390 research outputs found
Principal noncommutative torus bundles
In this paper we study continuous bundles of C*-algebras which are
non-commutative analogues of principal torus bundles. We show that all such
bundles, although in general being very far away from being locally trivial
bundles, are at least locally trivial with respect to a suitable bundle version
of bivariant K-theory (denoted RKK-theory) due to Kasparov. Using earlier
results of Echterhoff and Williams, we shall give a complete classification of
principal non-commutative torus bundles up to equivariant Morita equivalence.
We then study these bundles as topological fibrations (forgetting the group
action) and give necessary and sufficient conditions for any non-commutative
principal torus bundle being RKK-equivalent to a commutative one. As an
application of our methods we shall also give a K-theoretic characterization of
those principal torus-bundles with H-flux, as studied by Mathai and Rosenberg
which possess "classical" T-duals.Comment: 33 pages, to appear in the Proceedings of the London Mathematical
Societ
C*-Structure and K-Theory of Boutet de Monvel's Algebra
We consider the norm closure of the algebra of all operators of order and
class zero in Boutet de Monvel's calculus on a manifold with boundary .
We first describe the image and the kernel of the continuous extension of the
boundary principal symbol to . If the is connected and is not empty,
we then show that the K-groups of are topologically determined. In case the
manifold, its boundary and the tangent space of the interior have torsion-free
K-theory, we prove that is isomorphic to the direct sum of
and , for i=0,1, with denoting the compact
ideal and the tangent bundle of the interior of . Using Boutet de
Monvel's index theorem, we also prove this result for i=1 without assuming the
torsion-free hypothesis. We also give a composition sequence for .Comment: Final version, to appear in J. Reine Angew. Math. Improved
K-theoretic result
Deformation quantization of gerbes
This is the first in a series of articles devoted to deformation quantization
of gerbes. Here we give basic definitions and interpret deformations of a given
gerbe as Maurer-Cartan elements of a differential graded Lie algebra (DGLA). We
classify all deformations of a given gerbe on a symplectic manifold, as well as
provide a deformation-theoretic interpretation of the first Rozansky-Witten
class.Comment: Revised versio
Ammonia production by human faecal bacteria, and the enumeration, isolation and characterization of bacteria capable of growth on peptides and amino acids
DA - 20130125 IS - 1471-2180 (Electronic) IS - 1471-2180 (Linking) LA - eng PT - Journal Article PT - Research Support, Non-U.S. Gov't SB - IMPeer reviewedPublisher PD
Dynamic Matter-Wave Pulse Shaping
In this paper we discuss possibilities to manipulate a matter-wave with
time-dependent potentials. Assuming a specific setup on an atom chip, we
explore how one can focus, accelerate, reflect, and stop an atomic wave packet,
with, for example, electric fields from an array of electrodes. We also utilize
this method to initiate coherent splitting. Special emphasis is put on the
robustness of the control schemes. We begin with the wave packet of a single
atom, and extend this to a BEC, in the Gross-Pitaevskii picture. In analogy to
laser pulse shaping with its wide variety of applications, we expect this work
to form the base for additional time-dependent potentials eventually leading to
matter-wave pulse shaping with numerous application
Which graph states are useful for quantum information processing?
Graph states are an elegant and powerful quantum resource for measurement
based quantum computation (MBQC). They are also used for many quantum protocols
(error correction, secret sharing, etc.). The main focus of this paper is to
provide a structural characterisation of the graph states that can be used for
quantum information processing. The existence of a gflow (generalized flow) is
known to be a requirement for open graphs (graph, input set and output set) to
perform uniformly and strongly deterministic computations. We weaken the gflow
conditions to define two new more general kinds of MBQC: uniform
equiprobability and constant probability. These classes can be useful from a
cryptographic and information point of view because even though we cannot do a
deterministic computation in general we can preserve the information and
transfer it perfectly from the inputs to the outputs. We derive simple graph
characterisations for these classes and prove that the deterministic and
uniform equiprobability classes collapse when the cardinalities of inputs and
outputs are the same. We also prove the reversibility of gflow in that case.
The new graphical characterisations allow us to go from open graphs to graphs
in general and to consider this question: given a graph with no inputs or
outputs fixed, which vertices can be chosen as input and output for quantum
information processing? We present a characterisation of the sets of possible
inputs and ouputs for the equiprobability class, which is also valid for
deterministic computations with inputs and ouputs of the same cardinality.Comment: 13 pages, 2 figure
- âŠ