7,469 research outputs found
Instanton Expansion of Noncommutative Gauge Theory in Two Dimensions
We show that noncommutative gauge theory in two dimensions is an exactly
solvable model. A cohomological formulation of gauge theory defined on the
noncommutative torus is used to show that its quantum partition function can be
written as a sum over contributions from classical solutions. We derive an
explicit formula for the partition function of Yang-Mills theory defined on a
projective module for arbitrary noncommutativity parameter \theta which is
manifestly invariant under gauge Morita equivalence. The energy observables are
shown to be smooth functions of \theta. The construction of noncommutative
instanton contributions to the path integral is described in some detail. In
general, there are infinitely many gauge inequivalent contributions of fixed
topological charge, along with a finite number of quantum fluctuations about
each instanton. The associated moduli spaces are combinations of symmetric
products of an ordinary two-torus whose orbifold singularities are not resolved
by noncommutativity. In particular, the weak coupling limit of the gauge theory
is independent of \theta and computes the symplectic volume of the moduli space
of constant curvature connections on the noncommutative torus.Comment: 52 pages LaTeX, 1 eps figure, uses espf. V2: References added and
repaired; V3: Typos corrected, some clarifying explanations added; version to
be published in Communications in Mathematical Physic
Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory
We use twist deformation techniques to analyse the behaviour under
area-preserving diffeomorphisms of quantum averages of Wilson loops in
Yang-Mills theory on the noncommutative plane. We find that while the classical
gauge theory is manifestly twist covariant, the holonomy operators break the
quantum implementation of the twisted symmetry in the usual formal definition
of the twisted quantum field theory. These results are deduced by analysing
general criteria which guarantee twist invariance of noncommutative quantum
field theories. From this a number of general results are also obtained, such
as the twisted symplectic invariance of noncommutative scalar quantum field
theories with polynomial interactions and the existence of a large class of
holonomy operators with both twisted gauge covariance and twisted symplectic
invariance.Comment: 23 page
Scalable Task-Based Algorithm for Multiplication of Block-Rank-Sparse Matrices
A task-based formulation of Scalable Universal Matrix Multiplication
Algorithm (SUMMA), a popular algorithm for matrix multiplication (MM), is
applied to the multiplication of hierarchy-free, rank-structured matrices that
appear in the domain of quantum chemistry (QC). The novel features of our
formulation are: (1) concurrent scheduling of multiple SUMMA iterations, and
(2) fine-grained task-based composition. These features make it tolerant of the
load imbalance due to the irregular matrix structure and eliminate all
artifactual sources of global synchronization.Scalability of iterative
computation of square-root inverse of block-rank-sparse QC matrices is
demonstrated; for full-rank (dense) matrices the performance of our SUMMA
formulation usually exceeds that of the state-of-the-art dense MM
implementations (ScaLAPACK and Cyclops Tensor Framework).Comment: 8 pages, 6 figures, accepted to IA3 2015. arXiv admin note: text
overlap with arXiv:1504.0504
Method of extending hyperfine coherence times in Pr^3+:Y_2SiO_5
In this letter we present a method for increasing the coherence time of
praseodymium hyperfine ground state transitions in Pr^3+:Y_2SiO_5 by the
application of a specific external magnetic field. The magnitude and angle of
the external field is applied such that the Zeeman splitting of a hyperfine
transition is at a critical point in three dimensions, making the first order
Zeeman shift vanishingly small for the transition. This reduces the influence
of the magnetic interactions between the praseodymium ions and the spins in the
host lattice on the transition frequency. Using this method a phase memory time
of 82ms was observed, a value two orders of magnitude greater than previously
reported. It is shown that the residual dephasing is amenable quantum error
correction
Proof of Kolmogorovian Censorship
Many argued (Accardi and Fedullo, Pitowsky) that Kolmogorov's axioms of
classical probability theory are incompatible with quantum probabilities, and
this is the reason for the violation of Bell's inequalities. Szab\'o showed
that, in fact, these inequalities are not violated by the experimentally
observed frequencies if we consider the real, ``effective'' frequencies. We
prove in this work a theorem which generalizes this result: ``effective''
frequencies associated to quantum events always admit a Kolmogorovian
representation, when these events are collected through different experimental
set ups, the choice of which obeys a classical distribution.Comment: 19 pages, LaTe
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