Common invariant subspaces for collections of operators

Let be a collection of bounded operators on a Banach spaceX of dimension at least two. We say that is finitely quasinilpotent at a vectorx ₀X whenever for any finite subset of the joint spectral radius of atx ₀ is equal 0. If such collection contains a non-zero compact operator, then and its commutant have a common non-trivial invariant, subspace. If in addition, is a collection of positive operators on a Banach lattice, then has a common non-trivial closed ideal. This result and a recent remarkable theorem of Turovskii imply the following extension of the famous result of de Pagter to semigroups. Let be a multiplicative semigroup of quasinilpotent compact positive operators on a Banach lattice of dimension at least two. Then has a common non-trivial invariant closed ideal.This work was supported by the Research Ministry of Slovenia.     

Spectral Theory of Pauli–Fierz Operators

We study spectral properties of Pauli–Fierz operators which are commonly used to describe the interaction of a small quantum system with a bosonic free field. We give precise estimates of the location and multiplicity of the singular spectrum of such operators. Applications of these estimates, which will be discussed elsewhere, concern spectral and ergodic theory of non-relativistic QED. Our proof has two ingredients: the Feshbach method, which is developed in an abstract framework, and Mourre theory applied to the operator restricted to the sector orthogonal to the vacuum.     

Observation of the transverse optical plasmon in SmLa0.8Sr0.2CuO4-delta

We present microwave and infrared measurements on SmLa0.8Sr0.2CuO4-delta, which are direct evidence for the existence of a transverse optical plasma mode, observed as a peak in the c-axis optical conductivity. This mode appears as a consequence of the existence of two different intrinsic Josephson couplings between the CuO2 layers, one with a Sm2O2 block layer, and the other one with a (La,Sr)2O2-delta block layer. From the frequencies and the intensities of the collective modes we determine the value of the compressibility of the two dimensional electron fluid in the copper oxygen planes.     

First measurement of the ratio B(t --> Wb)/B(t --> Wq) and associated limit on the Cabibbo-Kobayashi-Maskawa element /V(tb)/

We present the first measurement of the ratio of branching fractions R identical withB(t-->Wb)/B(t-->Wq) from p_p collisions at sqrt[s] = 1.8 TeV. The data set corresponds to 109 pb(-1) of data recorded by the Collider Detector at Fermilab during the 1992-95 Tevatron run. We measure R = 0.94(+0.31)(-0.24)(stat+syst) or R>0.61 (0.56) at 90% (95)% C.L., in agreement with the standard model predictions. This measurement yields a limit on the Cabibbo-Kobayashi-Maskawa quark mixing matrix element /V(tb)/ under the assumption of three generations and unitarity.     

Nonexistence of some Antipodal Distance-regular Graphs of Diameter Four

We find an inequality involving the eigenvalues of a regular graph; equality holds if and only if the graph is strongly regular. We apply this inequality to the first subconstituents of a distance-regular graph and obtain a simple proof of the fundamental bound for distance-regular graphs, discovered by Juri i , Koolen and Terwilliger. Using this we show that for distance-regular graphs with certain intersection arrays, the first subconstituent graphs are strongly regular. From these results we prove the nonexistence of distance-regular graphs associated to 20 feasible intersection arrays from the book Distance-Regular Graphs by Brouwer, Cohen and Neumaier .     

Tight Distance-Regular Graphs

We consider a distance-regular graph with diameter d 3 and eigenvalues k = ₀ > ₁ > ... > _d . We show the intersection numbers a ₁, b ₁ satisfy

A Generalization of Herrlich's Question on Almost Reflective and Coreflective Subclasses of Top and Unif

H. Herrlich asked in Topology Appl. 49 (1993), 251–264, whether there are nontrivial classes of topological spaces that are almost reflective and almost coreflective at the same time. This question was dealt with (in Huek and Tozzi, Appl. Categ. Structures 4 (1996), 57–68) in a more general setting than almost reflective and almost coreflective classes. The present paper investigates a modified question: when a nontrivial generalized reflective class of topological or uniform spaces is equivalent to a generalized coreflective class of spaces.     

Extreme-ultraviolet harmonic generation near 13 nm with a two-color elliptically polarized laser field

Theoretical results for high-harmonic generation by a two-color elliptically polarized laser field are presented. Special emphasis is placed on coherent radiation near 13 nm in connection with the development of extreme-ultraviolet lithography. Linearly polarized radiation at this wavelength can be obtained with a linearly polarized bichromatic laser field, whereas circularly polarized radiation can be generated with a bichromatic circularly polarized field with counterrotating coplanar components. In both cases the harmonic emission efficiencies at the saturation intensity are more than 1 order of magnitude larger than for harmonic generation with a monochromatic linearly polarized field.     

Shaping of picosecond pulses for pumping optical parametric amplification

The use of temporally shaped pump pulses for optical parametric chirped-pulse amplification can increase the efficiency and suppress possible spectral distortions in this process. With this goal in mind a novel method for shaping narrowband picosecond pulses has been developed. The method is based on the pulse stacking principle, where replicas of the incoming pulse are created in a specially designed four-beam interferometer. The replicas are recombined with appropriate relative delays. The interferometer design allows for a unique flexibility in varying the pulse shape, since all relevant degrees of freedom, such as relative intensities and delays between the pulse replicas are independently adjustable. Here we describe the design of our device in detail and report on the experimental demonstration of its pulse-shaping capabilities. PACS 42.65.Yj; 42.65.Re; 42.81.Gs