fidelity susceptibility, and the amplitude of Bloch oscillations via density-matrix renormalization-group methods. We apply a generic scaling procedure for the gap, which allows us to determine the critical points with very high accuracy. We also study how the fidelity susceptibility behaves across the phase transition. Furthermore, we show that in the BHM, and in a system of spinless fermions, the amplitude of Bloch oscillations after a tilt of the lattice vanishes at the critical points. This indicates that Bloch oscillations can serve as a tool to detect the transition point in ongoing experiments with ultracold gases.Comment: 6 pages and 4 figures, URL: http://link.aps.org/doi/10.1103/PhysRevA.87.04360

Characterization of the Bose-glass phase in low-dimensional lattices

We study by numerical simulation a disordered Bose-Hubbard model in low-dimensional lattices. We show that a proper characterization of the phase diagram on finite disordered clusters requires the knowledge of probability distributions of physical quantities rather than their averages. This holds in particular for determining the stability region of the Bose-glass phase, the compressible but not superfluid phase that exists whenever disorder is present. This result suggests that a similar statistical analysis should be performed also to interpret experiments on cold gases trapped in disordered lattices, limited as they are to finite sizes.Comment: 4+ epsilon pages and 4 figure

Phase diagram of the half-filled one-dimensional t-V-V' model

We study the phase diagram of spinless fermions with nearest and next-nearest-neighbor interactions in one dimension utilizing the (finite-size) density-matrix renormalization group (DMRG) method. The competition between nearest and next-nearest-neighbor interactions and nearest-neighbor hopping generates four phases in this model: two charge-density-wave insulators, a Luttinger liquid phase, and a bond-order phase. We use finite-size scaling of the gap and various structure factors to determine the phase diagram.Comment: 7 pages, 9 figure

Síntesis estereoselectiva de nuevos inhibidores de la agregación plaquetaria

Chirality is a feature instrinsically linked to life. For this reason, the use of stereochemically pure compounds presents numerous advantages compared to the use of racemates in pharmaceutical industry. Therefore, the present work is a part of a broader project aimed to the development of new strategies for the design and the stereoselective synthesis of chiral compounds with biological activity. In particular, we focus on the enantioselective synthesis of a new family of 4-aminocroman-2-one derivatives as antiplatelet drugs and their phosphorated analogous. These compounds constitute the basic structure of a family of inhibitors of platelet aggregation, modulator of thrombus formation, whose synthesis in optically pure form has not been developed so far. Our methodology is based on the efficiency of the tert-butylsulfinylsulfinil group as chiral inductor in nucleophilic additions to chiral N-sulfinylimines. On the one hand, the addition of the ethyl acetate anion allows the preparation of the corresponding optically pure 2-aminocromanones. On the other hand, the addition of the methyl phenylphosphinate carbanion leads to the corresponding phosphinyl bioisosteres. In both cases, the addition takes place stereoselectively and it allows, for the first time, the preparation of a diverse array of enantiopure 4-amino-croman-2-one derivatives, allowing the study of the activity of both enantiomers separately. To sum up, we have developed a new, general, easy, effective and modular methodology for the stereoselective synthesis of both enantiomers of a wide range o β-amino esters, which constitute a new family of pharmacologically relevant compoundsUniversidad de Sevilla. Grado en Farmaci