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

Superconductor-Ferromagnet Bi-Layers: a Comparison of s-Wave and d-Wave Order Parameters

We study superconductor-ferromagnet bi-layers, not only for s-wave but also for d-wave superconductors. We observe oscillations of the critical temperature when varying the thickness of the ferromagnetic layer for both s-wave and d-wave superconductors. However, for a rotated d-wave order parameter the critical temperature differs considerably from that for the unrotated case. In addition we calculate the density of states for different thicknesses of the ferromagnetic layer; the results reflect the oscillatory behaviour of the superconducting correlations.Comment: 11 pages, 5 figures, accepted for publication in J. Phys.: Condens. Matte

Obstructions to Fibering a Manifold

Given a map f: M \to M of closed topological manifolds we define torsion obstructions whose vanishing is a necessary condition for f being homotopy equivalent to a projection of a locally trivial fiber bundle. If N = S^1, these torsion obstructions are identified with the ones due to Farrell. We have changed the exposition according to the comments of the referee and corrected some typos. The paper will appear in Geometriae Dedicata.Comment: 33 page

Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory

We study D-branes and Ramond-Ramond fields on global orbifolds of Type II string theory with vanishing H-flux using methods of equivariant K-theory and K-homology. We illustrate how Bredon equivariant cohomology naturally realizes stringy orbifold cohomology. We emphasize its role as the correct cohomological tool which captures known features of the low-energy effective field theory, and which provides new consistency conditions for fractional D-branes and Ramond-Ramond fields on orbifolds. We use an equivariant Chern character from equivariant K-theory to Bredon cohomology to define new Ramond-Ramond couplings of D-branes which generalize previous examples. We propose a definition for groups of differential characters associated to equivariant K-theory. We derive a Dirac quantization rule for Ramond-Ramond fluxes, and study flat Ramond-Ramond potentials on orbifolds.Comment: 46 pages; v2: typos correcte

Analytic and Reidemeister torsion for representations in finite type Hilbert modules

For a closed Riemannian manifold we extend the definition of analytic and Reidemeister torsion associated to an orthogonal representation of fundamental group on a Hilbert module of finite type over a finite von Neumann algebra. If the representation is of determinant class we prove, generalizing the Cheeger-M\"uller theorem, that the analytic and Reidemeister torsion are equal. In particular, this proves the conjecture that for closed Riemannian manifolds with positive Novikov-Shubin invariants, the L2 analytic and Reidemeister torsions are equal.Comment: 78 pages, AMSTe

Biblioteca de la Revista Matemática Iberoamericana Proceedings of the “Segundas Jornadas de Teoría de Números ” (Madrid, 2007), 119–134

In this note, we survey results concerning variations of the Lück-Fuglede-Kadison determinant with respect to the base group. Further, we discuss recurrences of coefficients in the determinant for certain distinguished base groups. The note is based on a talk that the second author gave at the “Segundas Jornadas de Teoría de Números”, Madrid, 2007. The object that we consider in this note is given by the following Definition 1. [5] Let Γ be a group finitely generated by x1,...,xl. Let P = ∑ g∈Γ cgg ∈ CΓ such that cg = cg−1. Letλbe a small complex number. More precisely, |λ | < 1, the reciprocal of the sum of the absolute values l1(P) of the coefficients of P. The Mahler measure (or Lück-Fuglede-Kadison determinant [10]) of 1 − λP is given by ∞ ∑ anλ mΓ(P, λ) =− n n, where an =[Pn]0 is the constant coefficient of the n-th power of P;inother words, an is the trace of the element P n ∈ CΓ. We will often consider the generating function for the an’s uΓ(P, λ) = anλ n

Gravitational waves from inspiraling binary black holes

Binary black holes are the most promising candidate sources for the first generation of earth-based interferometric gravitational-wave detectors. We summarize and discuss the state-of-the-art analytic techniques developed during the last years to better describe the late dynamical evolution of binary black holes of comparable masses.Comment: References added and updated; few typos correcte

Passive-performance, analysis, and upgrades of a 1-ton seismic attenuation system

The 10m Prototype facility at the Albert-Einstein-Institute (AEI) in Hanover, Germany, employs three large seismic attenuation systems to reduce mechanical motion. The AEI Seismic-Attenuation-System (AEI-SAS) uses mechanical anti-springs in order to achieve resonance frequencies below 0.5Hz. This system provides passive isolation from ground motion by a factor of about 400 in the horizontal direction at 4Hz and in the vertical direction at 9Hz. The presented isolation performance is measured under vacuum conditions using a combination of commercial and custom-made inertial sensors. Detailed analysis of this performance led to the design and implementation of tuned dampers to mitigate the effect of the unavoidable higher order modes of the system. These dampers reduce RMS motion substantially in the frequency range between 10 and 100Hz in 6 degrees of freedom. The results presented here demonstrate that the AEI-SAS provides substantial passive isolation at all the fundamental mirror-suspension resonances

Interplay between single-particle and two-particle tunneling in normal metal-d-wave superconductor junctions probed by shot noise

We discuss how life-time broadening of quasiparticle states influences single- and two-particle current transport through zero-energy states at normal metal/d-wave superconductor junctions. We distinguish between intrinsic broadening (imaginary part $\eta$ of the energy), which couples the bound states with the superconducting reservoir, and broadening due to leakage through the junction barrier, which couples the bound states with the normal metal reservoir. We show that shot noise is highly sensitive to the mechanism of broadening, while the conductance is not. In the limit of small but finite intrinsic broadening, compared to the junction transparency $D$, $\eta/\Delta_0\ll D$, the low-voltage shot noise at zero frequency and zero temperature becomes proportional to the magnitude $\eta$ of intrinsic broadening ($\Delta_0$ is the maximum d-wave gap).Comment: 6 pages, 4 figures; presented at the SDP2001 conference in Toky

Disordered Josephson Junctions of d-Wave Superconductors

We study the Josephson effect between weakly coupled d-wave superconductors within the quasiclassical theory, in particular, the influence of interface roughness on the current-phase relation and the critical current of mirror junctions and $45^\circ$ asymmetric junctions. For mirror junctions the temperature dependence of the critical current is non-monotonic in the limit of low roughness, but monotonic for very rough interfaces. For $45^\circ$ asymmetric junctions with a linear dimension much larger than the superconducting coherence length we find a $\sin(2\phi)$-like current-phase relation, whereas for contacts on the scale of the coherence length or smaller the usual $\sin\phi$-like behavior is observed. Our results compare well with recent experimental observations.Comment: 10 pages, 12 figures; accepted for publication in Phys. Rev.