On the theory of collective motion in nuclei. III. From Hamiltonian dynamics to vortex-free fluidity

It is assumed that the Hamiltonian for collective motion in nuclei is invariant under the orthogonal group O(n, $\text{R}$). For degenerate orbits in phase space it is shown that the classical Hamiltonian equations reduce to the equations of a vortex-free fluid with a velocity field determined by independent equations of motion.     

On measures integrating all functions of a given vector lattice

LetE be a vector lattice of real-valued functions defined on a setX, and (E):={{f1}:fE}. Among others, it is shown that, under some additional assumptions onE, every measure that integrates all functionsfE is (E)--smooth iffX is (E)-complete. An application of this general result to various topological situations yields some new measure-theoretic characterizations of realcompact, Borel-complete andN-compact spaces, respectively.     

Algebraic properties of discrete box splines

The central objective of this paper is to discuss linear independence of translates of discrete box splines which we introduced earlier as a device for the fast computation of multivariate splines. The results obtained here allow us to draw conclusions about the structure of such discrete splines which have, in particular, applications to counting the number of nonnegative integer solutions of linear diophantine equations.     

The hyperbolic n-space as a graph in Euclidean (6n−6)-space

We construct for each n2 an isometric C-imbedding HⁿE^6n–6 of the n-dim. hyperbolic space into the Euclidean space E^6n–6 whose image is the graph of a C-map RⁿR^5n–6. This generalizes a well known result of D. Blanusa 1955 (the case n=2).     

Calculus of variations as a basic tool for modelling of reaction paths and localisation of stationary points on potential energy surfaces

ABSTRACT

The theory of calculus of variations is a mathematical tool which is widely used in different scientific areas in particular in physics and chemistry. This theory is strongly related with optimisation. In fact the former seeks to optimise an integral related with some physical magnitude over some space to an extremum by varying a function of the coordinates. On the other hand, reaction paths and potential energy surfaces, in particular their stationary points, are the basis of many chemical theories, in particular reactions rate theories. We present a review where it is gathered together the variational nature of many types of reaction paths: steepest descent, Newton trajectories, artificial force induced reaction (AFIR) paths, gradient extremals, and gentlest ascent dynamics (GAD) curves. The variational basis permits to select the best optimisation technique in order to locate important theoretical objects on a potential energy surface.     

Spin-flip limited exciton dephasing in CdSe/ZnS colloidal quantum dots

The dephasing time of the lowest bright exciton in CdSe/ZnS wurtzite quantum dots is measured from 5 to 170 K and compared with density dynamics within the exciton fine structure using a sensitive three-beam four-wave-mixing technique unaffected by spectral diffusion. Pure dephasing via acoustic phonons dominates the initial dynamics, followed by an exponential zero-phonon line dephasing of 109 ps at 5 K, much faster than the ~10 ns exciton radiative lifetime. The zero-phonon line dephasing is explained by phonon-assisted spin flip from the lowest bright state to dark-exciton states. This is confirmed by the temperature dependence of the exciton lifetime and by direct measurements of the bright-dark-exciton relaxation. Our results give an unambiguous evidence of the physical origin of the exciton dephasing in these nanocrystals.     

Waveform-controlled near-single-cycle milli-joule laser pulses generate sub-10 nm extreme ultraviolet continua

We demonstrate the generation of waveform-controlled laser pulses with 1?mJ pulse energy and a full-width-half-maximum duration of ～4 fs, therefore lasting less than two cycles of the electric field oscillating at their carrier frequency. The laser source is carrier-envelope-phase stabilized and used as the backbone of a kHz repetition rate source of high-harmonic continua with unprecedented flux at photon energies between 100 and 200?eV (corresponding to a wavelength range between 12-6?nm respectively). In combination we use these tools for the complete temporal characterization of the laser pulses via attosecond streaking spectroscopy.