Isomeric state and rotational band in 158Ho

The odd-odd 158Ho nucleus is studied by means of the reactions 159Tb(α, 5n)158Ho and 160Dy(p, 3n)158 Ho. The life-time of an isomeric state is measured as T 1/2 = (29 ± 3) ns. A rotational band is developed up to spin 16 -

The random link approximation for the Euclidean traveling salesman problem

The traveling salesman problem (TSP) consists of finding the length of the shortest closed tour visiting N ``cities''. We consider the Euclidean TSP where the cities are distributed randomly and independently in a d-dimensional unit hypercube. Working with periodic boundary conditions and inspired by a remarkable universality in the kth nearest neighbor distribution, we find for the average optimum tour length = beta_E(d) N^{1-1/d} [1+O(1/N)] with beta_E(2) = 0.7120 +- 0.0002 and beta_E(3) = 0.6979 +- 0.0002. We then derive analytical predictions for these quantities using the random link approximation, where the lengths between cities are taken as independent random variables. From the ``cavity'' equations developed by Krauth, Mezard and Parisi, we calculate the associated random link values beta_RL(d). For d=1,2,3, numerical results show that the random link approximation is a good one, with a discrepancy of less than 2.1% between beta_E(d) and beta_RL(d). For large d, we argue that the approximation is exact up to O(1/d^2) and give a conjecture for beta_E(d), in terms of a power series in 1/d, specifying both leading and subleading coefficients.Comment: 29 pages, 6 figures; formatting and typos correcte

Cryptotomography: reconstructing 3D Fourier intensities from randomly oriented single-shot diffraction patterns

We reconstructed the 3D Fourier intensity distribution of mono-disperse prolate nano-particles using single-shot 2D coherent diffraction patterns collected at DESY's FLASH facility when a bright, coherent, ultrafast X-ray pulse intercepted individual particles of random, unmeasured orientations. This first experimental demonstration of cryptotomography extended the Expansion-Maximization-Compression (EMC) framework to accommodate unmeasured fluctuations in photon fluence and loss of data due to saturation or background scatter. This work is an important step towards realizing single-shot diffraction imaging of single biomolecules.Comment: 4 pages, 4 figure

Toeplitz Quantization of K\"ahler Manifolds and gl(N)gl(N) N→∞N\to\infty

For general compact K\"ahler manifolds it is shown that both Toeplitz quantization and geometric quantization lead to a well-defined (by operator norm estimates) classical limit. This generalizes earlier results of the authors and Klimek and Lesniewski obtained for the torus and higher genus Riemann surfaces, respectively. We thereby arrive at an approximation of the Poisson algebra by a sequence of finite-dimensional matrix algebras $gl(N)$, $N\to\infty$.Comment: 17 pages, AmsTeX 2.1, Sept. 93 (rev: only typos are corrected

Toeplitz operators on symplectic manifolds

We study the Berezin-Toeplitz quantization on symplectic manifolds making use of the full off-diagonal asymptotic expansion of the Bergman kernel. We give also a characterization of Toeplitz operators in terms of their asymptotic expansion. The semi-classical limit properties of the Berezin-Toeplitz quantization for non-compact manifolds and orbifolds are also established.Comment: 40 page

Low lying spectrum of weak-disorder quantum waveguides

We study the low-lying spectrum of the Dirichlet Laplace operator on a randomly wiggled strip. More precisely, our results are formulated in terms of the eigenvalues of finite segment approximations of the infinite waveguide. Under appropriate weak-disorder assumptions we obtain deterministic and probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas argument allows us to obtain so-called 'initial length scale decay estimates' at they are used in the proof of spectral localization using the multiscale analysis.Comment: Accepted for publication in Journal of Statistical Physics http://www.springerlink.com/content/0022-471

Mean field and corrections for the Euclidean Minimum Matching problem

Consider the length $L_{MM}^E$ of the minimum matching of N points in d-dimensional Euclidean space. Using numerical simulations and the finite size scaling law $= \beta_{MM}^E(d) N^{1-1/d}(1+A/N+... )$, we obtain precise estimates of $\beta_{MM}^E(d)$ for $2 \le d \le 10$. We then consider the approximation where distance correlations are neglected. This model is solvable and gives at $d \ge 2$ an excellent ``random link'' approximation to $\beta_{MM}^E(d)$. Incorporation of three-link correlations further improves the accuracy, leading to a relative error of 0.4% at d=2 and 3. Finally, the large d behavior of this expansion in link correlations is discussed.Comment: source and one figure. Submitted to PR

The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications

The inverse spectral transform for the Zakharov-Shabat equation on the semi-line is reconsidered as a Hilbert problem. The boundary data induce an essential singularity at large k to one of the basic solutions. Then solving the inverse problem means solving a Hilbert problem with particular prescribed behavior. It is demonstrated that the direct and inverse problems are solved in a consistent way as soon as the spectral transform vanishes with 1/k at infinity in the whole upper half plane (where it may possess single poles) and is continuous and bounded on the real k-axis. The method is applied to stimulated Raman scattering and sine-Gordon (light cone) for which it is demonstrated that time evolution conserves the properties of the spectral transform.Comment: LaTex file, 1 figure, submitted to J. Phys.

Bulk Universality and Related Properties of Hermitian Matrix Models

We give a new proof of universality properties in the bulk of spectrum of the hermitian matrix models, assuming that the potential that determines the model is globally $C^{2}$ and locally $C^{3}$ function (see Theorem \ref{t:U.t1}). The proof as our previous proof in \cite{Pa-Sh:97} is based on the orthogonal polynomial techniques but does not use asymptotics of orthogonal polynomials. Rather, we obtain the $sin$-kernel as a unique solution of a certain non-linear integro-differential equation that follows from the determinant formulas for the correlation functions of the model. We also give a simplified and strengthened version of paper \cite{BPS:95} on the existence and properties of the limiting Normalized Counting Measure of eigenvalues. We use these results in the proof of universality and we believe that they are of independent interest

A statistical approach to detect protein complexes at X-ray free electron laser facilities

The Flash X-ray Imaging (FXI) technique, under development at X-ray free electron lasers (XFEL), aims to achieve structure determination based on diffraction from individual macromolecular complexes. We report an FXI study on the first protein complex-RNA polymerase II-ever injected at an XFEL. A successful 3D reconstruction requires a high number of observations of the sample in various orientations. The measured diffraction signal for many shots can be comparable to background. Here we present a robust and highly sensitive hit-identification method based on automated modeling of beamline background through photon statistics. It can operate at controlled false positive hit-rate of 3 x10(-5). We demonstrate its power in determining particle hits and validate our findings against an independent hit-identification approach based on ion time-of-flight spectra. We also validate the advantages of our method over simpler hit-identification schemes via tests on other samples and using computer simulations, showing a doubled hit-identification power