Improved non-perturbative renormalization without cNGIc_{NGI}

Recently, a method for O(a) improvement of composite operators has been proposed which uses the large momentum behavior of fixed gauge quark and gluon correlation functions (G. Martinelli et al., hep-lat/0106003). A practical problem with this method is that a particular improvement coefficient, $c_{NGI}$, which has a gauge non-covariant form, is difficult to determine. Here I work out the size of the errors made in improvement coefficients and physical quantities if one does not include the $c_{NGI}$ term.Comment: 3 pages. Lattice2001(improvement

Numerical Exploration of the RI/MOM Scheme Gauge Dependence

The gauge dependence of some fermion bilinear RI/MOM renormalization constants is studied by comparing data which have been gauge-fixed in two different realizations of the Landau gauge and in a generic covariant gauge. The very good agreement between the various sets of results and the theory indicates that the numerical uncertainty induced by the lattice gauge-fixing procedure is below the statistical errors of our data sample which is of the order of (1-1.5)%.Comment: 3 pages, 2 figures, Lattice2002(theoretical

Glauber dynamics for the quantum Ising model in a transverse field on a regular tree

Motivated by a recent use of Glauber dynamics for Monte-Carlo simulations of path integral representation of quantum spin models [Krzakala, Rosso, Semerjian, and Zamponi, Phys. Rev. B (2008)], we analyse a natural Glauber dynamics for the quantum Ising model with a transverse field on a finite graph $G$. We establish strict monotonicity properties of the equilibrium distribution and we extend (and improve) the censoring inequality of Peres and Winkler to the quantum setting. Then we consider the case when $G$ is a regular $b$-ary tree and prove the same fast mixing results established in [Martinelli, Sinclair, and Weitz, Comm. Math. Phys. (2004)] for the classical Ising model. Our main tool is an inductive relation between conditional marginals (known as the "cavity equation") together with sharp bounds on the operator norm of the derivative at the stable fixed point. It is here that the main difference between the quantum and the classical case appear, as the cavity equation is formulated here in an infinite dimensional vector space, whereas in the classical case marginals belong to a one-dimensional space

Comparison of Swendsen-Wang and Heat-Bath Dynamics

We prove that the spectral gap of the Swendsen-Wang process for the Potts model on graphs with bounded degree is bounded from below by some constant times the spectral gap of any single-spin dynamics. This implies rapid mixing of the Swendsen-Wang process for the two-dimensional Potts model at all temperatures above the critical one, as well as rapid mixing at the critical temperature for the Ising model. After this we introduce a modified version of the Swendsen-Wang algorithm for planar graphs and prove rapid mixing for the two-dimensional Potts models at all non-critical temperatures.Comment: 22 pages, 1 figur

A High-Statistics Lattice Calculation of λ1\lambda_1 and λ2\lambda_2 in the BB meson

We present a high-statistics lattice calculation of the kinetic energy $-\lambda_1/2 m_b$ of the heavy quark inside the $B$-meson and of the chromo-magnetic term $\lambda_2$, related to the $B^*$--$B$ mass splitting, performed in the HQET. Our results have been obtained from a numerical simulation based on 600 gauge field configurations generated at $\beta=6.0$, on a lattice volume $24^3 \times 40$ and using, for the meson correlators, the results obtained with the SW-Clover $O(a)$ improved lattice action for the light quarks. For the kinetic energy we found $-\lambda_1=\langle B \vert \bar h (i\vec{D})^{2} h \vert B \rangle /(2 M_B )=-(0.09 \pm 0.14)$~GeV$^2$, which is interesting for phenomenological applications. We also find $\lambda_2= 0.07 \pm 0.01$ GeV$^2$, corresponding to $M^2_{B^*}-M^2_B= 4 \lambda_2= 0.280 \pm 0.060$ GeV$^2$, which is about one half of the experimental value. The origin of the discrepancy with the experimental number needs to be clarified.Comment: 26 pages, latex, 5 figure

Organocatalytic stereodivergent synthesis of β,β-disubstituted-α-aminoacids

In this work, we present an organocatalytic stereodivergent synthesis of β,β-disubstituted-α-aminoacids using arylidene azlactones as starting materials. The developed two step synthesis involves a sequential catalysis approach, in which two different catalysts act sequentially to control the absolute configuration of two different stereocenters. With an accurate selection of the catalysts absolute configuration it is possible to obtain all the stereoisomers of the product. The first synthetic step is a catalytic asymmetric transfer hydrogenation of the azlactone C=C double bond. A Jacobsen type thiourea and a Hantzsch ester were chosen as chiral catalyst and hydride donor, respectively. Different azlactones, Hantzsch esters and thioureas were synthetized and tested in the asymmetric transfer hydrogenation to achieve the best stereoselectivity. The second step involves a dynamic kinetic resolution on the reduced azlactone, through a nucleophilic addition to the carbonyl moiety promoted by a bifunctional chiral catalyst. A wide range of nucleophiles and organocatalysts were tested; the best results were reached with alcohols as nucleophiles and squaramide-based cinchona alkaloids as a chiral catalysts. With the optimized conditions two stereodivergent syntheses were then performed, enabling the selective obtainment of both diastereoisomeric product with high enantioselectivities

Small firms, borrowing constraints, and reputation

This paper presents a simple model relating firm age with firm size and access to credit markets. Lending to new firms is risky because lenders have had no time to accumulate observations about them. As a result, interest rates are high and loans are small for entering firms. As firms need credit to operate, credit markets impose a limit on the scale of operation of new firms. Reputation building by the firms allows markets to overcome these difficulties over time. Large firms face lower interest rates than small firms, and credit markets fluctuations are shown to have different effects on firms of different size