Variational Approach to Yang--Mills Theory with non-Gaussian Wave Functionals

A general method for treating non-Gaussian wave functionals in quantum field theory is presented and applied to the Hamiltonian approach to Yang-Mills theory in Coulomb gauge in order to include a three-gluon kernel in the exponential of the vacuum wave functional. The three-gluon vertex is calculated using the propagators found in the variational approach with a Gaussian trial wave functional as input.Comment: 3 pages, 4 figures, talk presented at "Quark Confinement and the Hadron Spectrum IX", Madrid, August 30-September 3, 2010, to appear in the proceeding

Dynamical Phase Transitions for Fluxes of Mass on Finite Graphs

We study the time-averaged flux in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate functional of the average flux is given by a variational formulation involving paths of the density and flux. We give sufficient conditions under which the large deviations of a given time averaged flux is determined by paths that are constant in time. We then consider a class of models on a discrete ring for which it is possible to show that a better strategy is obtained producing a time-dependent path. This phenomenon, called a dynamical phase transition, is known to occur for some particle systems in the hydrodynamic scaling limit, which is thus extended to the setting of a finite graph

Non-Gaussian wave functionals in Coulomb gauge Yang--Mills theory

A general method to treat non-Gaussian vacuum wave functionals in the Hamiltonian formulation of a quantum field theory is presented. By means of Dyson--Schwinger techniques, the static Green functions are expressed in terms of the kernels arising in the Taylor expansion of the exponent of the vacuum wave functional. These kernels are then determined by minimizing the vacuum expectation value of the Hamiltonian. The method is applied to Yang--Mills theory in Coulomb gauge, using a vacuum wave functional whose exponent contains up to quartic terms in the gauge field. An estimate of the cubic and quartic interaction kernels is given using as input the gluon and ghost propagators found with a Gaussian wave functional.Comment: 27 pages, 21 figure

The deconfinement phase transition in the Hamiltonian approach to Yang--Mills theory in Coulomb gauge

The deconfinement phase transition of SU(2) Yang--Mills theory is investigated in the Hamiltonian approach in Coulomb gauge assuming a quasi-particle picture for the grand canonical gluon ensemble. The thermal equilibrium state is found by minimizing the free energy with respect to the quasi-gluon energy. Above the deconfinement phase transition the ghost form factor remains infrared divergent but its infrared exponent is approximately halved, while the gluon energy, being infrared divergent in the confined phase, becomes infrared finite in the deconfined phase. For the effective gluon mass we find a critical exponent of 0.37. Using the lattice results for the gluon propagator to fix the scale, the deconfinement transition temperature is obtained in the range of 275 to 290 MeV.Comment: 20 pages, 13 figures, accepted for publication by Phys. Rev.

Autonomous propulsion of carbon nanotubes powered by a multienzyme ensemble

Covalent attachment of the enzymes glucose oxidase and catalase to carbon nanotubes enables the tandem catalytic conversion of glucose and H2O2 formed to power autonomous movement of the nanotubes.