Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

Bohr's discussion of the fourth uncertainty relation revisited

Bohr's 1930 derivation of the uncertainty relation c ² m th bears a close relationship to Einstein's 1913 derivation of the gravitational redshift via the equivalence principle. A rewording of Bohr's argument is presented here, not taking the last step of acceleration as equivalent to a uniform gravity field, thus yielding a derivation of the formula c ² m th, avoiding Treder's 1971 objection.     

Direction-Dependent Free Energy Singularity of the Antiferroelectric Asymmetric Six-Vertex Model

The transition from the ordered commensurate phase to the incommensurate Gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the external fields (h, v). In the (h, v) plane, the phase boundary is approached along straight lines v = k h, where (h, v) measures the displacement from the phase boundary. It is found that the free energy singularity displays the exponent 3/2 typical of the Pokrovski–Talapov transition f const(h)^3/2 for any direction other than the tangential one. In the latter case f shows a discontinuity in the third derivative.     

The hydrodynamic limit of a one-dimensional nearest neighbor gradient system

We study the hydrodynamic behavior of a one-dimensional nearest neighbor gradient system with respect to a positive convex potential . In the hydrodynamic limit the density distribution is shown to evolve according to the nonlinear diffusion equation ,(q)/t= (²/dq²){F([1/₁(q)]), with F= –.     

Femtosecond relaxation dynamics of electronic processes and electron-phonon coupling in YBa2Cu3O7-δ and PrBa2Cu3O7 epitaxial films

The room temperature femtosecond relaxation dynamics of reflection spectra of YBa₂Cu₃O_7- with different oxygen contents and PrBa₂Cu₃O₇ epitaxial films have been studied. The relaxation times of R(t) in YBa₂Cu₃O_7- increase from less than 100 fs to more than 1 ps with increasing and with substitution of Pr for Y. The electron and lattice temperature profiles at these quasi-equilibrium state are calculated from the nonequilibrium energy-balance model. The process of electronphonon energy transfer was found to be dominated in our experiments. These results reveal that in 123 phase superconductors decrease of carrier concentration slows down the carrier-phonon coupling and the type of the electron-phonon interaction would be localized. The dependence of electron-phonon coupling to oxygen defects in YBa₂Cu₃O_7- was found to be exp(–).     

Cu-EPR in YBa2Cu3O6+δ single crystals

We report on the observation of Cu-EPR signals in single crystalline material of YBa₂Cu₃O₆₊ in the narrow oxygen concentration range 0.7<<0.9 and for temperatures 80 K<T<200 K. We provide evidence that the signal results from Cu²⁺ ions located in Cu(1)OCu(1) chain fragments.     

Mosaic Structure of (001)YBa2Cu3O7-δ/(10.2)Al2O3 Epitaxial Films and Millimeter Waveband Properties of Microstrip Resonators

The c-axis single-phase YBa₂Cu₃O_7- films ( = 0-0.15) on sapphire substrates prepared by the laser ablation technique and the band-pass stripline resonators for 34 GHz-range have been investigated. Increasing disorientation of mosaic block structure of YBa₂Cu₃O_7- films is related to increasing surface resistance R_s at 135 GHz-range and decreasing unloaded quality factor Q_o of linear stripline resonators. The linear dependence between the YBa₂Cu₃O_7- film mosaicity (M) and half-width B₁ of 00.13 reflecting component is determined. The reflection spreading is due to microstrains resulted mainly from the coherent adjustment of the YBa₂Cu₃O_7- film lattice to GdBa₂Cu₃O_7- sub-layer and sapphire substrate. Increasing number of the block characterized by a weak radial lattice adjustment () is demonstrated by spreading of 00.13 reflection. It is found out that depends on the Bragg angle of reflection due to inhomogenity of YBa₂Cu₃O_7- mosaic structure, which resulted from the gradual mosaicity decreasing with the depth.     

Subsolidus phase relation and crystal structure in the Pr<Subscript>1+x-y</Subscript>Ba<Subscript>2-x-z</Subscript>Ca<Subscript>y+z</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7±δ</Subscript> system

The Pr_1+xBa_2-xCu₃O_7± solid solution was investigated by means of X-ray powder diffraction combined with Rietveld analysis. A Pr123 single phase could be synthesized under Pr-rich conditions by sintering at 950 °C in air. The solubility range of Pr_1+xBa_2-xCu₃O_7± solid solution is 0.08x0.80. The structure of Pr_1+xBa_2-xCu₃O_7± for 0.08x<0.30 is orthorhombic. The structure transforms into tetragonal for 0.30x0.80. To form the Pr123 single phase, the Ba sites in the Pr123 structure must have partial Pr ions, and the least amount is x=0.08. Ba ions cannot occupy the sites of Pr ions. In the Pr123 structure, Ca ions can replace Pr ions; the highest value is x=0.4 in the PrBa_2-xCa_xCu₃O_7± system under our experimental conditions. However, Ca ions cannot replace Ba ions. The ionic radius plays a more important role than the chemical properties in the substitution between Pr, Ba and Ca ions in the Pr123 structure. PACS 61.50.Ah; 64.70.Kb; 61.72.Ff     

Derivations commuting with abelian gauge actions on lattice systems

Let be an action of a compact abelian groupG on aC*-algebraA, and assume that the fixed-point subalgebraA is an AF-algebra. We show that if is a closed *-derivation onA commuting with , and the restriction of toA generates a one-parameter group of *-automorphisms, then itself is a generator. In particular, the result applies if is an infinite product action ofG on a UHF algebra. Furthermore, if in this situation ₁ and ₂ are two derivations both satisfying the hypotheses on , and ₁ and ₂ have the same restriction toA , then there exists a one-parameter subgroup of the action with generator ₀ such thatD(₁)D(₂)D(₀) is a joint core for the three derivations, and ₂=₁+₀ on this core.     

Remark on the equations δR 2/δg ij = 0

It is shown that the 4-dimensional equationsR ²/g _ij =0 may be rewritten as 5-dimensional equations which are linear in the components of the Riemann tensor.