4,472 research outputs found
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 -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 -norm on . Here we
generalize this finding by showing that every weighted -norm on
with 1\le p \le \limitingp induces a metric and a
pseudo-metric on -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 formaldehydeâsulphite 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 âASYSTâ 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 -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 âdomain-generalâ 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 patientsâ 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 (âŒ2 weeks) and then âŒ4 months after the ictus. The functional magnetic resonance imaging tasks were designed to differentiate between activation related to language production (sentential overt speech productionâSpeech 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 âŒ4 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 , 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 and but
relatively real amplitudes in the charge states for . 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.
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