Entanglement of several blocks in fermionic chains

In this paper we propose an expression for the entanglement entropy of several intervals in a stationary state of a free, translational invariant Hamiltonian in a fermionic chain. We check numerically the accuracy of our proposal and conjecture a formula for the asymptotic behavior of principal submatrices of a Toeplitz matrix

Nonextensive thermodynamic functions in the Schrödinger-Gibbs ensemble

© 2015 American Physical Society. Schrödinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum system [E. Schrödinger, Statistical Thermodynamics (Courier Dover, Mineola, 1967)]. Different authors have interpreted this statement by introducing density distributions on the space of quantum pure states with weights obtained as functions of the expectation value of the Hamiltonian of the system. In this work we focus on one of the best known of these distributions and prove that, when considered in composite quantum systems, it defines partition functions that do not factorize as products of partition functions of the noninteracting subsystems, even in the thermodynamical regime. This implies that it is not possible to define extensive thermodynamical magnitudes such as the free energy, the internal energy, or the thermodynamic entropy by using these models. Therefore, we conclude that this distribution inspired by Schrödinger's idea cannot be used to construct an appropriate quantum equilibrium thermodynamics.Peer Reviewe

Algebraic Quantization, Good Operators and Fractional Quantum Numbers

The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the ``failure" of the Ehrenfest theorem is clarified in terms of the already defined notion of {\it good} (and {\it bad}) operators. The analysis of ``constrained" Heisenberg-Weyl groups according to this quantization scheme reveals the possibility for new quantum (fractional) numbers extending those allowed for Chern classes in traditional Geometric Quantization. This study is illustrated with the examples of the free particle on the circumference and the charged particle in a homogeneous magnetic field on the torus, both examples featuring ``anomalous" operators, non-equivalent quantization and the latter, fractional quantum numbers. These provide the rationale behind flux quantization in superconducting rings and Fractional Quantum Hall Effect, respectively.Comment: 29 pages, latex, 1 figure included with EPSF. Revised version with minor changes intended to clarify notation. Acepted for publication in Comm. Math. Phy

Moderating influences on the firm's strategic orientation-performance relationship

This paper is focused on the factors that moderate the relationship between firm's strategic orientation and performance in small and medium-sized firms. Much prior research has focused simply on identifying environmental conditions conducive to the effectiveness of the strategic orientation approach. However, recent research has called for studies focused on investigating internal moderators of the strategic orientation-performance relationship. As a result, we propose a contingency framework, considering how corporate and competitive strategies, top management characteristics, and environmental conditions may moderate this relationship. Based on a survey of 295 small and medium sized enterprises pertaining to seven manufacturing sectors, our study shows that the positive influence of firm's strategic orientation may be moderated by the environment conditions, the previous experience of top management team, and the corporate and competitive strategies developed by the firm

SO(2,1) conformal anomaly: Beyond contact interactions

The existence of anomalous symmetry-breaking solutions of the SO(2,1) commutator algebra is explicitly extended beyond the case of scale-invariant contact interactions. In particular, the failure of the conservation laws of the dilation and special conformal charges is displayed for the two-dimensional inverse square potential. As a consequence, this anomaly appears to be a generic feature of conformal quantum mechanics and not merely an artifact of contact interactions. Moreover, a renormalization procedure traces the emergence of this conformal anomaly to the ultraviolet sector of the theory, within which lies the apparent singularity.Comment: 11 pages. A few typos corrected in the final versio

Inequivalent quantization of the rational Calogero model with a Coulomb type interaction

We consider the inequivalent quantizations of a $N$-body rational Calogero model with a Coulomb type interaction. It is shown that for certain range of the coupling constants, this system admits a one-parameter family of self-adjoint extensions. We analyze both the bound and scattering state sectors and find novel solutions of this model. We also find the ladder operators for this system, with which the previously known solutions can be constructed.Comment: 15 pages, 3 figures, revtex4, typos corrected, to appear in EPJ

The Drosophila melanogaster Genetic Reference Panel

A major challenge of biology is understanding the relationship between molecular genetic variation and variation in quantitative traits, including fitness. This relationship determines our ability to predict phenotypes from genotypes and to understand how evolutionary forces shape variation within and between species. Previous efforts to dissect the genotype-phenotype map were based on incomplete genotypic information. Here, we describe the Drosophila melanogaster Genetic Reference Panel (DGRP), a community resource for analysis of population genomics and quantitative traits. The DGRP consists of fully sequenced inbred lines derived from a natural population. Population genomic analyses reveal reduced polymorphism in centromeric autosomal regions and the X chromosome, evidence for positive and negative selection, and rapid evolution of the X chromosome. Many variants in novel genes, most at low frequency, are associated with quantitative traits and explain a large fraction of the phenotypic variance. The DGRP facilitates genotype-phenotype mapping using the power of Drosophila genetics