Bound on the string tension by the excitation probability for a vortex

A lower bound on the string tension for large beta in SU(2) LGT is derived. The derivation is from first principles and bounds the string tension from below by the expectation for the excitation of a single `tagged' thick vortex winding around the lattice. Thus confinement follows if this expectation remains nonvanishing at large beta. Numerical simulations are presented to show that this is indeed the case.Comment: LATTICE99(confine), 3 pages, 3 epsf figures, LaTeX, espcrc2.st

Absence of confinement in the absence of vortices

We consider the Wilson loop expectation in SU(2) lattice gauge theory in the presence of constraints. The constraints eliminate from the functional measure gauge field configurations whose physical interpretation is that of thick center vortices linking with the loop. We give a simple proof that, for dimension $d \geq 3$, the so constrained Wilson loop follows perimeter law, i.e. non-confining behavior, at weak coupling (low temperature). Thus the presence of vortex configurations is a necessary condition for confinement.Comment: 14 pages, LaTeX fil

SO(3) vortices and disorder in the 2d SU(2) chiral model

We study the correlation function of the 2d SU(2) principal chiral model on the lattice. By rewriting the model in terms of Z(2) degrees of freedom coupled to SO(3) vortices we show that the vortices play a crucial role in disordering the correlations at low temperature. Using a series of exact transformations we prove that, if satisfied, certain inequalities between vortex correlations imply exponential fall-off of the correlation function at arbitrarily low temperatures. We also present some Monte Carlo evidence that these correlation inequalities are indeed satisfied. Our method can be easily translated to the language of 4d SU(2) gauge theory to establish the role of corresponding SO(3) monopoles in maintaining confinement at small couplings.Comment: 13 pages LaTe

Description of two-electron atoms with correct cusp conditions

New sets of functions with arbitrary large finite cardinality are constructed for two-electron atoms. Functions from these sets exactly satisfy the Kato's cusp conditions. The new functions are special linear combinations of Hylleraas- and/or Kinoshita-type terms. Standard variational calculation, leading to matrix eigenvalue problem, can be carried out to calculate the energies of the system. There is no need for optimization with constraints to satisfy the cusp conditions. In the numerical examples the ground state energy of the He atom is considered

Pion condensation in the two--flavor chiral quark model at finite baryochemical potential

Pion condensation is studied at one--loop level and nonzero baryochemical potential in the framework of two flavor constituent quark model using the one--loop level optimized perturbation theory for the resummation of the perturbative series. A Landau type of analysis is presented for the investigation of the phase boundary between the pion condensed/non-condensed phases. The statement that the condensation starts at \muI = m_{\pi} is slightly modified by one--loop corrections. The second order critical surface is determined and analysed in the \muI-\muB-T space. The \muI dependence of the one--loop level charged pion pole masses is also studied.Comment: 12 pages, 5 figures, submitted to PR

SO(3) vortices as a mechanism for generating a mass gap in the 2d SU(2) principal chiral model

We propose a mechanism that can create a mass gap in the SU(2) chiral spin model at arbitrarily small temperatures. We give a sufficient condition for the mass gap to be non-zero in terms of the behaviour of an external Z(2) flux introduced by twisted boundary conditions. This condition in turn is transformed into an effective dual Ising model with an external magnetic field generated by SO(3) vortices. We show that having a nonzero magnetic field in the effective Ising model is sufficient for the SU(2) system to have a mass gap. We also show that certain vortex correlation inequalities, if satisfied, would imply a nonzero effective magnetic field. Finally we give some plausibility arguments and Monte Carlo evidence for the required correlation inequalities.Comment: 33 pages, LaTeX2e, all figures included in LaTeX forma

Anderson Localization in Quark-Gluon Plasma

At low temperature the low end of the QCD Dirac spectrum is well described by chiral random matrix theory. In contrast, at high temperature there is no similar statistical description of the spectrum. We show that at high temperature the lowest part of the spectrum consists of a band of statistically uncorrelated eigenvalues obeying essentially Poisson statistics and the corresponding eigenvectors are extremely localized. Going up in the spectrum the spectral density rapidly increases and the eigenvectors become more and more delocalized. At the same time the spectral statistics gradually crosses over to the bulk statistics expected from the corresponding random matrix ensemble. This phenomenon is reminiscent of Anderson localization in disordered conductors. Our findings are based on staggered Dirac spectra in quenched SU(2) lattice simulations.Comment: 11 pages, 8 figure

Building valoristaion strategies for biodiverse products - the approach

The market valorisation of ‘diverse food products’ is crucial to increase diversity in farming systems. It involves multiple actors, from the field to the table, and requires an integrated approach to take into account several dimensions involved

Building Valorisation Strategies for Biodiverse Products - Case Studies

The market valorisation of ‘diverse food products’ is crucial to promote agrobiodiversity. Despite the differences due to the specific contexts, valorisation strategies show relevant common features