Low-temperature quantum fluctuations in overdamped ratchets

At low temperatures and strong friction the time evolution of the density distribution in position follows a quantum Smoluchowski equation. Recently, also higher-order contributions of quantum fluctuations to drift and diffusion coefficients have been systematically derived. As a non-trivial situation to reveal the impact of subleading quantum corrections and to demonstrate convergence properties of the perturbation series, directed transport in ratchets is studied. It is shown that the perturbation series typically has a non-monotonous behavior. Depending on symmetry properties higher order contributions may even compensate current reversals induced by leading quantum fluctuations. This analysis demonstrates how to consistently treat the dynamics of overdamped quantum systems at low temperatures also in numerical applications.Comment: 5 pages, 3 figure

Angular distribution in two-photon double ionization of helium by intense attosecond soft X-ray pulses

We investigate two-photon double ionization of helium by intense ($10^{15} W/cm^2$) ultrashort ($\approx 300$ as) soft X-ray pulses (E = 91.6 eV). The time-dependent two-electron Schr\"odinger equation is solved using a coupled channel method. We show that for ultrashort pulses the angular distribution of ejected electrons depends on the pulse duration and provides novel insights into the role of electron correlations in the two-electron photoemission process. The angular distribution at energies near the ``independent electron'' peaks is close to dipolar while it acquires in the ``valley'' of correlated emission a significant quadrupolar component within a few hundred attoseconds.Comment: 17 pages, 6 fig

Toda brackets and cup-one squares for ring spectra

In this paper we prove the laws of Toda brackets on the homotopy groups of a connective ring spectrum and the laws of the cup-one square in the homotopy groups of a commutative connective ring spectrum.Comment: 22 page

Anti-Coarsening and Complex Dynamics of Step Bunches on Vicinal Surfaces during Sublimation

A sublimating vicinal crystal surface can undergo a step bunching instability when the attachment-detachment kinetics is asymmetric, in the sense of a normal Ehrlich-Schwoebel effect. Here we investigate this instability in a model that takes into account the subtle interplay between sublimation and step-step interactions, which breaks the volume-conserving character of the dynamics assumed in previous work. On the basis of a systematically derived continuum equation for the surface profile, we argue that the non-conservative terms pose a limitation on the size of emerging step bunches. This conclusion is supported by extensive simulations of the discrete step dynamics, which show breakup of large bunches into smaller ones as well as arrested coarsening and periodic oscillations between states with different numbers of bunches.Comment: 26 pages, 11 figure

Soil Fertility Characterization in Mvumi and Mbogo - Komtonga Irrigation Schemes in Kilosa and Mvomero Districts, Morogoro Region, Tanzania.

Soil samples from three (3) mapping units in Mvumi and four (4) mapping units in Mbogo Komtonga representing two irrigation schemes in Kilosa and Mvomero Districts in eastern Tanzania were collected and analyzed for different mineral elements. Using zigzag sampling techniques, 9 composite samples with three replicates were collected at depth 0 – 30 cm from the delineated pedogeomorphic units at a radius of 20 m around the soil pits. Soil samples from each soil type were bulked, thoroughly mixed, sub sampled to obtain a representative composite sample, packed and sent to Mlingano National Soil Service laboratory (NSS), Tanga, Tanzania for the determination of physical chemical fertility indicators. The data showed overall significant (P ≤ 0.05) difference in fertility status in the selected irrigation schemes. The pH of top soils in Mvumi and Mbogo - Komtonga irrigation schemes ranged from 4.4 to 6.3. These were rated as extremely and/or strongly acid to slightly acid. Of the total area studied in Mvumi and Mbogo Komtonga irrigation schemes, 25.5 % is slightly acid, 40.2 % is medium acid, 31.0 % is extremely acid and 3.3 % extremely acid. Similarly, results of organic carbon (OC) determination from the top soil (0 - 30 cm) samples ranged from 26.6 g kg-1 to 51.8 g kg-1. This corresponds to 45.7 g kg-1 to 89.0 g kg-1 SOM in both irrigation schemes. The data showed that % OC in all irrigation schemes was very high in 92.2 % and high in 7.8 % of the surveyed areas. The results show that the top soils of all the surveyed areas in Mvumi and Mbogo - Komtonga irrigation schemes had N in the range of 1.2 to 3.8 mg kg-1, 48.7 % had N below the critical limits whereas 51.3 % were above the same. Available P in both schemes range from 0.68 – 6.53 mg kg-1. Based on the generally accepted threshold P level, all the observed P values in Mvumi and Mbogo - Komtonga respectively were considered to be below the critical range. Cation exchange capacity values in most topsoil in Mvumi and Mbogo - Komtonga irrigation schemes were rated as medium or high to very high. These values range between 27.0 – 54.6 cmol (+) kg-1 and were rated as medium in 25.5 %, high in 35.3 % and very high in 39.2 % of the total surveyed areas. Exchangeable Ca in the topsoil of Mvumi and Mbogo - Komtonga irrigation schemes ranged from 3.99 – 31.3 cmol (+) kg-1. These were rated as medium in 0.96 %, high in 34.3 % and very high in 70.2 %. Based on the critical limits, MV – Pa3 in Mvumi is likely to be deficient of Ca2+ for most crops as it lies below the proposed critical limits. Exchangeable Mg2+ in the irrigation schemes range from 0.28 – 5.07 cmol (+) kg-1, rated as high to very high. These data suggests that all the MUs except for MV – Pa3 in Mvumi and Mbogo - Komtonga have sufficient Mg2+ supplies for crop growth. Potassium in Mvumi and Mbogo – Komtonga irrigation schemes, range from 0.61 - 2.97 cmol (+) kg-1. These were rated as medium in 64.3 % to very high in 35.7 % of the total area. The data shows that in Mvumi K is unlikely to respond similar to Mbogo – Komtonga. The results of Naexch indicates that the levels of Na+ in the top soils corresponds to 0.15 – 0.47 cmol (+) kg-1 soil in both irrigation schemes. These values were rated as low in 16.4 % and medium in 83.6 % and the corresponding ESP range from 0.5 – 2.2 % in Mvumi considered non-sodic. These results suggest that the surveyed areas have no threat to sodicity problems and the major soil fertility constraints were soil reaction (pH), Nitrogen (N), Phosphorus (P) and poor Soil Organic Matter (SOM)

Branching Instabilities in Rapid Fracture: Dynamics and Geometry

We propose a theoretical model for branching instabilities in 2-dimensional fracture, offering predictions for when crack branching occurs, how multiple cracks develop, and what is the geometry of multiple branches. The model is based on equations of motion for crack tips which depend only on the time dependent stress intensity factors. The latter are obtained by invoking an approximate relation between static and dynamic stress intensity factors, together with an essentially exact calculation of the static ones. The results of this model are in good agreement with a sizeable quantity of experimental data.Comment: 9 pages, 11 figure

Centrifugal terms in the WKB approximation and semiclassical quantization of hydrogen

A systematic semiclassical expansion of the hydrogen problem about the classical Kepler problem is shown to yield remarkably accurate results. Ad hoc changes of the centrifugal term, such as the standard Langer modification where the factor l(l+1) is replaced by (l+1/2)^2, are avoided. The semiclassical energy levels are shown to be exact to first order in $\hbar$ with all higher order contributions vanishing. The wave functions and dipole matrix elements are also discussed.Comment: 5 pages, to appear in Phys. Rev.

Towards defining the role of glycans as hardware in information storage and transfer: Basic principles, experimental approaches and recent progress

The term `code' in biological information transfer appears to be tightly and hitherto exclusively connected with the genetic code based on nucleotides and translated into functional activities via proteins. However, the recent appreciation of the enormous coding capacity of oligosaccharide chains of natural glycoconjugates has spurred to give heed to a new concept: versatile glycan assembly by the genetically encoded glycosyltransferases endows cells with a probably not yet fully catalogued array of meaningful messages. Enciphered by sugar receptors such as endogenous lectins the information of code words established by a series of covalently linked monosaccharides as fetters for example guides correct intra- and intercellular routing of glycoproteins, modulates cell proliferation or migration and mediates cell adhesion. Evidently, the elucidation of the structural frameworks and the recognition strategies within the operation of the sugar code poses a fascinating conundrum. The far-reaching impact of this recognition mode on the level of cells, tissues and organs has fueled vigorous investigations to probe the subtleties of protein-carbohydrate interactions. This review presents information on the necessarily concerted approach using X-ray crystallography, molecular modeling, nuclear magnetic resonance spectroscopy, thermodynamic analysis and engineered ligands and receptors. This part of the treatise is flanked by exemplarily chosen insights made possible by these techniques. Copyright (C) 2001 S. Karger AG, Basel

Quantum Smoluchowski equation: A systematic study

The strong friction regime at low temperatures is analyzed systematically starting from the formally exact path integral expression for the reduced dynamics. This quantum Smoluchowski regime allows for a type of semiclassical treatment in the inverse friction strength so that higher order quantum corrections to the original quantum Smoluchowski equation [PRL 87, 086802 (2001), PRL 101, 11903 (2008)] can be derived. Drift and diffusion coefficients are determined by the equilibrium distribution in position and are directly related to the corresponding action of extremal paths and fluctuations around them. It is shown that the inclusion of higher order corrections reproduces the quantum enhancement above crossover for the decay rate out of a metastable well exactly.Comment: 15 pages, 4 figure

Fluctuations and Ergodicity of the Form Factor of Quantum Propagators and Random Unitary Matrices

We consider the spectral form factor of random unitary matrices as well as of Floquet matrices of kicked tops. For a typical matrix the time dependence of the form factor looks erratic; only after a local time average over a suitably large time window does a systematic time dependence become manifest. For matrices drawn from the circular unitary ensemble we prove ergodicity: In the limits of large matrix dimension and large time window the local time average has vanishingly small ensemble fluctuations and may be identified with the ensemble average. By numerically diagonalizing Floquet matrices of kicked tops with a globally chaotic classical limit we find the same ergodicity. As a byproduct we find that the traces of random matrices from the circular ensembles behave very much like independent Gaussian random numbers. Again, Floquet matrices of chaotic tops share that universal behavior. It becomes clear that the form factor of chaotic dynamical systems can be fully faithful to random-matrix theory, not only in its locally time-averaged systematic time dependence but also in its fluctuations.Comment: 12 pages, RevTEX, 4 figures in eps forma