877 research outputs found
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 MatemĂĄtica Iberoamericana Proceedings of the âSegundas Jornadas de TeorĂa de NĂșmeros â (Madrid, 2007), 119â134
In this note, we survey results concerning variations of the LĂŒck-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 âSegundas Jornadas de TeorĂa de NĂșmerosâ, Madrid, 2007. The object that we consider in this note is given by the following Definition 1. [5] Let Î be a group finitely generated by x1,...,xl. Let P = â gâÎ cgg â CÎ such that cg = cgâ1. 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 LĂŒck-Fuglede-Kadison determinant [10]) of 1 â λP is given by â â anλ mÎ(P, λ) =â 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 â CÎ. We will often consider the generating function for the anâs uÎ(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 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 ,
, the low-voltage shot noise at zero frequency and zero
temperature becomes proportional to the magnitude of intrinsic
broadening ( 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 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
asymmetric junctions with a linear dimension much larger than the
superconducting coherence length we find a -like current-phase
relation, whereas for contacts on the scale of the coherence length or smaller
the usual -like behavior is observed. Our results compare well with
recent experimental observations.Comment: 10 pages, 12 figures; accepted for publication in Phys. Rev.
- âŠ