Necessary conditions for Schatten class localization operators

We study time-frequency localization operators of the form , where is the symbol of the operator and are the analysis and synthesis windows, respectively. It is shown in an earlier paper by the authors that a sufficient condition for , the Schatten class of order , is that belongs to the modulation space and the window functions to the modulation space . Here we prove a partial converse: if for every pair of window functions with a uniform norm estimate, then the corresponding symbol must belong to the modulation space . In this sense, modulation spaces are optimal for the study of localization operators. The main ingredients in our proofs are frame theory and Gabor frames. For and , we recapture earlier results, which were obtained by different methods.

     

79Se investigated by the reaction76Ge(α, nγ)

⁷⁹Se has been investigated by the reaction⁷⁶Ge(α, nγ). Gamma excitation functions (E _{α=10?15 MeV)}, gamma angular distributions and gamma-gamma coincidences (both at (E _{α=12 MeV)}, have been taken. A level scheme has been established, spins and partities have been assigned. The results are compared with rotational bands in neighbouring odd Se isotopes. Nuclear reaction⁷⁶Ge(α, nγ)E _α =12 MeV; measuredE _γ,I _γ,γ-γ coincidences,γ-angular distribution,γ-excitation function.⁷⁹Se deduced levels,J, π. Enriched target, Ge(Li).     

Influence of exchange fields in hybrid pairing superconductors II. Selfconsistent ground states

A previously investigated model of a two band superconductor with hybrid pairing and molecular fields is enlarged by exchange interactions generating those fields. The fields are calculated selfconsistently in molecular field approximation at zero temperature. They turn out to stabilise the previously found new state of gapless superconductivity and non vanishing spin polarization for a wide range of exchange couplings, in particular for zero external field.Dedicated to B. Mühlschlegel on the occasion of his 60th birthdayWork performed within the research program of Sonderforschungsbereich 125 Aachen-Jülich-Köln     

Formation and decomposition of chemically activated cyclopentoxy radicals from the c-C5H9 + O reaction

The formation and the decomposition of chemically activated cyclopentoxy radicals from the c-C5H9 + O reaction have been studied in the gas phase at room temperature. Two different experimental arrangements have been used. Arrangement A consisted of a laser-flash photolysis set up combined with quantitative Fourier transform infrared spectroscopy and allowed the determination of the stable products at 4 mbar. The c-C5H9 radicals were produced via the reaction c-C5H10 + Cl with chlorine atoms from the photolysis of CFCl3; the O atoms were generated by photolysis of SO2. Arrangement B, a conventional discharge flow-reactor with molecular beam sampling, was used to determine the rate coefficient. Here, the hydrocarbon radicals (c-C5H9, C2H5, CH2OCH3) were produced via the reaction of atomic fluorine with c-C5H10, C2H6, and CH3OCH3, respectively, and detected by mass spectrometry after laser photoionization. For the c-C5H9 + O reaction, the relative contributions of intermediate formation (c-C5H9O) and direct abstraction (c-C5H8 + OH) were found to be 68 +/- 5 and 32 +/- 4%, respectively. The decomposition products of the chemically activated intermediate could be identified, and the following relative branching fractions were obtained: c-C5H8O + H (31 +/- 2%), CH2CH(CH2)2CHO + H (40 +/- 5%), 2 C2H4 + H + CO (17 +/- 5%), and C3H4O + C2H4 + H (12 +/- 5%). Additionally, the product formation of the c-C5H8 + O reaction was studied, and the following relative yields were obtained (mol %): C2H4, 24%; C3H4O, 18%; c-C5H8O, 30%; c-C5H8O, 23%; 4-pentenal, 5%. The rate coefficient of the c-C5H9 + O reaction was determined relative to the reactions C2H5 + O and CH3OCH2 + O leading to k = (1.73 +/- 0.05) x 10(14) cm3 mol(-1) s(-1). The experimental branching fractions are analyzed in terms of statistical rate theory with molecular and transition-state data from quantum chemical calculations, and high-pressure limiting Arrhenius parameters for the unimolecular decomposition reactions of C5H9O species are derived.     

Dynamics of long-living excitons in tunable potential landscapes

A novel method to experimentally study the dynamics of long-living excitons in coupled quantum well semiconductor heterostructures is presented. Lithographically defined top gate electrodes imprint in-plane artificial potential landscapes for excitons via the quantum confined Stark effect. Excitons are shuttled laterally in a time-dependent potential landscape defined by an interdigitated gate structure. Long-range drift exceeding a distance of at an exciton drift velocity is observed in a gradient potential formed by a resistive gate stripe.     

Symmetries in the representation of grain boundary-plane distributions

Symmetries play a crucial role in the theoretical analysis and visualization of the five macroscopic grain boundary parameters, including the misorientation (three parameters) and the orientation of the boundary-plane (two parameters). The symmetry aspects of the misorientation spaces are very well documented and in this article all possible boundary-plane symmetries are enumerated for the 32 crystallographic point groups. It is observed that the boundary-plane spaces exhibit a wide variety of point group symmetries, which depend both on the crystallographic point group and on the corresponding misorientation (i.e. location in the fundamental zone). The list of symmetries presented here should serve as a guide for graphical representations of not only the distributions of boundary-plane orientations but also for the representation of boundary-plane related properties such as energy, mobility etc.     

Interference of ballistic electrons in an open quantum dot at high temperatures

The Aharonov-Bohm-type oscillations in the ballistic magnetoconductivity of an open quantum dot ～1 μm in size created in the GaAs/AlGaAs heterostructure by local anode oxidation have been studied. The measurements have been performed at temperatures of 4.2 and 1.5 K, which are high enough to expect a considerable suppression of the oscillations with period h/e (in magnetic flux units). The magnetoconductivity oscillations with a period less than the quantum h/e with respect to the magnetic field are observed at 1.5 K. The explanation is proposed on the basis of the interference of the electrons moving along the time-reversed paths inscribed into the quantum dot that have their initial and final points at one of the contacts, i.e., corresponding to a period of h/2e.     

Deformation of Gabor systems

We introduce a new notion for the deformation of Gabor systems. Such deformations are in general nonlinear and, in particular, include the standard jitter error and linear deformations of phase space. With this new notion we prove a strong deformation result for Gabor frames and Gabor Riesz sequences that covers the known perturbation and deformation results. Our proof of the deformation theorem requires a new characterization of Gabor frames and Gabor Riesz sequences. It is in the style of Beurling's characterization of sets of sampling for bandlimited functions and extends significantly the known characterization of Gabor frames “without inequalities” from lattices to non-uniform sets.