Towards Noncommutative Linking Numbers Via the Seiberg-Witten Map

In the present work some geometric and topological implications of noncommutative Wilson loops are explored via the Seiberg-Witten map. In the abelian Chern-Simons theory on a three dimensional manifold, it is shown that the effect of noncommutativity is the appearance of $6^n$ new knots at the $n$-th order of the Seiberg-Witten expansion. These knots are trivial homology cycles which are Poincar\'e dual to the high-order Seiberg-Witten potentials. Moreover the linking number of a standard 1-cycle with the Poincar\'e dual of the gauge field is shown to be written as an expansion of the linking number of this 1-cycle with the Poincar\'e dual of the Seiberg-Witten gauge fields. In the process we explicitly compute the noncommutative 'Jones-Witten' invariants up to first order in the noncommutative parameter. Finally in order to exhibit a physical example, we apply these ideas explicitly to the Aharonov-Bohm effect. It is explicitly displayed at first order in the noncommutative parameter, we also show the relation to the noncommutative Landau levels.Comment: 19 pages, 1 figur

Luttinger liquid superlattices: realization of gapless insulating phases

We investigate Luttinger Liquid superlattices, a periodic structure composed of two kinds of one-dimensional systems of interacting electrons. We calculate several properties of the low-energy sector: the effective charge and spin velocities, the compressibility, various correlation functions, the Landauer conductance and the Drude weight. The low-energy properties are subsumed into effective parameters, much like homogeneous one-dimensional systems. A generic result is the weighted average nature of these parameters, in proportion to the spatial extent of the underlying subunits, pointing to the possibility of ``engineered'' structures. As a specific realization, we consider a one-dimensional Hubbard superlattice, which consists of a periodic arrangement of two long Hubbard chains with different coupling constants and different hopping amplitudes. This system exhibits a rich phase diagram with several phases, both metallic and insulating. We have found that gapless insulating phases are present over a wide range of parameters.Comment: 16 pages, 15 figures, RevTeX

Jeans' gravitational instability and nonextensive kinetic theory

The concept of Jeans gravitational instability is rediscussed in the framework of nonextensive statistics and its associated kinetic theory. A simple analytical formula generalizing the Jeans criterion is derived by assuming that the unperturbed self- gravitating collisionless gas is kinetically described by the $q$-parameterized class of power law velocity distributions. It is found that the critical values of wavelength and mass depend explicitly on the nonextensive $q$-parameter. The standard Jeans wavelength derived for a Maxwellian distribution is recovered in the limiting case $q$=1. For power-law distributions with cutoff, the instability condition is weakened with the system becoming unstable even for wavelengths of the disturbance smaller than the standard Jeans length $\lambda_J$.Comment: 5 pages, including 3 figures. Accepted for publication in A&

Genetic diversity of Lusitano horse in Brazil using pedigree information

This study aimed to evaluate population parameters and to describe the genetic diversity of the Lusitano breed in Brazil using pedigree data. Two populations were evaluated: total population (TP) containing 18,922 animals, and reference population (RP) composed of a part of TP containing 8,329 animals, representing the last generation. The generation interval (10.1 ± 5.1 years) was in the range for horse populations. Pedigree completeness in RP shows almost 100% filling in the three most recent generations, indicating improvement in the pedigree data and accuracy of the results, and the inbreeding coefficient (4.46%) and average relatedness (5.97%) for RP, indicating control on the part of breeders. The effective population size was 89 (TP) and 90 (RP). The effective number of founders (fe) were 33 and 29, effective number of ancestors (fa) were 30 and 26, and effective number of founder genomes (fg) were 19 and 15 for TP and RP, respectively, indicating a reduction of genetic variability in the last generations. The total number of ancestors that explains 100% of the genetic diversity in the Lusitano breed in Brazil was 427 (TP) and 341 (RP). The reproductive parameters, probabilities of gene origin showing loss of variability in the last generations, and the genetic contributions of ancestors suggest the need to monitor genetic diversity over time in breeding programs to allow control of the next generations and to increase their variability.info:eu-repo/semantics/publishedVersio