24 research outputs found
Fluctuation, time-correlation function and geometric Phase
We establish a fluctuation-correlation theorem by relating the quantum
fluctuations in the generator of the parameter change to the time integral of
the quantum correlation function between the projection operator and force
operator of the ``fast'' system. By taking a cue from linear response theory we
relate the quantum fluctuation in the generator to the generalised
susceptibility. Relation between the open-path geometric phase, diagonal
elements of the quantum metric tensor and the force-force correlation function
is provided and the classical limit of the fluctuation-correlation theorem is
also discussed.Comment: Latex, 12 pages, no figures, submitted to J. Phys. A: Math & Ge
(Re)constructing Dimensions
Compactifying a higher-dimensional theory defined in R^{1,3+n} on an
n-dimensional manifold {\cal M} results in a spectrum of four-dimensional
(bosonic) fields with masses m^2_i = \lambda_i, where - \lambda_i are the
eigenvalues of the Laplacian on the compact manifold. The question we address
in this paper is the inverse: given the masses of the Kaluza-Klein fields in
four dimensions, what can we say about the size and shape (i.e. the topology
and the metric) of the compact manifold? We present some examples of
isospectral manifolds (i.e., different manifolds which give rise to the same
Kaluza-Klein mass spectrum). Some of these examples are Ricci-flat, complex and
K\"{a}hler and so they are isospectral backgrounds for string theory. Utilizing
results from finite spectral geometry, we also discuss the accuracy of
reconstructing the properties of the compact manifold (e.g., its dimension,
volume, and curvature etc) from measuring the masses of only a finite number of
Kaluza-Klein modes.Comment: 23 pages, 3 figures, 2 references adde
L^{2}-restriction bounds for eigenfunctions along curves in the quantum completely integrable case
We show that for a quantum completely integrable system in two dimensions,the
-normalized joint eigenfunctions of the commuting semiclassical
pseudodifferential operators satisfy restriction bounds ofthe form for generic
curves on the surface. We also prove that the maximal restriction
bounds of Burq-Gerard-Tzvetkov are always attained for certain exceptional
subsequences of eigenfunctions.Comment: Correct some typos and added some more detail in section
Bounding Helly numbers via Betti numbers
We show that very weak topological assumptions are enough to ensure the
existence of a Helly-type theorem. More precisely, we show that for any
non-negative integers and there exists an integer such that
the following holds. If is a finite family of subsets of such that for any
and every
then has Helly number at most . Here
denotes the reduced -Betti numbers (with singular homology). These
topological conditions are sharp: not controlling any of these first Betti numbers allow for families with unbounded Helly number.
Our proofs combine homological non-embeddability results with a Ramsey-based
approach to build, given an arbitrary simplicial complex , some well-behaved
chain map .Comment: 29 pages, 8 figure
Approach to ergodicity in quantum wave functions
According to theorems of Shnirelman and followers, in the semiclassical limit
the quantum wavefunctions of classically ergodic systems tend to the
microcanonical density on the energy shell. We here develop a semiclassical
theory that relates the rate of approach to the decay of certain classical
fluctuations. For uniformly hyperbolic systems we find that the variance of the
quantum matrix elements is proportional to the variance of the integral of the
associated classical operator over trajectory segments of length , and
inversely proportional to , where is the Heisenberg
time, being the mean density of states. Since for these systems the
classical variance increases linearly with , the variance of the matrix
elements decays like . For non-hyperbolic systems, like Hamiltonians
with a mixed phase space and the stadium billiard, our results predict a slower
decay due to sticking in marginally unstable regions. Numerical computations
supporting these conclusions are presented for the bakers map and the hydrogen
atom in a magnetic field.Comment: 11 pages postscript and 4 figures in two files, tar-compressed and
uuencoded using uufiles, to appear in Phys Rev E. For related papers, see
http://www.icbm.uni-oldenburg.de/icbm/kosy/ag.htm
Travelers With Cutaneous Leishmaniasis Cured Without Systemic Therapy
Guidelines recommend wound care and/or local therapy as first-line treatment for cutaneous leishmaniasis. An analysis of a referral treatment program in 135 travelers showed that this approach was feasible in 62% of patients, with positive outcome in 83% of evaluable patient
Simple scoring system to predict in-hospital mortality after surgery for infective endocarditis
BACKGROUND:
Aspecific scoring systems are used to predict the risk of death postsurgery in patients with infective endocarditis (IE). The purpose of the present study was both to analyze the risk factors for in-hospital death, which complicates surgery for IE, and to create a mortality risk score based on the results of this analysis.
METHODS AND RESULTS:
Outcomes of 361 consecutive patients (mean age, 59.1\ub115.4 years) who had undergone surgery for IE in 8 European centers of cardiac surgery were recorded prospectively, and a risk factor analysis (multivariable logistic regression) for in-hospital death was performed. The discriminatory power of a new predictive scoring system was assessed with the receiver operating characteristic curve analysis. Score validation procedures were carried out. Fifty-six (15.5%) patients died postsurgery. BMI >27 kg/m2 (odds ratio [OR], 1.79; P=0.049), estimated glomerular filtration rate 55 mm Hg (OR, 1.78; P=0.032), and critical state (OR, 2.37; P=0.017) were independent predictors of in-hospital death. A scoring system was devised to predict in-hospital death postsurgery for IE (area under the receiver operating characteristic curve, 0.780; 95% CI, 0.734-0.822). The score performed better than 5 of 6 scoring systems for in-hospital death after cardiac surgery that were considered.
CONCLUSIONS:
A simple scoring system based on risk factors for in-hospital death was specifically created to predict mortality risk postsurgery in patients with IE
Multiple westward propagating signals in South Pacific sea level anomalies
The characteristics of multiple westward propagating signals in the satellite observed South Pacific sea level anomalies (SLA) between 10°S and 50°S are analyzed using the two-dimensional Radon transform (2D-RT). We test the hypothesis that these signals are most likely to be the signature of the first few baroclinic Rossby wave modes. This involves a comparison of the estimated phase speeds of the 2D-RT peaks against the first four baroclinic mode Rossby wave speeds predicted from the extended theory. The 2D-RT analysis typically identified up to three propagating signals in the SLA and very occasionally, a fourth. The first Radon transform (RT) peak phase speeds corresponded very well with first baroclinic mode Rossby wave phase speed estimates from linear theory between 15°S and 25°S and the extended theory phase speed estimates poleward of 25°S. RT peak 2 speeds were less coherent but fell within the range of extended theory estimates of the first four baroclinic Rossby wave modes, consistent with large-scale Rossby wave dynamics. The relationship between peaks 3 and 4 and the extended theory higher-order baroclinic mode speed estimates varied markedly across the basin. Regional variability in the spectral characteristics of the peaks suggests that different dynamical regimes dominate north and south of 30°S in the South Pacific basin. The presence of secondary peaks in the middle to high latitudes suggests that higher-order modes may play a role in these regions