Integrals of motion in the Many-Body localized phase

We construct a complete set of quasi-local integrals of motion for the many-body localized phase of interacting fermions in a disordered potential. The integrals of motion can be chosen to have binary spectrum $\{0,1\}$, thus constituting exact quasiparticle occupation number operators for the Fermi insulator. We map the problem onto a non-Hermitian hopping problem on a lattice in operator space. We show how the integrals of motion can be built, under certain approximations, as a convergent series in the interaction strength. An estimate of its radius of convergence is given, which also provides an estimate for the many-body localization-delocalization transition. Finally, we discuss how the properties of the operator expansion for the integrals of motion imply the presence or absence of a finite temperature transition.Comment: 65 pages, 12 figures. Corrected typos, added reference

Studying the infrared region in Landau gauge QCD

We report on the progress we made in studying the infrared behavior of the ghost and gluon dressing functions in Landau gauge. Related to this we also investigate a running coupling given in terms of those functions and compare our results to those coming from the Dyson-Schwinger approach. We present first numerical results for the SU(3) ghost-ghost-gluon vertex renormalization constant. In addition the spectrum of low-lying eigenvalues and eigenfunctions of the Faddeev-Popov operator is determined. The saturation of the ghost propagator in terms of those eigenvalues and eigenmodes is discussed at lower momenta.Comment: 6 pages, 4 figures, talk presented at Lattice 2005 (Topology and Confinement

The influence of Gribov copies on the gluon and ghost propagator

The dependence of the gluon and ghost propagator in pure SU(3) gauge theory on the choice of Gribov copies in Landau gauge is studied. Simulations were performed on several lattice sizes at $\beta$=5.8, 6.0 and 6.2. In the infrared region the ghost propagator turns out to depend on the choice, while the impact on the gluon propagator is not resolvable. Also the eigenvalue distribution of the Faddeev-Popov operator is sensitive to Gribov copies.Comment: Talk presented at Quark Confinement and the Hadron Spectrum VI, Villasimius, Sardinia, Italy, September 21-25, 2004, 3 pages, 2 figure

A Modified "Bottom-up" Thermalization in Heavy Ion Collisions

In the initial stage of the bottom-up picture of thermalization in heavy ion collisions, the gluon distribution is highly anisotropic which can give rise to plasma instability. This has not been taken account in the original paper. It is shown that in the presence of instability there are scaling solutions, which depend on one parameter, that match smoothly onto the late stage of bottom-up when thermalization takes place.Comment: 8 pages and 1 embedded figure, talk presented at the Workshop on "Quark-Gluon Plasma Thermalization", Vienna, Austria, 10-12 August 200

Confinement potential in dual Monopole Nambu-Jona-Lasinio model with dual Dirac strings

Interquark confinement potential is calculated in the dual Monopole Nambu-Jona-Lasinio model with dual Dirac strings as a functional of a dual Dirac string length. The calculation is carried out by the explicit integration over quantum fluctuations of a dual-vector field (monopole-antimonopole collective excitation) around the Abrikosov flux line and string shape fluctuations. The contribution of the scalar field (monopole-antimonopole collective excitation) exchange is taken into account in the tree approximation due to the London limit regime.Comment: 10 pages, Latex, no figure

Quantum and string shape fluctuations in the dual Monopole Nambu-Jona-Lasinio model with dual Dirac strings

The magnetic monopole condensate is calculated in the dual Monopole Nambu-Jona-Lasinio model with dual Dirac strings suggested in Refs.[1,2] as a functional of the dual Dirac string shape. The calculation is carried out in the tree approximation in the scalar monopole-antimonopole collective excitation field. The integration over quantum fluctuations of the dual-vector monopole-antimonopole collective excitation field around the Abrikosov flux line and string shape fluctuations are performed explicitly. We claim that there are important contributions of quantum and string shape fluctuations to the magnetic monopole condensate.Comment: 19 pages, Latex, 2 figure

The core helium flash revisited: II. Two and three-dimensional hydrodynamic simulations

We study turbulent convection during the core helium flash close to its peak by comparing the results of two and three-dimensional hydrodynamic simulations. We use a multidimensional Eulerian hydrodynamics code based on state-of-the-art numerical techniques to simulate the evolution of the helium core of a $1.25 M_{\odot}$ Pop I star. Our three-dimensional hydrodynamic simulations of the evolution of a star during the peak of the core helium flash do not show any explosive behavior. The convective flow patterns developing in the three-dimensional models are structurally different from those of the corresponding two-dimensional models, and the typical convective velocities are smaller than those found in their two-dimensional counterparts. Three-dimensional models also tend to agree better with the predictions of mixing length theory. Our hydrodynamic simulations show the presence of turbulent entrainment that results in a growth of the convection zone on a dynamic time scale. Contrary to mixing length theory, the outer part of the convection zone is characterized by a sub-adiabatic temperature gradient.Comment: 19 pages, 18 figure