Effects of a CPT-even and Lorentz-violating nonminimal coupling on the electron-positron scattering

We propose a new \emph{CPT}-even and Lorentz-violating nonminimal coupling between fermions and Abelian gauge fields involving the CPT-even tensor $(K_{F})_{\mu\nu\alpha\beta}$ of the standard model extension. We thus investigate its effects on the cross section of the electron-positron scattering by analyzing the process $e^{+}+e^{-}\rightarrow\mu^{+}+\mu^{-}$. Such a study was performed for the parity-odd and parity-even nonbirefringent components of the Lorentz-violating $(K_{F})_{\mu\nu\alpha\beta}$ tensor. Finally, by using experimental data available in the literature, we have imposed upper bounds as tight as $10^{-12}(eV)^{-1}$ on the magnitude of the CPT-even and Lorentz-violating parameters while nonminimally coupled.Comment: LaTeX2e, 06 pages, 01 figure

Radiative generation of the CPT-even gauge term of the SME from a dimension-five nonminimal coupling term

In this letter we show for the first time that the usual CPT-even gauge term of the standard model extension (SME) can be radiatively generated, in a gauge invariant level, in the context of a modified QED endowed with a dimension-five nonminimal coupling term recently proposed in the literature. As a consequence, the existing upper bounds on the coefficients of the tensor $(K_{F})$ can be used improve the bounds on the magnitude of the nonminimal coupling, $\lambda(K_{F}),$ by the factors $10^{5}$ or $10^{25}.$ The nonminimal coupling also generates higher-order derivative contributions to the gauge field effective action quadratic terms.Comment: Revtex style, two columns, 6 pages, revised final version to be published in the Physics Letters B (2013

Phase Transition in the Number Partitioning Problem

Number partitioning is an NP-complete problem of combinatorial optimization. A statistical mechanics analysis reveals the existence of a phase transition that separates the easy from the hard to solve instances and that reflects the pseudo-polynomiality of number partitioning. The phase diagram and the value of the typical ground state energy are calculated.Comment: minor changes (references, typos and discussion of results

The initial conditions of the universe: how much isocurvature is allowed?

We investigate the constraints imposed by the current data on correlated mixtures of adiabatic and non-adiabatic primordial perturbations. We discover subtle flat directions in parameter space that tolerate large (~60%) contributions of non-adiabatic fluctuations. In particular, larger values of the baryon density and a spectral tilt are allowed. The cancellations in the degenerate directions are explored and the role of priors elucidated.Comment: 4 pages, 4 figures. Submitted to PR

Critical temperature of a fully anisotropic three-dimensional Ising model

The critical temperature of a three-dimensional Ising model on a simple cubic lattice with different coupling strengths along all three spatial directions is calculated via the transfer matrix method and a finite size scaling for L x L oo clusters (L=2 and 3). The results obtained are compared with available calculations. An exact analytical solution is found for the 2 x 2 oo Ising chain with fully anisotropic interactions (arbitrary J_x, J_y and J_z).Comment: 17 pages in tex using preprint.sty for IOP journals, no figure

Instance Space of the Number Partitioning Problem

Within the replica framework we study analytically the instance space of the number partitioning problem. This classic integer programming problem consists of partitioning a sequence of N positive real numbers \{a_1, a_2,..., a_N} (the instance) into two sets such that the absolute value of the difference of the sums of $a_j$ over the two sets is minimized. We show that there is an upper bound $\alpha_c N$ to the number of perfect partitions (i.e. partitions for which that difference is zero) and characterize the statistical properties of the instances for which those partitions exist. In particular, in the case that the two sets have the same cardinality (balanced partitions) we find $\alpha_c=1/2$. Moreover, we show that the disordered model resulting from hte instance space approach can be viewed as a model of replicators where the random interactions are given by the Hebb rule.Comment: 7 page