Trace functions as Laplace transforms

We study trace functions on the form t\to\tr f(A+tB) where $f$ is a real function defined on the positive half-line, and $A$ and $B$ are matrices such that $A$ is positive definite and $B$ is positive semi-definite. If $f$ is non-negative and operator monotone decreasing, then such a trace function can be written as the Laplace transform of a positive measure. The question is related to the Bessis-Moussa-Villani conjecture. Key words: Trace functions, BMV-conjecture.Comment: Minor change of style, update of referenc

Intersalação de caulinitas separadas de latossolos.

bitstream/item/31928/1/CPATU-BP61.pd

The χ2\chi^2 - divergence and Mixing times of quantum Markov processes

We introduce quantum versions of the $\chi^2$-divergence, provide a detailed analysis of their properties, and apply them in the investigation of mixing times of quantum Markov processes. An approach similar to the one presented in [1-3] for classical Markov chains is taken to bound the trace-distance from the steady state of a quantum processes. A strict spectral bound to the convergence rate can be given for time-discrete as well as for time-continuous quantum Markov processes. Furthermore the contractive behavior of the $\chi^2$-divergence under the action of a completely positive map is investigated and contrasted to the contraction of the trace norm. In this context we analyse different versions of quantum detailed balance and, finally, give a geometric conductance bound to the convergence rate for unital quantum Markov processes

Corrections to Tribimaximal Mixing from Nondegenerate Phases

We propose a seesaw scenario that possible corrections to the tribimaximal pattern of lepton mixing are due to the small phase splitting of the right-handed neutrino mass matrix. we show that the small deviations can be expressed analytically in terms of two splitting parameters($\delta_1$ and $\delta_2$) in the leading order. The solar mixing angle $\theta_{12}$ favors a relatively smaller value compared to zero order value ($35.3^\circ$), and the Dirac type CP phase $\delta$ chooses a nearly maximal one. The two Majorana type CP phases $\rho$ and $\sigma$ turn out to be a nearly linear dependence. Also a normal hierarchy neutrino mass spectrum is favored due to the stability of perturbation calculations.Comment: 19 pages 6 figures, Accepted by Mod. Phy. Lett.

Super-KMS functionals for graded-local conformal nets

Motivated by a few preceding papers and a question of R. Longo, we introduce super-KMS functionals for graded translation-covariant nets over R with superderivations, roughly speaking as a certain supersymmetric modification of classical KMS states on translation-covariant nets over R, fundamental objects in chiral algebraic quantum field theory. Although we are able to make a few statements concerning their general structure, most properties will be studied in the setting of specific graded-local (super-) conformal models. In particular, we provide a constructive existence and partial uniqueness proof of super-KMS functionals for the supersymmetric free field, for certain subnets, and for the super-Virasoro net with central charge c>= 3/2. Moreover, as a separate result, we classify bounded super-KMS functionals for graded-local conformal nets over S^1 with respect to rotations.Comment: 30 pages, revised version (to appear in Ann. H. Poincare

Local Nature of Coset Models

The local algebras of the maximal Coset model C_max associated with a chiral conformal subtheory A\subset B are shown to coincide with the local relative commutants of A in B, provided A contains a stress energy tensor. Making the same assumption, the adjoint action of the unique inner-implementing representation U^A associated with A\subset B on the local observables in B is found to define net-endomorphisms of B. This property is exploited for constructing from B a conformally covariant holographic image in 1+1 dimensions which proves useful as a geometric picture for the joint inclusion A\vee C_max \subset B. Immediate applications to the analysis of current subalgebras are given and the relation to normal canonical tensor product subfactors is clarified. A natural converse of Borchers' theorem on half-sided translations is made accessible.Comment: 33 pages, no figures; typos, minor improvement