2,601 research outputs found
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 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 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 (ABCD) Crystals
Elpasolite is the predominant quaternary crystal structure (AlNaKF
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 2 M pristine ABCD 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 NFAlCa,
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, (HO)-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 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
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