Free states of the canonical anticommutation relations

Each gauge invariant generalized free state _A of the anticommutation relation algebra over a complex Hilbert spaceK is characterized by an operatorA onK. It is shown that the cyclic representations induced by two gauge invariant generalized free states _A and _B are quasi-equivalent if and only if the operatorsA ^1/2–B ^1/2 and (I–A)^1/2–(I–B)^1/2 are of Hilbert-Schmidt class. The combination of this result with results from the theory of isomorphisms of von Neumann algebras yield necessary and sufficient conditions for the unitary equivalence of the cyclic representations induced by gauge invariant generalized free states.Work supported in part by US Atomic Energy Commission, under Contract AT (30-1)-2171 and by the National Science Foundation.     

Search for giant Franz-Keldysh-like effects in GaSe and other layered semiconductors

Recently, an anomalously large redshift of the absorption edge with electric field was claimed for -GaSe_1–x S _x layered crystals. We have studied Bridgman grown -GaSe crystals as well as vapor transport grown -GaS, and 2H-WSe₂. While we have observed a shift in the absorption edge for -GaSe similar to that reported in previous work, our results demonstrate that the redshift arises from Joule heating, and is thus temperature induced, rather than intrinsic. For -GaS, much larger resistivities virtually eliminate Joule heating, and our measurements of the electric field induced absorption edge shift yield an estimated upper limit of approximately 0.04 meV · cm/kV for a field of 2.4×10³ kV/cm, in good agreement with the theoretical value expected for the Franz-Keldysh effect.Also at University of Konstanz     

Hadronic equation of state and the onset of kaon condensation

An equation of state is presented which takes the finite size of baryons and of mesons consistently into account and incorporates the contributions of both nonstrange and strange hadrons. All extensive quantities (energy, particle number, entropy) are modified by a factor taking into account the excluded volume due to baryon repulsion. Intensive quantities (pressure) are not modified. This is achieved by introducing a baryon chemical potential, _B, which is shifted from its point-like value, _B ⁰ , by a term proportional to the finite volume of a hadron,V ₀, as follows: _B= _B ⁰ + V₀[P⁰(T, _B ⁰ )–P⁰(T, 0)], whereP ⁰ is the pressure for pointlike particles. The last term is necessary to conserve baryon number at the phase transition point. The differences between the new equation of state and those considered previously in the literature are discussed. It is shown that kaon condensation sets in only in the mixed phase of the transition, where hadrons, quarks and gluons are present simultaneously in thermodynamical equilibrium.     

Phase transition to hyperon matter in neutron stars

Recent progress in the understanding of the high density phase of neutron stars advances the view that a substantial fraction of the matter consists of hyperons. The possible impacts of a highly attractive interaction between hyperons on the properties of compact stars are investigated. We find that a hadronic equation of state with hyperons allows for a first order phase transition to hyperonic matter. The corresponding hyperon stars can have rather small radii of R approximately equal 8 km.     

Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers

We report on an experimental study of supercontinuum generation in photonic crystal fibers with low-intensity femtosecond pulses, which provides evidence for a novel spectral broadening mechanism. The observed results agree with our theoretical calculations carried out without making the slowly varying envelope approximation. Peculiarities of the measured spectra and their theoretical explanation demonstrate that the reason for the white-light generation in photonic crystal fibers is fission of higher-order solitons into redshifted fundamental solitons and blueshifted nonsolitonic radiation.     

From Multifractal Measures to Multifractal Wavelet Series

Given a positive locally finite Borel measure μ on R, a natural way to construct multifractal wavelet series is to set , where . Indeed, under suitable conditions, it is shown that the function F_μ inherits the multifractal properties of μ. The transposition of multifractal properties works with many classes of statistically selfsimilar multifractal measures, enlarging the class of processes which have self-similarity properties and controlled multifractal behaviors. Several perturbations of the wavelet coefficients and their impact on the multifractal nature of F_μ are studied. As an application, multifractal Gaussian processes associated with F_μ are created. We obtain results for the multifractal spectrum of the so-called W-cascades introduced by Arnéodo et al.     

Beam lifetimes of low-charged ions in storage rings

The beam lifetimes and the charge-changing cross-sections for fast low-charged ions are calculated for the energy range of 1–100 MeV/u and compared with experimental data for Mg¹⁺ and U¹⁰⁺ ions recently measured at SIS GSI, Darmstadt. A moderate agreement of calculations with experiment was obtained. The results show that the heavy components of the residual gas (N₂ and Ar) play a key role for projectile charge-changing processes in the energy range considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fibrillar crystals of isotactic polystyrene. II. Aggregation in stirred suspensions

Macroscopic particles of various morphological forms are created by the crystallization of isotactic polystyrene from rapidly stirred solutions. Crystallization from trimethylbenzene over a 150° C temperature range produced spherical particles, globules, fibers, and rings depending upon the growth temperature. Crystallization from cyclohexanol (θ = 83.5°C) produced fibers in the temperature range of 85° to 140° C. Globular structures, similar to those formed by stirrer crystallization in trimethylbenzene developed during the Ziegler-Natta polymerization of styrene in trimethylbenzene between 25° and 75°C. Highly birefringent conical appendages appeared on many of the globules and fibers. The fibers often exhibited a skin-core effect with an average longitudinal and transverse orientation of the chain molecules in the skin and core, respectively. The skin frequently displayed periodic banded extinctions. All of these macrostructures consisted of a highly porous assembly of constituent microfibrillar units. It is believed that the morphogenesis of these structures involves the gradual aggregation of microfibrils under the influence of the flow patterns of the system.     

Fluorescence Properties of Selected Benzo[c]phenanthridines

The fluorescence properties of selected benzo[c]phenanthridines (BPs) were examined. The effect of structure, pH and solvent on the fluorescence properties has been investigated. It was found out that the presence of charged iminium nitrogen significantly decreased the fluorescence of the compounds. The fluorescence (intensity as well as emission spectra shape) of the investigated compounds was significantly dependent on pH as well as used solvent. The utilization in epigenetic modification mechanisms studies as demethylase probe and as possible pH indicator was suggested.     

Spectral properties of operators of the theory of harmonic potential

We classify the points of the spectrum of the operatorsB andB ^* of the theory of harmonic potential on a smooth closed surfaceS ³. These operators give the direct value onS of the normal derivative of the simple layer potential and the double layer potential. We show that zero can belong to the point spectrum of both operators inL ₂ (S). We prove that the half-interval [–2, 2) is densely filled by spectrum points of the operators for a varying surface; this is a generalization of the classical result of Plemelj. We obtain a series of new spectral properties of the operatorsB andB ^* on ellipsoidal surfaces.Translated fromMatematicheskie Zametki, Vol. 59, No. 1, pp. 3–11, January, 1996.This research was partially supported by the Russian Foundation for Basic Research.