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

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

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

Life and death of a hero - Lessons learned from modeling the dwarf spheroidal Hercules: an incorrect orbit?

Hercules is a dwarf spheroidal satellite of the Milky Way, found at a distance of about 138 kpc, and showing evidence of tidal disruption. It is very elongated and exhibits a velocity gradient of 16 +/- 3 km/s/kpc. Using this data a possible orbit of Hercules has previously been deduced in the literature. In this study we make use of a novel approach to find a best fit model that follows the published orbit. Instead of using trial and error, we use a systematic approach in order to find a model that fits multiple observables simultaneously. As such, we investigate a much wider parameter range of initial conditions and ensure we have found the best match possible. Using a dark matter free progenitor that undergoes tidal disruption, our best-fit model can simultaneously match the observed luminosity, central surface brightness, effective radius, velocity dispersion, and velocity gradient of Hercules. However, we find it is impossible to reproduce the observed elongation and the position angle of Hercules at the same time in our models. This failure persists even when we vary the duration of the simulation significantly, and consider a more cuspy density distribution for the progenitor. We discuss how this suggests that the published orbit of Hercules is very likely to be incorrect.Comment: accepted by MNRAS; 19 pages, 19 figures, 2 table

Ursa Major II - Reproducing the observed properties through tidal disruption

Recent deep photometry of the dwarf spheroidal Ursa Major II's morphology, and spectroscopy of individual stars, have provided a number of new constraints on its properties. With a velocity dispersion $\sim$6 km s$^{-1}$, and under the assumption that the galaxy is virialised, the mass-to-light ratio is found to be approaching $\sim$2000 - apparently heavily dark matter dominated. Using N-Body simulations, we demonstrate that the observed luminosity, ellipticity, irregular morphology, velocity gradient, and the velocity dispersion can be well reproduced through processes associated with tidal mass loss, and in the absence of dark matter. These results highlight the considerable uncertainty that exists in measurements of the dark matter content of Ursa Major II. The dynamics of the inner tidal tails, and tidal stream, causes the observed velocity dispersion of stars to be boosted to values of $>$5 km s$^{-1}$ ($>$20 km s$^{-1}$ at times). This effect is responsible for raising the velocity dispersion of our model to the observed values in UMaII. We test an iterative rejection technique for removing unbound stars from samples of UMaII stars whose positions on the sky, and line-of-sight velocities, are provided. We find this technique is very effective at providing an accurate bound mass from this information, and only fails when the galaxy has a bound mass less than 10$$ of its initial mass. However when $<2$ mass remains bound, mass overestimation by $>$3 orders of magnitude are seen. Additionally we find that mass measurements are sensitive to measurement uncertainty in line-of-sight velocities. Measurement uncertainties of 1-4 km s$^{-1}$ result in mass overestimates by a factor of $\sim$1.3-5.7.Comment: 17 pages, 12 figures, accepted to MNRAS: 23rd, May, 201

Electric and magnetic fields effects on the excitonic properties of elliptic core-multishell quantum wires

The effect of eccentricity distortions of core-multishell quantum wires on their electron, hole and exciton states is theoretically investigated. Within the effective mass approximation, the Schrodinger equation is numerically solved for electrons and holes in systems with single and double radial heterostructures, and the exciton binding energy is calculated by means of a variational approach. We show that the energy spectrum of a core-multishell heterostructure with eccentricity distortions, as well as its magnetic field dependence, are very sensitive to the direction of an externally applied electric field, an effect that can be used to identify the eccentricity of the system. For a double heterostructure, the eccentricities of the inner and outer shells play an important role on the excitonic binding energy, specially in the presence of external magnetic fields, and lead to drastic modifications in the oscillator strength.Comment: 17 pages, 10 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.