805 research outputs found
Decoherence free algebra
We consider the decoherence free subalgebra which satisfies the minimal
condition introduced by Alicki. We show the manifest form of it and relate the
subalgebra with the Kraus representation. The arguments also provides a new
proof for generalized L\"{u}ders theorem.Comment: To appear in Physics Letters A v2.minor chang
Continuous and discrete flows on operator algebras
Let be a centrally ergodic W* dynamical system. When is
not a factor, we show that, for each , the crossed product induced by
the time automorphism is not a factor if and only if there exist
a rational number and an eigenvalue of the restriction of to
the center of , such that . In the C* setting, minimality seems to
be the notion corresponding to central ergodicity. We show that if
is a minimal unital C* dynamical system and is either prime
or commutative but not simple, then, for each , the crossed product
induced by the time automorphism is not simple if and only if
there exist a rational number and an eigenvalue of the restriction of
to the center of , such that .Comment: 7 page
Approximations of subhomogeneous algebras
Let be a natural number. Recall that a C*-algebra is said to be
-subhomogeneous if all its irreducible representations have dimension at
most . In this short note, we give various approximation properties
characterising -subhomogeneous C*-algebras.Comment: 9 pages; v2 minor improvement in the introduction, 10 page
Quantum group connections
The Ahtekar-Isham C*-algebra known from Loop Quantum Gravity is the algebra
of continuous functions on the space of (generalized) connections with a
compact structure Lie group. The algebra can be constructed by some inductive
techniques from the C*-algebra of continuous functions on the group and a
family of graphs embedded in the manifold underlying the connections. We
generalize the latter construction replacing the commutative C*-algebra of
continuous functions on the group by a non-commutative C*-algebra defining a
compact quantum group.Comment: 40 pages, LaTeX2e, minor mistakes corrected, abstract slightly
change
Generators of von Neumann algebras associated with spectral measures
Let be the set of all values of a spectral measure and be
the smallest von Neumann algebra containing . We give a simple description
of all sets of generators of in terms of the integrals with respect to
. The treatment covers not only the case of generators belonging to
, but also the case of (possibly unbounded) generators affiliated with
this algebra.Comment: 10 pages, published versio
Entanglement, Haag-duality and type properties of infinite quantum spin chains
We consider an infinite spin chain as a bipartite system consisting of the
left and right half-chain and analyze entanglement properties of pure states
with respect to this splitting. In this context we show that the amount of
entanglement contained in a given state is deeply related to the von Neumann
type of the observable algebras associated to the half-chains. Only the type I
case belongs to the usual entanglement theory which deals with density
operators on tensor product Hilbert spaces, and only in this situation
separable normal states exist. In all other cases the corresponding state is
infinitely entangled in the sense that one copy of the system in such a state
is sufficient to distill an infinite amount of maximally entangled qubit pairs.
We apply this results to the critical XY model and show that its unique ground
state provides a particular example for this type of entanglement.Comment: LaTeX2e, 34 pages, 1 figure (pstricks
Endomorphisms and automorphisms of locally covariant quantum field theories
In the framework of locally covariant quantum field theory, a theory is
described as a functor from a category of spacetimes to a category of
*-algebras. It is proposed that the global gauge group of such a theory can be
identified as the group of automorphisms of the defining functor. Consequently,
multiplets of fields may be identified at the functorial level. It is shown
that locally covariant theories that obey standard assumptions in Minkowski
space, including energy compactness, have no proper endomorphisms (i.e., all
endomorphisms are automorphisms) and have a compact automorphism group.
Further, it is shown how the endomorphisms and automorphisms of a locally
covariant theory may, in principle, be classified in any single spacetime. As
an example, the endomorphisms and automorphisms of a system of finitely many
free scalar fields are completely classified.Comment: v2 45pp, expanded to include additional results; presentation
improved and an error corrected. To appear in Rev Math Phy
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