23 research outputs found
Strict weak mixing of some C*-dynamical systems based on free shifts
We define a stronger property than unique ergodicity with respect to the
fixed-point subalgebra previously investigated by Abadie and Dykema. Such a
property is denoted as F-strict weak mixing (F stands for the Markov projection
onto the fixed-point operator system). Then we show that the free shifts on the
reduced C*-algebras of RD-groups, including the free group on infinitely many
generators, and amalgamated free product C*-algebras, considered by Abadie and
Dykema, are all strictly weak mixing and not merely uniquely ergodic.Comment: 10 page
Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics
We extend the mathematical theory of quantum hypothesis testing to the
general -algebraic setting and explore its relation with recent
developments in non-equilibrium quantum statistical mechanics. In particular,
we relate the large deviation principle for the full counting statistics of
entropy flow to quantum hypothesis testing of the arrow of time.Comment: 60 page
Compact Hypergroups from Discrete Subfactors
Conformal inclusions of chiral conformal field theories, or more generally
inclusions of quantum field theories, are described in the von Neumann
algebraic setting by nets of subfactors, possibly with infinite Jones index if
one takes non-rational theories into account. With this situation in mind, we
study in a purely subfactor theoretical context a certain class of braided
discrete subfactors with an additional commutativity constraint, that we call
locality, and which corresponds to the commutation relations between field
operators at space-like distance in quantum field theory. Examples of
subfactors of this type come from taking a minimal action of a compact group on
a factor and considering the fixed point subalgebra. We show that to every
irreducible local discrete subfactor of type
there is an associated canonical compact hypergroup (an invariant
for the subfactor) which acts on by unital completely positive
(ucp) maps and which gives as fixed points. To show this, we
establish a duality pairing between the set of all -bimodular ucp
maps on and a certain commutative unital -algebra, whose
spectrum we identify with the compact hypergroup. If the subfactor has depth 2,
the compact hypergroup turns out to be a compact group. This rules out the
occurrence of compact \emph{quantum} groups acting as global gauge symmetries
in local conformal field theory.Comment: 58 page