Towards the Deconfinement Phase Transition in Hot Gauge Theories

The phase structure of hot gauge theories with dynamical matter fields is reexamined in the canonical ensemble with respect to triality. We discuss properties of chromoelectric and chromomagnetic sectors of the theory and show whereas electric charges carrying a unit of Z(N) charge are screened at high temperatures via dynamical matter loops, this is not the case for the Z(N) magnetic flux. An order parameter is constructed to probe the realization of local Z(N) symmetry in the magnetic sector. We argue this order parameter may be used to detect the deconfinement phase transition which is defined in terms of the screening mechanism.Comment: poster presented at LATTICE97; 3 pages, late

Deconfinement in QCD with dynamical quarks

We study the phase structure of full QCD within the canonical ensemble with respect to triality in a lattice formulation. The procedure for the calculation of the effective potentials in this case is given. As an example we consider the three dimensional SU(2) gauge model at finite temperatures in the strong coupling region. The potential exhibits a deconfinement phase transition unlike the similar potential obtained in the grand canonical ensemble which demonstrates explicit Z(N) symmetry breaking at any temperature. Furthermore, we investigate the effective potential with the chiral condensate included. In contradiction to other authors, we find chiral symmetry restoration in all triality sectors. In the scheme with massless staggered fermions we observe chiral symmetry restoration accompanying a deconfinement phase transition of first order. Above the critical point, besides two Z(2) symmetric "deconfining" vacua there exists a metastable "confining" vacuum in a wide region of parameters. Such a picture could be interpreted as an indication on a mixed state of hadrons and quarks in the vicinity of the critical line.Comment: 17 pages with 6 eps. figures include

Fresh look on triality

Investigating the $Z_3$ symmetry in Quantum Chromodynamics (QCD) we show that full QCD with a vacuum of vanishing baryonic number does not lead to metastable phases. Rather in QCD with dynamical fermions, the degeneracy of $Z_3$ phases manifests itself in observables without open triality.Comment: 9 pages, 0 figures, latex, IK-TUW-Preprint 930840

Zero-gravity and reduced-gravity simulation on a magnetic-colloid pool-boiling system

Zero and reduced gravity simulation on magnetic colloid pool-boiling syste

Crystal Structure Representations for Machine Learning Models of Formation Energies

We introduce and evaluate a set of feature vector representations of crystal structures for machine learning (ML) models of formation energies of solids. ML models of atomization energies of organic molecules have been successful using a Coulomb matrix representation of the molecule. We consider three ways to generalize such representations to periodic systems: (i) a matrix where each element is related to the Ewald sum of the electrostatic interaction between two different atoms in the unit cell repeated over the lattice; (ii) an extended Coulomb-like matrix that takes into account a number of neighboring unit cells; and (iii) an Ansatz that mimics the periodicity and the basic features of the elements in the Ewald sum matrix by using a sine function of the crystal coordinates of the atoms. The representations are compared for a Laplacian kernel with Manhattan norm, trained to reproduce formation energies using a data set of 3938 crystal structures obtained from the Materials Project. For training sets consisting of 3000 crystals, the generalization error in predicting formation energies of new structures corresponds to (i) 0.49, (ii) 0.64, and (iii) 0.37 eV/atom for the respective representations

Machine Learning Energies of 2 M Elpasolite (ABC2_2D6_6) Crystals

Elpasolite is the predominant quaternary crystal structure (AlNaK$_2$F$_6$ prototype) reported in the Inorganic Crystal Structure Database. We have developed a machine learning model to calculate density functional theory quality formation energies of all $\sim$2 M pristine ABC$_2$D$_6$ elpasolite crystals which can be made up from main-group elements (up to bismuth). Our model's accuracy can be improved systematically, reaching 0.1 eV/atom for a training set consisting of 10 k crystals. Important bonding trends are revealed, fluoride is best suited to fit the coordination of the D site which lowers the formation energy whereas the opposite is found for carbon. The bonding contribution of elements A and B is very small on average. Low formation energies result from A and B being late elements from group (II), C being a late (I) element, and D being fluoride. Out of 2 M crystals, 90 unique structures are predicted to be on the convex hull---among which NFAl$_2$Ca$_6$, with peculiar stoichiometry and a negative atomic oxidation state for Al

Alchemical and structural distribution based representation for improved QML

We introduce a representation of any atom in any chemical environment for the generation of efficient quantum machine learning (QML) models of common electronic ground-state properties. The representation is based on scaled distribution functions explicitly accounting for elemental and structural degrees of freedom. Resulting QML models afford very favorable learning curves for properties of out-of-sample systems including organic molecules, non-covalently bonded protein side-chains, (H$_2$O)$_{40}$-clusters, as well as diverse crystals. The elemental components help to lower the learning curves, and, through interpolation across the periodic table, even enable "alchemical extrapolation" to covalent bonding between elements not part of training, as evinced for single, double, and triple bonds among main-group elements

Noncommutative resolutions of discriminants

We give an introduction to the McKay correspondence and its connection to quotients of $\mathbb{C}^n$ by finite reflection groups. This yields a natural construction of noncommutative resolutions of the discriminants of these reflection groups. This paper is an extended version of E.F.'s talk with the same title delivered at the ICRA.Comment: 15 pages, 4 figures. Final version to appear in Contemporary Mathematics 705, "Representations of Algebras