517 research outputs found
Phase transitions in a gas of anyons
We continue our numerical Monte Carlo simulation of a gas of closed loops on
a 3 dimensional lattice, however now in the presence of a topological term
added to the action corresponding to the total linking number between the
loops. We compute the linking number using certain notions from knot theory.
Adding the topological term converts the particles into anyons. Using the
correspondence that the model is an effective theory that describes the
2+1-dimensional Abelian Higgs model in the asymptotic strong coupling regime,
the topological linking number simply corresponds to the addition to the action
of the Chern-Simons term. We find the following new results. The system
continues to exhibit a phase transition as a function of the anyon mass as it
becomes small \cite{mnp}, although the phases do not change the manifestation
of the symmetry. The Chern-Simons term has no effect on the Wilson loop, but it
does affect the {\rm '}t Hooft loop. For a given configuration it adds the
linking number of the 't Hooft loop with all of the dynamical vortex loops to
the action. We find that both the Wilson loop and the 't Hooft loop exhibit a
perimeter law even though there are no massless particles in the theory, which
is unexpected.Comment: 6 pages, 5 figure
Markov quantum fields on a manifold
We study scalar quantum field theory on a compact manifold. The free theory
is defined in terms of functional integrals. For positive mass it is shown to
have the Markov property in the sense of Nelson. This property is used to
establish a reflection positivity result when the manifold has a reflection
symmetry. In dimension d=2 we use the Markov property to establish a sewing
operation for manifolds with boundary circles. Also in d=2 the Markov property
is proved for interacting fields.Comment: 14 pages, 1 figure, Late
A Novel Approach to Multimedia Ontology Engineering for Automated Reasoning over Audiovisual LOD Datasets
Multimedia reasoning, which is suitable for, among others, multimedia content
analysis and high-level video scene interpretation, relies on the formal and
comprehensive conceptualization of the represented knowledge domain. However,
most multimedia ontologies are not exhaustive in terms of role definitions, and
do not incorporate complex role inclusions and role interdependencies. In fact,
most multimedia ontologies do not have a role box at all, and implement only a
basic subset of the available logical constructors. Consequently, their
application in multimedia reasoning is limited. To address the above issues,
VidOnt, the very first multimedia ontology with SROIQ(D) expressivity and a
DL-safe ruleset has been introduced for next-generation multimedia reasoning.
In contrast to the common practice, the formal grounding has been set in one of
the most expressive description logics, and the ontology validated with
industry-leading reasoners, namely HermiT and FaCT++. This paper also presents
best practices for developing multimedia ontologies, based on my ontology
engineering approach
Measuring the Hausdorff Dimension of Quantum Mechanical Paths
We measure the propagator length in imaginary time quantum mechanics by Monte
Carlo simulation on a lattice and extract the Hausdorff dimension . We
find that all local potentials fall into the same universality class giving
like the free motion. A velocity dependent action () in the path integral (e.g. electrons moving in
solids, or Brueckner's theory of nuclear matter) yields if and if . We discuss the
relevance of fractal pathes in solid state physics and in , in particular
for the Wilson loop in .Comment: uuencoded and compressed shell archive file. 8 pages with 7 figure
Thermal Quantum Fields without Cut-offs in 1+1 Space-time Dimensions
We construct interacting quantum fields in 1+1 dimensional Minkowski space,
representing neutral scalar bosons at positive temperature. Our work is based
on prior work by Klein and Landau and Hoegh-KrohnComment: 48 page
Spectral stochastic processes arising in quantum mechanical models with a non-L2 ground state
A functional integral representation is given for a large class of quantum
mechanical models with a non--L2 ground state. As a prototype the particle in a
periodic potential is discussed: a unique ground state is shown to exist as a
state on the Weyl algebra, and a functional measure (spectral stochastic
process) is constructed on trajectories taking values in the spectrum of the
maximal abelian subalgebra of the Weyl algebra isomorphic to the algebra of
almost periodic functions. The thermodynamical limit of the finite volume
functional integrals for such models is discussed, and the superselection
sectors associated to an observable subalgebra of the Weyl algebra are
described in terms of boundary conditions and/or topological terms in the
finite volume measures.Comment: 15 pages, Plain Te
Quantum Sturm-Liouville Equation, Quantum Resolvent, Quantum Integrals, and Quantum KdV : the Fast Decrease Case
We construct quantum operators solving the quantum versions of the
Sturm-Liouville equation and the resolvent equation, and show the existence of
conserved currents. The construction depends on the following input data: the
basic quantum field and the regularization .Comment: minor correction
The embedding structure and the shift operator of the U(1) lattice current algebra
The structure of block-spin embeddings of the U(1) lattice current algebra is
described. For an odd number of lattice sites, the inner realizations of the
shift automorphism areclassified. We present a particular inner shift operator
which admits a factorization involving quantum dilogarithms analogous to the
results of Faddeev and Volkov.Comment: 14 pages, Plain TeX; typos and a terminological mishap corrected;
version to appear in Lett.Math.Phy
Projected SO(5) Hamiltonian for Cuprates and Its Applications
The projected SO(5) (pSO(5)) Hamiltonian incorporates the quantum spin and
superconducting fluctuations of underdoped cuprates in terms of four bosons
moving on a coarse grained lattice. A simple mean field approximation can
explain some key feautures of the experimental phase diagram: (i) The Mott
transition between antiferromagnet and superconductor, (ii) The increase of T_c
and superfluid stiffness with hole concentration x and (iii) The increase of
antiferromagnetic resonance energy as sqrt{x-x_c} in the superconducting phase.
We apply this theory to explain the ``two gaps'' problem found in underdoped
cuprate Superconductor-Normal- Superconductor junctions. In particular we
explain the sharp subgap Andreev peaks of the differential resistance, as
signatures of the antiferromagnetic resonance (the magnon mass gap). A critical
test of this theory is proposed. The tunneling charge, as measured by shot
noise, should change by increments of Delta Q= 2e at the Andreev peaks, rather
than by Delta Q=e as in conventional superconductors.Comment: 3 EPS figure
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