Presentations: from Kac-Moody groups to profinite and back

We go back and forth between, on the one hand, presentations of arithmetic and Kac-Moody groups and, on the other hand, presentations of profinite groups, deducing along the way new results on both

Geometry of entangled states, Bloch spheres and Hopf fibrations

We discuss a generalization to 2 qubits of the standard Bloch sphere representation for a single qubit, in the framework of Hopf fibrations of high dimensional spheres by lower dimensional spheres. The single qubit Hilbert space is the 3-dimensional sphere S3. The S2 base space of a suitably oriented S3 Hopf fibration is nothing but the Bloch sphere, while the circular fibres represent the qubit overall phase degree of freedom. For the two qubits case, the Hilbert space is a 7-dimensional sphere S7, which also allows for a Hopf fibration, with S3 fibres and a S4 base. A main striking result is that suitably oriented S7 Hopf fibrations are entanglement sensitive. The relation with the standard Schmidt decomposition is also discussedComment: submitted to J. Phys.

Separation of phosphorylated from non-phosphorylated LHCP polypeptides by two-dimensional electrophoresis

Abstract‘In vitro’ phosphorylated thylakoid polypeptides were studied by means of different electrophoretic techniques. A highly resolving two-dimensional electrophoresis method, recently developed in the laboratory using CHAPS and SDS as detergent for electrofocusing, allows the separation of each of the LHCP apoproteins into several molecular species. Those having more acidic isoelectric points correspond to the phosphorylated forms

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

Bloch oscillations of ultracold atoms: a tool for a metrological determination of h/mRbh/m_{Rb}

We use Bloch oscillations in a horizontal moving standing wave to transfer a large number of photon recoils to atoms with a high efficiency (99.5% per cycle). By measuring the photon recoil of $^{87}Rb$, using velocity selective Raman transitions to select a subrecoil velocity class and to measure the final accelerated velocity class, we have determined $h/m_{Rb}$ with a relative precision of 0.4 ppm. To exploit the high momentum transfer efficiency of our method, we are developing a vertical standing wave set-up. This will allow us to measure $h/m_{Rb}$ better than $10^{-8}$ and hence the fine structure constant $\alpha$ with an uncertainty close to the most accurate value coming from the ($g-2$) determination