Analytic Methods in Nonperturbative QCD

Recently developed analytic methods in the framework of the Field Correlator Method are reviewed in this series of four lectures and results of calculations are compared to lattice data and experiment. Recent lattice data demonstrating the Casimir scaling of static quark interaction strongly support the FCM and leave very little space for all other theoretical models, e.g. instanton gas/liquid model. Results of calculations for mesons, baryons, quark-gluon plasma and phase transition temperature demonstrate that new analytic methods are a powerful tool of nonperturbative QCD along with lattice simulations.Comment: LaTeX, 34 pages; Lectures given at the 13th Indian-Summer School "Understanding the Structure of Hadrons", August 28 - September 1, 2000, Prague, Czech Republi

Bethe--Salpeter equation in QCD

We extend to regular QCD the derivation of a confining $q \bar{q}$ Bethe--Salpeter equation previously given for the simplest model of scalar QCD in which quarks are treated as spinless particles. We start from the same assumptions on the Wilson loop integral already adopted in the derivation of a semirelativistic heavy quark potential. We show that, by standard approximations, an effective meson squared mass operator can be obtained from our BS kernel and that, from this, by ${1\over m^2}$ expansion the corresponding Wilson loop potential can be reobtained, spin--dependent and velocity--dependent terms included. We also show that, on the contrary, neglecting spin--dependent terms, relativistic flux tube model is reproduced.Comment: 23 pages, revte

Magnetic string contribution to hadron dynamics in QCD

Dynamics of a light quark in the field of static source (heavy-light meson) is studied using the nonlinear Dirac equation, derived recently. Special attention is paid to the contribution of magnetic correlators and it is found that it yields a significant increase of string tension at intermediate distances. The spectrum of heavy-light mesons is computed with account of this contribution and compared to experimental and lattice data.Comment: 10 pages Revte

Parton Saturation-An Overview

The idea of partons and the utility of using light-cone gauge in QCD are introduced. Saturation of quark and gluon distributions are discussed using simple models and in a more general context. The Golec-Biernat W\usthoff model and some simple phenomenology are described. A simple, but realistic, equation for unitary, the Kovchegov equation, is discussed, and an elementary derivation of the JIMWLK equation is given.Comment: Cargese Lectures, 34 pages, 19 figure

The three-dimensional randomly dilute Ising model: Monte Carlo results

We perform a high-statistics simulation of the three-dimensional randomly dilute Ising model on cubic lattices $L^3$ with $L\le 256$. We choose a particular value of the density, x=0.8, for which the leading scaling corrections are suppressed. We determine the critical exponents, obtaining $\nu = 0.683(3)$, $\eta = 0.035(2)$, $\beta = 0.3535(17)$, and $\alpha = -0.049(9)$, in agreement with previous numerical simulations. We also estimate numerically the fixed-point values of the four-point zero-momentum couplings that are used in field-theoretical fixed-dimension studies. Although these results somewhat differ from those obtained using perturbative field theory, the field-theoretical estimates of the critical exponents do not change significantly if the Monte Carlo result for the fixed point is used. Finally, we determine the six-point zero-momentum couplings, relevant for the small-magnetization expansion of the equation of state, and the invariant amplitude ratio $R^+_\xi$ that expresses the universality of the free-energy density per correlation volume. We find $R^+_\xi = 0.2885(15)$.Comment: 34 pages, 7 figs, few correction

Chiral Lagrangian with confinement from the QCD Lagrangian

An effective Lagrangian for the light quark in the field of a static source is derived systematically using the exact field correlator expansion. The lowest Gaussian term is bosonized using nonlocal colorless bosonic fields and a general structure of effective chiral Lagrangian is obtained containing all set of fields. The new and crucial result is that the condensation of scalar isoscalar field which is a usual onset of chiral symmetry breaking and is constant in space-time, assumes here the form of the confining string and contributes to the confining potential, while the rest bosonic fields describe mesons with the q\bar q quark structure and pseudoscalars play the role of Nambu-Goldstone fields. Using derivative expansion the effective chiral Lagrangian is deduced containing both confinement and chiral effects for heavy-light mesons. The pseudovector quark coupling constant is computed to be exactly unity in the local limit,in agreement with earlier large N_c arguments.Comment: LaTeX2e, 17 page

Magnetic field strength and orientation effects on co-fe discontinuous multilayers close to percolation

International audienceMagnetization and magnetoresistance in function of the magnitude and orientation of applied magnetic field were studied in Co-Fe discontinuous multilayers close to their structural percolation. The high pulsed magnetic fields up to 33 T were used in the 120–310 K temperature range. Comparison between longitudinal and transverse with respect to the film plane field configurations was made in the low-field and high-field regimes in order to clarify the nature of the measured negative magnetoresistance. Coexistence of two distinct magnetic fractions, superparamagnetic SPM, consisting of small spherical Co-Fe granules and superferromagnetic SFM, by bigger Co-Fe clusters, was established in this system. These fractions were shown to have different relevance for the system magnetization and magnetotransport. While the magnetization is almost completely up to 97% defined by the SFM contribution and practically independent of temperature in this range, the magnetoresistance experiences a crossover from a regime dominated by Langevin correlations suppressed with temperature between neighbor SPM and SFM moments at low fields, to that dominated by spin scattering enhanced with temperature of charge carriers within SFM clusters at high fields. Also, the demagnetizing effects, sensitive to the field orientation, were found to essentially define the low-field behavior and characteristic crossover field

Nonlinear atom optics and bright gap soliton generation in finite optical lattices

We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture for the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due the atom-atom interaction are discussed in detail, such as atom optical limiting and atom optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A new scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded in a controlled way starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties

Quantitative Treatment of Decoherence

We outline different approaches to define and quantify decoherence. We argue that a measure based on a properly defined norm of deviation of the density matrix is appropriate for quantifying decoherence in quantum registers. For a semiconductor double quantum dot qubit, evaluation of this measure is reviewed. For a general class of decoherence processes, including those occurring in semiconductor qubits, we argue that this measure is additive: It scales linearly with the number of qubits.Comment: Revised version, 26 pages, in LaTeX, 3 EPS figure