Electronic Raman scattering on under-doped Hg-1223 high-Tc superconductors:investigations on the symmetry of the order parameter

In order to obtain high quality, reliable electronic Raman spectra of a high-Tc superconductor compound, we have studied strongly under-doped HgBa2Ca2Cu3O8+d. This choice was made such as to i)minimize oxygen disorder in the Hg-plane generated by oxygen doping ii) avoid the need of phonon background subtraction from the raw data iii)eliminate traces of parasitic phases identified and monitored on the crystal surface. Under these experimental conditions we are able to present the pure electronic Raman response function in the B2g, B1g, A1g+B2g and A1g+B1g channels. The B2g spectrum exhibits a linear frequency dependence at low energy whereas the B1g one shows a cubic-like dependence. The B2g and B1g spectra display two well defined maxima at 5.6kBTc and 9kBTc respectively. In mixed A1g channels an intense electronic peak centered around 6.4 kBTc is observed. The low energy parts of the spectra correspond to the electronic response expected for a pure dx2-y2 gap symmetry and can be fitted up to the gap energy for the B1g channel. However, in the upper parts, the relative position of the B1g and B2g peaks needs expanding the B2g Raman vertex to second order Fermi surface harmonics to fit the data with the dx2-y2 model. The sharper and more intense A1g peak appears to challenge the Coulomb screening efficiency present for this channel. As compared to previous data on more optimally doped, less stoichiometric Hg-1223 compounds, this work reconciles the electronic Raman spectra of under- doped Hg-1223 crystals with the dx2-y2 model, provided that the oxygen doping is not too strong. This apparent extreme sensitivity of the electronic Raman spectra to the low lying excitations induced by oxygen doping in the superconducting state is emphasized here and remains an open question.Comment: 12 pages, 5 figure

Property (T) and rigidity for actions on Banach spaces

We study property (T) and the fixed point property for actions on $L^p$ and other Banach spaces. We show that property (T) holds when $L^2$ is replaced by $L^p$ (and even a subspace/quotient of $L^p$), and that in fact it is independent of $1\leq p<\infty$. We show that the fixed point property for $L^p$ follows from property (T) when 1. For simple Lie groups and their lattices, we prove that the fixed point property for $L^p$ holds for any $1< p<\infty$ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive Banach spaces.Comment: Many minor improvement

Intrinsic Low Temperature Paramagnetism in B-DNA

We present experimental study of magnetization in $\lambda$-DNA in conjunction with structural measurements. The results show the surprising interplay between the molecular structures and their magnetic property. In the B-DNA state, $\lambda$-DNA exhibits paramagnetic behaviour below 20 K that is non-linear in applied magnetic field whereas in the A-DNA state, remains diamagnetic down to 2 K. We propose orbital paramagnetism as the origin of the observed phenomena and discuss its relation to the existence of long range coherent transport in B-DNA at low temperature.Comment: 5 pages, 4 figures, submitted to Physical Review Letters October 200

Orbit equivalence rigidity for ergodic actions of the mapping class group

We establish orbit equivalence rigidity for any ergodic, essentially free and measure-preserving action on a standard Borel space with a finite positive measure of the mapping class group for a compact orientable surface with higher complexity. We prove similar rigidity results for a finite direct product of mapping class groups as well.Comment: 11 pages, title changed, a part of contents remove

Fermi Velocity Spectrum and Incipient Magnetism in TiBe2

We address the origin of the incipient magnetism in TiBe$_2$ through precise first principles calculations, which overestimate the ferromagnetic tendency and therefore require correction to account for spin fluctuations. TiBe$_2$ has sharp fine structure in its electronic density of states, with a van Hove singularity only 3 meV above the Fermi level. Similarly to the isovalent weak ferromagnet ZrZn$_2$, it is flat bands along the K-W-U lines of hexagonal face of the fcc Brillouin zone make the system prone to magnetism, and more so if electrons are added. We find that the Moriya $B$ coefficient (multiplying $\frac{\omega}{q}$ in the fluctuation susceptibility $\Delta \chi(q,\omega)$) is divergent when the velocity vanishes at a point on the Fermi surface, which is very close (3 meV) to occurring in TiBe$_2$. In exploring how the FM instability (the $q$=0 Stoner enhancement is $S\approx 60$) might be suppressed by fluctuations in TiBe$_2$, we calculate that the Moriya A coefficient (of $q^2$) is negative, so $q$=0 is not the primary instability. Explicit calculation of $\chi_o(q)$ shows that its maximum occurs at the X point $(1,0,0)\frac{2\pi}{a}$; TiBe$_2$ is thus an incipient {\it anti}ferromagnet rather than ferromagnet as has been supposed. We further show that simple temperature smearing of the peak accounts for most of the temperature dependence of the susceptibility, which previously had been attributed to local moments (via a Curie-Weiss fit), and that energy dependence of the density of states also strongly affects the magnetic field variation of $\chi$

A lattice in more than two Kac--Moody groups is arithmetic

Let $\Gamma$ be an irreducible lattice in a product of n infinite irreducible complete Kac-Moody groups of simply laced type over finite fields. We show that if n is at least 3, then each Kac-Moody groups is in fact a simple algebraic group over a local field and $\Gamma$ is an arithmetic lattice. This relies on the following alternative which is satisfied by any irreducible lattice provided n is at least 2: either $\Gamma$ is an S-arithmetic (hence linear) group, or it is not residually finite. In that case, it is even virtually simple when the ground field is large enough. More general CAT(0) groups are also considered throughout.Comment: Subsection 2.B was modified and an example was added ther

Bose-Einstein distribution, condensation transition and multiple stationary states in multiloci evolution of diploid population

The mapping between genotype and phenotype is encoded in the complex web of epistatic interaction between genetic loci. In this rugged fitness landscape, recombination processes, which tend to increase variation in the population, compete with selection processes that tend to reduce genetic variation. Here we show that the Bose-Einstein distribution describe the multiple stationary states of a diploid population under this multi-loci evolutionary dynamics. Moreover, the evolutionary process might undergo an interesting condensation phase transition in the universality class of a Bose-Einstein condensation when a finite fraction of pairs of linked loci, is fixed into given allelic states. Below this phase transition the genetic variation within a species is significantly reduced and only maintained by the remaining polymorphic loci.Comment: (12 pages, 7 figures

On the distortion of twin building lattices

We show that twin building lattices are undistorted in their ambient group; equivalently, the orbit map of the lattice to the product of the associated twin buildings is a quasi-isometric embedding. As a consequence, we provide an estimate of the quasi-flat rank of these lattices, which implies that there are infinitely many quasi-isometry classes of finitely presented simple groups. In an appendix, we describe how non-distortion of lattices is related to the integrability of the structural cocycle

Ordering in a spin glass under applied magnetic field

Torque, torque relaxation, and magnetization measurements on a AuFe spin glass sample are reported. The experiments carried out up to 7 T show a transverse irreversibility line in the (H,T) plane up to high applied fields, and a distinct strong longitudinal irreversibility line at lower fields. The data demonstrate for that this type of sample, a Heisenberg spin glass with moderately strong anisotropy, the spin glass ordered state survives under high applied fields in contrast to predictions of certain "droplet" type scaling models. The overall phase diagram closely ressembles those of mean field or chiral models, which both have replica symmetry breaking transitions.Comment: 4 pages, 3 figures, accepted for PR