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

Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures

A limitation on simultaneous measurement of two arbitrary positive operator valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner's formulation, we introduce a distance between observables to quantify an accuracy of measurement. We derive an inequality that relates the achievable accuracy with noncommutativity between two observables. As a byproduct a necessary condition for two positive operator valued measures to be simultaneously measurable is obtained.Comment: 7 pages, 1 figure. To appear in Phys. Rev.

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.

Precise measurement of sin⁡22θ13\sin^22\theta_{13} using Japanese Reactors

After the KamLAND results, the remaining important targets in neutrino experiments are to measure still unknown 3 basic parameters; absolute neutrino mass scale, CP violation phase $\delta_{CP}$ and last mixing angle $\theta_{13}$. The angle $\theta_{13}$ among them is expected to be measured in near future by long baseline accelerator experiments and reactor experiments. In this paper, a realistic idea of high sensitivity reactor measurement of $\sin^22\theta_{13}$ is described. This experiment uses a giant nuclear power plant as the neutrino source and three identical detectors are used to cancel detector and neutrino flux uncertainties. The sensitivity reach on $\sin^22\theta_{13}$ is $0.017\sim0.026$ at $\Delta m^2_{13} \sim 3 \times 10^{-3}eV^2$, which is five to seven times better than the current upper limit measured by CHOOZ.Comment: 8 pages, 4 figures, uses ws-procs9x6.cls. To appear in the proceedings of 4th Workshop on Neutrino Oscillations and their Origin (NOON2003), Kanazawa, Japan, 10-14 Feb 200

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