The Ore condition, affiliated operators, and the lamplighter group

Let G be the wreath product of Z and Z/2, the so called lamplighter group and k a commutative ring. We show that kG does not have a classical ring of quotients (i.e. does not satisfy the Ore condition). This answers a Kourovka notebook problem. Assume that kG is contained in a ring R in which the element 1-x is invertible, with x a generator of Z considered as subset of G. Then R is not flat over kG. If k is the field of complex numbers, this applies in particular to the algebra UG of unbounded operators affiliated to the group von Neumann algebra of G. We present two proofs of these results. The second one is due to Warren Dicks, who, having seen our argument, found a much simpler and more elementary proof, which at the same time yielded a more general result than we had originally proved. Nevertheless, we present both proofs here, in the hope that the original arguments might be of use in some other context not yet known to us.Comment: LaTex2e, 7 pages. Added a new proof of the main result (due to Warren Dicks) which is shorter, easier and more elementary, and at the same time yields a slightly more general result. Additionally: misprints removed. to appear in Proceedings of "Higher dimensional manifold theory", Conference at ICTP Trieste 200

On a conjecture of Atiyah

In this note we explain how the computation of the spectrum of the lamplighter group from \cite{Grigorchuk-Zuk(2000)} yields a counterexample to a strong version of the Atiyah conjectures about the range of $L^2$-Betti numbers of closed manifolds.Comment: 8 pages, A4 pape

Following Strain-Induced Mosaicity Changes of Ferroelectric Thin Films by Ultrafast Reciprocal Space Mapping

We investigate coherent phonon propagation in a thin film of ferroelectric PbZr0.2Ti0.8O3 (PZT) by ultrafast x-ray diffraction (UXRD) experiments, which are analyzed as time-resolved reciprocal space mapping (RSM) in order to observe the in- and out-of-plane structural dynamics simultaneously. The mosaic structure of the PZT leads to a coupling of the excited out-of-plane expansion to in-plane lattice dynamics on a picosecond timescale, which is not observed for out-of-plane compression.Comment: 5 pages, 4 figure

Synopsis of biological data on the pink shrimp, Pandalus borealis Kroyer, 1838

This synopsis of the literature was designed to summarize the biological and biochemical studies involving Pandalus borealis as well as to provide a summary of the literature regarding the fisheries data published before early 1984. Included are many unpublished observations, drawn from studies at the State of Maine Department of Marine Resources Laboratory in West Boothbay Harbor, Maine. (PDF file contains 63 pages.

Thermoelastic study of nanolayered structures using time-resolved x-ray diffraction at high repetition rate

We investigate the thermoelastic response of a nanolayered sample composed of a metallic SrRuO3 (SRO) electrode sandwiched between a ferroelectric Pb(Zr0.2Ti0.8)O3 (PZT) film with negative thermal expansion and a SrTiO3 substrate. SRO is rapidly heated by fs-laser pulses with 208 kHz repetition rate. Diffraction of x-ray pulses derived from a synchrotron measures the transient out-of-plane lattice constant c of all three materials simultaneously from 120 ps to 5 mus with a relative accuracy up to Delta c/c = 10^-6. The in-plane propagation of sound is essential for understanding the delayed out of plane expansion.Comment: 5 pages, 3 figure

Quantum interface unbinding transitions

We consider interfacial phenomena accompanying bulk quantum phase transitions in presence of surface fields. On general grounds we argue that the surface contribution to the system free energy involves a line of singularities characteristic of an interfacial phase transition, occurring below the bulk transition temperature T_c down to T=0. This implies the occurrence of an interfacial quantum critical regime extending into finite temperatures and located within the portion of the phase diagram where the bulk is ordered. Even in situations, where the bulk order sets in discontinuously at T=0, the system's behavior at the boundary may be controlled by a divergent length scale if the tricritical temperature is sufficiently low. Relying on an effective interfacial model we compute the surface phase diagram in bulk spatial dimensionality $d\geq 2$ and extract the values of the exponents describing the interfacial singularities in $d\geq 3$

Localized excited charge carriers generate ultrafast inhomogeneous strain in the multiferroic BiFeO3_3

We apply ultrafast X-ray diffraction with femtosecond temporal resolution to monitor the lattice dynamics in a thin film of multiferroic BiFeO$_3$ after above-bandgap photoexcitation. The sound-velocity limited evolution of the observed lattice strains indicates a quasi-instantaneous photoinduced stress which decays on a nanosecond time scale. This stress exhibits an inhomogeneous spatial profile evidenced by the broadening of the Bragg peak. These new data require substantial modification of existing models of photogenerated stresses in BiFeO$_3$: the relevant excited charge carriers must remain localized to be consistent with the data

Heterogeneous nucleation near a metastable vapour-liquid transition: the effect of wetting transitions

Phase transformations such as freezing typically start with heterogeneous nucleation. Heterogeneous nucleation near a wetting transition, of a crystalline phase is studied. The wetting transition occurs at or near a vapour-liquid transition which occurs in a metastable fluid. The fluid is metastable with respect to crystallisation, and it is the crystallisation of this fluid phase that we are interested in. At a wetting transition a thick layer of a liquid phase forms at a surface in contact with the vapour phase. The crystalline nucleus is then immersed in this liquid layer, which reduces the free energy barrier to nucleation and so dramatically increases the nucleation rate. The variation in the rate of heterogeneous nucleation close to wetting transitions is calculated for systems in which the longest-range forces are dispersion forces.Comment: 11 pages including 3 figure