Elementary Proofs Of Two Theorems Involving Arguments Of Eigenvalues Of A Product Of Two Unitary Matrices

We give elementary proofs of two theorems concerning bounds on the maximum argument of the eigenvalues of a product of two unitary matrices --- one by Childs \emph{et al.} [J. Mod. Phys., \textbf{47}, 155 (2000)] and the other one by Chau [arXiv:1006.3614]. Our proofs have the advantages that the necessary and sufficient conditions for equalities are apparent and that they can be readily generalized to the case of infinite-dimensional unitary operators.Comment: 8 pages in Revtex 4.1 preprint format, to appear in Journal of Inequalities and Application

Statistics Of The Burst Model At Super-critical Phase

We investigate the statistics of a model of type-I X-ray burst [Phys. Rev. E, {\bf 51}, 3045 (1995)] in its super-critical phase. The time evolution of the burnable clusters, places where fire can pass through, is studied using simple statistical arguments. We offer a simple picture for the time evolution of the percentage of space covered by burnable clusters. A relation between the time-average and the peak percentage of space covered by burnable clusters is also derived.Comment: 11 Pages in Revtex 3.0. Two figures available by sending request to [email protected]

Relation Between Quantum Speed Limits And Metrics On U(n)

Recently, Chau [Quant. Inform. & Comp. 11, 721 (2011)] found a family of metrics and pseudo-metrics on $n$-dimensional unitary operators that can be interpreted as the minimum resources (given by certain tight quantum speed limit bounds) needed to transform one unitary operator to another. This result is closely related to the weighted $\ell^1$-norm on ${\mathbb R}^n$. Here we generalize this finding by showing that every weighted $\ell^p$-norm on ${\mathbb R}^n$ with 1\le p \le \limitingp induces a metric and a pseudo-metric on $n$-dimensional unitary operators with quantum information-theoretic meanings related to certain tight quantum speed limit bounds. Besides, we investigate how far the correspondence between the existence of metrics and pseudo-metrics of this type and the quantum speed limits can go.Comment: minor amendments, 6 pages, to appear in J.Phys.

A computer-enhanced pH study of the formaldehyde–sulphite clock reaction

The formaldehyde-sulphite clock reaction was studied using an Orion SA 720 pH/ISE meter interfaced to an IBM PC. The laboratory software ‘ASYST’ was employed to facilitate data acquisition and data treatment. Experimental pH profiles thus obtained for the first time were simulated by invoking a theoretical model based on the reaction mechanism suggested by Burnett [1]. The variation of rate constants with compositions of reaction mixtures was also discuseed in light of the empirical expression proposed by Bell and Evans [2] for instantaneous rate constant of the clock reaction

Simultaneous multiwavelength study of the reaction of phenolphthalein with sodium hydroxide

A photodiode array (PDA) spectrophotometer was used to study the fading reaction of phenolpthalein in dilute sodium hydroxide solution. The principal component analysis (PCA) method was employed to identify the number of light absorbing species in the kinetics system. The target factor analysis (TFA) procedure, coupled with the Broyden-Fletcher-Goldfard-Shanno (BFGS) optimization method, was applied to the observed data to deduce the rate constants and the concentration-time profile of the reaction. The internal referencing method was shown to be essential in improving the quality of data obtained by a single beam PDA spectrophotomer

Analysis of Two-Body Decays of Charmed Baryons Using the Quark-Diagram Scheme

We give a general formulation of the quark-diagram scheme for the nonleptonic weak decays of baryons. We apply it to all the decays of the antitriplet and sextet charmed baryons and express their decay amplitudes in terms of the quark-diagram amplitudes. We have also given parametrizations for the effects of final-state interactions. For SU(3) violation effects, we only parametrize those in the horizontal $W$-loop quark diagrams whose contributions are solely due to SU(3)-violation effects. In the absence of all these effects, there are many relations among various decay modes. Some of the relations are valid even in the presence of final-state interactions when each decay amplitude in the relation contains only a single phase shift. All these relations provide useful frameworks to compare with future experiments and to find out the effects of final-state interactions and SU(3) symmetry violations.Comment: 28 pages, 20 Tables in landscape form, 4 figures. Main changes are: (i) some errors in the Tables and in the relations between the quark-diagram amplitudes of this paper and those of Ref.[10] are corrected, (ii) improvements are made in the presentation so that comparisons with previous works and what have been done to include SU(3) breaking and final-state interactions are more clearly stated; to appear in the Physical Review

Domain-general subregions of the medial prefrontal cortex contribute to recovery of language after stroke

We hypothesized that the recovery of speech production after left hemisphere stroke not only depends on the integrity of language-specialized brain systems, but also on ‘domain-general’ brain systems that have much broader functional roles. The presupplementary motor area/dorsal anterior cingulate forms part of the cingular-opercular network, which has a broad role in cognition and learning. Consequently, we have previously suggested that variability in the recovery of speech production after aphasic stroke may relate in part to differences in patients’ abilities to engage this domain-general brain region. To test our hypothesis, 27 patients (aged 59 ± 11 years) with a left hemisphere stroke performed behavioural assessments and event-related functional magnetic resonance imaging tasks at two time points; first in the early phase (∼2 weeks) and then ∼4 months after the ictus. The functional magnetic resonance imaging tasks were designed to differentiate between activation related to language production (sentential overt speech production—Speech task) and activation related to cognitive processing (non-verbal decision making). Simple rest and counting conditions were also included in the design. Task-evoked regional brain activations during the early and late phases were compared with a longitudinal measure of recovery of language production. In accordance with a role in cognitive processing, substantial activity was observed within the presupplementary motor area/dorsal anterior cingulate during the decision-making task. Critically, the level of activation within this region during speech production correlated positively with the longitudinal recovery of speech production across the two time points (as measured by the in-scanner performance in the Speech task). This relationship was observed for activation in both the early phase (r = 0.363, P = 0.03 one-tailed) and the late phase (r = 0.538, P = 0.004). Furthermore, presupplementary motor area/dorsal anterior cingulate activity was a predictor of both language recovery over time and language outcome at ∼4 months, over and above that predicted by lesion volume, age and the initial language impairment (general linear model overall significant at P < 0.0001; ExpB 1.01, P = 0.02). The particularly prominent relationship of the presupplementary motor area/dorsal anterior cingulate region with recovery of language was confirmed in voxel-wise correlation analysis, conducted unconstrained for the whole brain volume. These results accord with the hypothesis that the functionality of the presupplementary motor area/dorsal anterior cingulate contributes to language recovery after stroke. Given that this brain region is often spared in aphasic stroke, we propose that it is a sensible target for future research into rehabilitative treatments. More broadly, baseline assessment of domain-general systems could help provide a better prediction of language recovery

Getting Information on Independently Prepared Quantum States -- When Are Individual Measurements as Powerful as Joint Measurements?

Given a composite quantum system in which the states of the subsystems are independently (but not necessarily identically) prepared, we construct separate measurements on the subsystems from any given joint measurement such that the former always give at least as large information as the latter. This construction offers new insights into the understanding of measurements on this type of composite systems. Moreover, this construction essentially proves the intuition that separate measurements on the subsystems are sufficient to extract the maximal information about the separately prepared subsystems, thus making a joint measurement unnecessary. Furthermore, our result implies that individual attacks are as powerful as collective attacks in obtaining information on the raw key in quantum key distribution.Comment: 5 pages, 1 figur

Universal Cubic Eigenvalue Repulsion for Random Normal Matrices

Random matrix models consisting of normal matrices, defined by the sole constraint $[N^{\dag},N]=0$, will be explored. It is shown that cubic eigenvalue repulsion in the complex plane is universal with respect to the probability distribution of matrices. The density of eigenvalues, all correlation functions, and level spacing statistics are calculated. Normal matrix models offer more probability distributions amenable to analytical analysis than complex matrix models where only a model wth a Gaussian distribution are solvable. The statistics of numerically generated eigenvalues from gaussian distributed normal matrices are compared to the analytical results obtained and agreement is seen.Comment: 15 pages, 2 eps figures. to appar in Physical Review

Final-State Phases in Charmed Meson Two-Body Nonleptonic Decays

Observed decay rates indicate large phase differences among the amplitudes for the charge states in $D \to \bar K \pi$ and $D \to \bar K^* \pi$ but relatively real amplitudes in the charge states for $D \to \bar K \rho$. This feature is traced using an SU(3) flavor analysis to a sign flip in the contribution of one of the amplitudes contributing to the latter processes in comparison with its contribution to the other two sets. This amplitude may be regarded as an effect of rescattering and is found to be of magnitude comparable to others contributing to charmed particle two-body nonleptonic decays.Comment: 19 pages, latex, 4 figures, to be submitted to Phys. Rev.