Cutoff-independent regularization of four-fermion interactions for color superconductivity

We implement a cutoff-independent regularization of four-fermion interactions to calculate the color-superconducting gap parameter in quark matter. The traditional cutoff regularization has difficulties for chemical potentials \mu of the order of the cutoff \Lambda, predicting in particular a vanishing gap at \mu \sim \Lambda. The proposed cutoff-independent regularization predicts a finite gap at high densities and indicates a smooth matching with the weak coupling QCD prediction for the gap at asymptotically high densities.Comment: 5 pages, 1 eps figure - Revised manuscript to match the published pape

Hadronic current correlation functions at finite temperature in the NJL model

Recently there have been suggestions that for a proper description of hadronic matter and hadronic correlation functions within the NJL model at finite density/temperature the parameters of the model should be taken density/temperature dependent. Here we show that qualitatively similar results can be obtained using a cutoff-independent regularization of the NJL model. In this regularization scheme one can express the divergent parts at finite density/temperature of the amplitudes in terms of their counterparts in vacuum.Comment: Presented at 9th Hadron Physics and 8th Relativistic Aspects of Nuclear Physics (HADRON-RANP 2004): A Joint Meeting on QCD and QGP, Angra dos Reis, Rio de Janeiro, Brazil, 28 Mar - 3 Apr 200

A comparison of unit root test criteria

During the past fifteen years, the ordinary least squares estimator and the corresponding pivotal statistic have been widely used for testing the unit root hypothesis in autoregressive processes. Recently, several new criteriia, based on the maximum likelihood estimators and weighted symmetric estimators, have been proposed. In this article, we describe several different test criteria. Results from a Monte Carlo study that compares the power of the different criteria indicates that the new tests are more powerful against the stationary alternative. Of the procedures studied, the weighted symmetric estimator and the unconditional maximum likelihood estimator provide the most powerful tests against the stationary alternative. As an illustration, we analyze the quarterly change in busine;ss investories

The split-operator technique for the study of spinorial wavepacket dynamics

The split-operator technique for wave packet propagation in quantum systems is expanded here to the case of propagating wave functions describing Schr\"odinger particles, namely, charge carriers in semiconductor nanostructures within the effective mass approximation, in the presence of Zeeman effect, as well as of Rashba and Dresselhaus spin-orbit interactions. We also demonstrate that simple modifications to the expanded technique allow us to calculate the time evolution of wave packets describing Dirac particles, which are relevant for the study of transport properties in graphene.Comment: 19 pages, 4 figure

Extension of the Nambu--Jona-Lasinio model at high densities and temperatures by using an implicit regularization scheme

Traditional cutoff regularization schemes of the Nambu--Jona-Lasinio model limit the applicability of the model to energy-momentum scales much below the value of the regularizing cutoff. In particular, the model cannot be used to study quark matter with Fermi momenta larger than the cutoff. In the present work an extension of the model to high temperatures and densities recently proposed by Casalbuoni, Gatto, Nardulli, and Ruggieri is used in connection with an implicit regularization scheme. This is done by making use of scaling relations of the divergent one-loop integrals that relate these integrals at different energy-momentum scales. Fixing the pion decay constant at the chiral symmetry breaking scale in the vacuum, the scaling relations predict a running coupling constant that decreases as the regularization scale increases, implementing in a schematic way the property of asymptotic freedom of quantum chromodynamics. If the regularization scale is allowed to increase with density and temperature, the coupling will decrease with density and temperature, extending in this way the applicability of the model to high densities and temperatures. These results are obtained without specifying an explicit regularization. As an illustration of the formalism, numerical results are obtained for the finite density and finite temperature quark condensate, and to the problem of color superconductivity at high quark densities and finite temperature.Comment: 7 pages, 5 eps figures - in version 3, substantial changes in text, results and conclusions unchanged. To be published in Phys. Rev.

Snake states in graphene quantum dots in the presence of a p-n junction

We investigate the magnetic interface states of graphene quantum dots that contain p-n junctions. Within a tight-binding approach, we consider rectangular quantum dots in the presence of a perpendicular magnetic field containing p-n, as well as p-n-p and n-p-n junctions. The results show the interplay between the edge states associated with the zigzag terminations of the sample and the snake states that arise at the p-n junction, due to the overlap between electron and hole states at the potential interface. Remarkable localized states are found at the crossing of the p-n junction with the zigzag edge having a dumb-bell shaped electron distribution. The results are presented as function of the junction parameters and the applied magnetic flux.Comment: 13 pages, 23 figures, to be appeared in Phys. Rev.