Mesoscopic Fermi gas in a harmonic trap

We study the thermodynamical properties of a mesoscopic Fermi gas in view of recent possibilities to trap ultracold atoms in a harmonic potential. We focus on the effects of shell closure for finite small atom numbers. The dependence of the chemical potential, the specific heat and the density distribution on particle number and temperature is obtained. Isotropic and anisotropic traps are compared. Possibilities of experimental observations are discussed.Comment: 8 pages, 9 eps-figures included, Revtex, submitted to Phys. Rev. A, minor changes to figures and captions, corrected typo

Rationality and the experimental study of reasoning

A survey of the results obtained during the past three decades in some of the most widely used tasks and paradigms in the experimental study of reasoning is presented. It is shown that, at first sight, human performance suffers from serious shortcomings. However, after the problems of communication between experimenter and subject are taken into account, which leads to clarify the subject's representation of the tasks, one observes a better performance, although still far from perfect. Current theories of reasoning, of which the two most prominent are very briefly outlined, agree in identifying the load in working memory as the main source of limitation in performance. Finally, a recent view on human rationality prompted by the foregoing results is described

A Rigourous Treatment of the Lattice Renormalization Problem of F_B

The $B$-meson decay constant can be measured on the lattice using a $1/m_b$ expansion. To relate the physical quantity to Monte Carlo data one has to know the renormalization coefficient, $Z$, between the lattice operators and their continuum counterparts. We come back to this computation to resolve discrepancies found in previous calculations. We define and discuss in detail the renormalization procedure that allows the (perturbative) computation of $Z$. Comparing the one-loop calculations in the effective Lagrangian approach with the direct two-loop calculation of the two-point $B$-meson correlator in the limit of large $b$-quark mass, we prove that the two schemes give consistent results to order $\alpha_s$. We show that there is, however, a renormalization prescription ambiguity that can have sizeable numerical consequences. This ambiguity can be resolved in the framework of an $O(a)$ improved calculation, and we describe the correct prescription in that case. Finally we give the numerical values of $Z$ that correspond to the different types of lattice approximations discussed in the paper.Comment: 27 pages, 2 figures (Plain TeX, figures in an appended postscript file

A sandpile model with tokamak-like enhanced confinement phenomenology

Confinement phenomenology characteristic of magnetically confined plasmas emerges naturally from a simple sandpile algorithm when the parameter controlling redistribution scalelength is varied. Close analogues are found for enhanced confinement, edge pedestals, and edge localised modes (ELMs), and for the qualitative correlations between them. These results suggest that tokamak observations of avalanching transport are deeply linked to the existence of enhanced confinement and ELMs.Comment: Manuscript is revtex (latex) 1 file, 7 postscript figures Revised version is final version accepted for publication in PRL Revisions are mino

Consistency of the Regularization of Gauge Theories by High Covariant Derivatives

We show that regularization of gauge theories by higher covariant derivatives and gauge invariant Pauli-Villars regulators is a consistent method if the Pauli-Villars vector fields are considered in a covariant in the regulating Pauli-Villars fields is pathological and the original Slavnov proposal in covariant Landau gauge is not correct because of the appearance of massless modes in the regulators which do not decouple when the ultraviolet regulator is removed. In such a case the method does not correspond to the regularization of a pure gauge theory but that of a gauge theory in interaction with massless ghost fields. This explains the problems pointed out by Martin and Ruiz in covariant Landau gauge. However, a minor modification of Slavnov method provides a consistent regularization even for such a case. The regularization that we introduce also solves the problem of overlapping divergences in a way similar to geometric regularization and yields the standard values of the $\beta$ and $\gamma$ functions of the renormalization group equations.Comment: 20 pages, latex, 3 Postscript figures (expanded version

Quark propagator and vertex: systematic corrections of hypercubic artifacts from lattice simulations

This is the first part of a study of the quark propagator and the vertex function of the vector current on the lattice in the Landau gauge and using both Wilson-clover and overlap actions. In order to be able to identify lattice artifacts and to reach large momenta we use a range of lattice spacings. The lattice artifacts turn out to be exceedingly large in this study. We present a new and very efficient method to eliminate the hypercubic (anisotropy) artifacts based on a systematic expansion on hypercubic invariants which are not SO(4) invariant. A simpler version of this method has been used in previous works. This method is shown to be significantly more efficient than the popular ``democratic'' methods. It can of course be applied to the lattice simulations of many other physical quantities. The analysis indicates a hierarchy in the size of hypercubic artifacts: overlap larger than clover and propagator larger than vertex function. This pleads for the combined study of propagators and vertex functions via Ward identities.Comment: 14 pags., 9 fig

Chiral phase transition at high temperature in the QCD-like gauge theory

The chiral phase transition at high temperature is investigated using the effect ive potential in the framework of the QCD-like gauge theory with a variational a pproach. We have a second order phase transition at $T_c=136$MeV. We also investigate numerically the temperature dependence of condensate, $f_\pi$ a nd $a_2(T)$(coefficient of the quadratic term in the effective potential) and es timate the critical exponents of these quantities.Comment: 12 pages,7 figure

Three-loop \beta-functions for top-Yukawa and the Higgs self-interaction in the Standard Model

We analytically compute the dominant contributions to the \beta-functions for the top-Yukawa coupling, the strong coupling and the Higgs self-coupling as well as the anomalous dimensions of the scalar, gluon and quark fields in the unbroken phase of the Standard Model at three-loop level. These are mainly the QCD and top-Yukawa corrections. The contributions from the Higgs self-interaction which are negligible for the running of the top-Yukawa and the strong coupling but important for the running of the Higgs self-coupling are also evaluated.Comment: 22 pages, 7 figures. Few extra citations are added; the plots are improved. Results in computer readable form can be retrieved from http://www-ttp.particle.uni-karlsruhe.de/Progdata/ttp12/ttp12-012

Finite N Fluctuation Formulas for Random Matrices

For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic $\sum_{j=1}^N (x_j - )$ is computed exactly and shown to satisfy a central limit theorem as $N \to \infty$. For the circular random matrix ensemble the p.d.f.'s for the linear statistics ${1 \over 2} \sum_{j=1}^N (\theta_j - \pi)$ and $- \sum_{j=1}^N \log 2|\sin \theta_j/2|$ are calculated exactly by using a constant term identity from the theory of the Selberg integral, and are also shown to satisfy a central limit theorem as $N \to \infty$.Comment: LaTeX 2.09, 11 pages + 3 eps figs (needs epsf.sty

Bragg spectroscopy of a Bose-Einstein condensate

Properties of a Bose-Einstein condensate were studied by stimulated, two-photon Bragg scattering. The high momentum and energy resolution of this method allowed a spectroscopic measurement of the mean-field energy and of the intrinsic momentum uncertainty of the condensate. The coherence length of the condensate was shown to be equal to its size. Bragg spectroscopy can be used to determine the dynamic structure factor over a wide range of energy and momentum transfers.Comment: 4 pages, 3 figure