2,091 research outputs found
KMS States, Entropy and the Variational Principle in full C*-dynamical systems
To any periodic, unital and full C*-dynamical system (A, \alpha, R) an
invertible operator s acting on the Banach space of trace functionals of the
fixed point algebra is canonically associated. KMS states correspond to
positive eigenvectors of s. A Perron-Frobenius type theorem asserts the
existence of KMS states at inverse temperatures equal the logarithms of the
inner and outer spectral radii of s (extremal KMS states). Examples arising
from subshifts in symbolic dynamics, self-similar sets in fractal geometry and
noncommutative metric spaces are discussed.
Certain subshifts are naturally associated to the system and the relationship
between their topological entropy and inverse temperatures of extremal KMS
states are given.
Noncommutative shift maps are considered. It is shown that their entropy is
bounded by the sum of the entropy of the associated subshift and a suitable
entropy computed in the homogeneous subalgebra. Examples are discussed among
Matsumoto algebras associated to certain non finite type subshifts.
The CNT entropy is compared to the classical measure-theoretic entropy of the
subshift. A noncommutative analogue of the classical variational principle for
the entropy of subshifts is obtained for the noncommutative shift of certain
Matsumoto algebras. More generally, a necessary condition is discussed. In the
case of Cuntz-Krieger algebras an explicit construction of the state with
maximal entropy from the unique KMS state is done.Comment: 52 pages, AMSTeX. An error in Prop. 7.3 v1 has been corrected, and
related text in sections 7-9 has been modified. References added. Abstract
modifie
Maximal rank of extremal marginal tracial states
States on coupled quantum system whose restrictions to each subsystems are
normalized traces are called marginal tracial states. We investigate extremal
marginal tracial states and maximal rank of such states. Diagonal marginal
tracial states are also considered.Comment: 10 page
Dixmier approximation and symmetric amenability for C*-algebras
We study some general properties of tracial C*-algebras. In the first part,
we consider Dixmier type approximation theorem and characterize symmetric
amenability for C*-algebras. In the second part, we consider continuous bundles
of tracial von Neumann algebras and classify some of them.Comment: 19 pages; minor update (v2
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