Graded commutative algebras: examples, classification, open problems

We consider \G-graded commutative algebras, where \G is an abelian group. Starting from a remarkable example of the classical algebra of quaternions and, more generally, an arbitrary Clifford algebra, we develop a general viewpoint on the subject. We then give a recent classification result and formulate an open problem

Orbital stability: analysis meets geometry

We present an introduction to the orbital stability of relative equilibria of Hamiltonian dynamical systems on (finite and infinite dimensional) Banach spaces. A convenient formulation of the theory of Hamiltonian dynamics with symmetry and the corresponding momentum maps is proposed that allows us to highlight the interplay between (symplectic) geometry and (functional) analysis in the proofs of orbital stability of relative equilibria via the so-called energy-momentum method. The theory is illustrated with examples from finite dimensional systems, as well as from Hamiltonian PDE's, such as solitons, standing and plane waves for the nonlinear Schr{\"o}dinger equation, for the wave equation, and for the Manakov system

Doubly dressed bosons - exciton-polaritons in a strong terahertz field

We demonstrate the existence of a novel quasiparticle: an exciton in a semiconductor doubly dressed with two photons of different wavelengths: near infrared cavity photon and terahertz (THz) photon, with the THz coupling strength approaching the ultra-strong coupling regime. This quasiparticle is composed of three different bosons, being a mixture of a matter-light quasiparticle. Our observations are confirmed by a detailed theoretical analysis, treating quantum mechanically all three bosonic fields. The doubly dressed quasiparticles retain the bosonic nature of their constituents, but their internal quantum structure strongly depends on the intensity of the applied terahertz field.Comment: 12 pages, 9 figure

A series of algebras generalizing the octonions and Hurwitz-Radon identity

International audienceWe study non-associative twisted group algebras over (ℤ2)n with cubic twisting functions. We construct a series of algebras that extend the classical algebra of octonions in the same way as the Clifford algebras extend the algebra of quaternions. We study their properties, give several equivalent definitions and prove their uniqueness within some natural assumptions. We then prove a simplicity criterion. We present two applications of the constructed algebras and the developed technique. The first application is a simple explicit formula for the following famous square identity: (a21+⋯+a2N)(b21+⋯+b2ρ(N))=c21+⋯+c2N , where c k are bilinear functions of the a i and b j and where ρ(N) is the Hurwitz-Radon function. The second application is the relation to Moufang loops and, in particular, to the code loops. To illustrate this relation, we provide an explicit coordinate formula for the factor set of the Parker loop

Nuclear phytochrome a signaling promotes phototropism in Arabidopsis.

Phototropin photoreceptors (phot1 and phot2 in Arabidopsis thaliana) enable responses to directional light cues (e.g., positive phototropism in the hypocotyl). In Arabidopsis, phot1 is essential for phototropism in response to low light, a response that is also modulated by phytochrome A (phyA), representing a classical example of photoreceptor coaction. The molecular mechanisms underlying promotion of phototropism by phyA remain unclear. Most phyA responses require nuclear accumulation of the photoreceptor, but interestingly, it has been proposed that cytosolic phyA promotes phototropism. By comparing the kinetics of phototropism in seedlings with different subcellular localizations of phyA, we show that nuclear phyA accelerates the phototropic response, whereas in the fhy1 fhl mutant, in which phyA remains in the cytosol, phototropic bending is slower than in the wild type. Consistent with this data, we find that transcription factors needed for full phyA responses are needed for normal phototropism. Moreover, we show that phyA is the primary photoreceptor promoting the expression of phototropism regulators in low light (e.g., PHYTOCHROME KINASE SUBSTRATE1 [PKS1] and ROOT PHOTO TROPISM2 [RPT2]). Although phyA remains cytosolic in fhy1 fhl, induction of PKS1 and RPT2 expression still occurs in fhy1 fhl, indicating that a low level of nuclear phyA signaling is still present in fhy1 fhl

XUV digital in-line holography using high-order harmonics

A step towards a successful implementation of timeresolved digital in-line holography with extreme ultraviolet radiation is presented. Ultrashort XUV pulses are produced as high-order harmonics of a femtosecond laser and a Schwarzschild objective is used to focus harmonic radiation at 38 nm and to produce a strongly divergent reference beam for holographic recording. Experimental holograms of thin wires are recorded and the objects reconstructed. Descriptions of the simulation and reconstruction theory and algorithms are also given. Spatial resolution of few hundreds of nm is potentially achievable, and micrometer resolution range is demonstrated.Comment: 8 pages, 8 figure

Cancellation of probe effects in measurements of spin polarized momentum density by electron positron annihilation

Measurements of the two dimensional angular correlation of the electron-positron annihilation radiation have been done in the past to detect the momentum spin density and the Fermi surface. We point out that the momentum spin density and the Fermi Surface of ferromagnetic metals can be revealed within great detail owing to the large cancellation of the electron-positron matrix elements which in paramagnetic multiatomic systems plague the interpretation of the experiments. We prove our conjecture by calculating the momentum spin density and the Fermi surface of the half metal CrO2, who has received large attention due to its possible applications as spintronics material

Experimental evidence for fast cluster formation of chain oxygen vacancies in YBa2Cu3O7-d being at the origin of the fishtail anomaly

We report on three different and complementary measurements, namely magnetisation measurements, positron annihilation spectroscopy and NMR measurements, which give evidence that the formation of oxygen vacancy clusters is on the origin of the fishtail anomaly in YBa2Cu3O7-d. While in the case of YBa2Cu3O7.0 the anomaly is intrinsically absent, it can be suppressed in the optimally doped state where vacancies are present. We therefore conclude that the single vacancies or point defects can not be responsible for this anomaly but that clusters of oxygen vacancies are on its origin.Comment: 10 pages, 4 figures, submitted to PR

Optical symmetries and anisotropic transport in high-Tc superconductors

A simple symmetry analysis of in-plane and out-of-plane transport in a family of high temperature superconductors is presented. It is shown that generalized scaling relations exist between the low frequency electronic Raman response and the low frequency in-plane and out-of-plane conductivities in both the normal and superconducting states of the cuprates. Specifically, for both the normal and superconducting state, the temperature dependence of the low frequency $B_{1g}$ Raman slope scales with the $c-$axis conductivity, while the $B_{2g}$ Raman slope scales with the in-plane conductivity. Comparison with experiments in the normal state of Bi-2212 and Y-123 imply that the nodal transport is largely doping independent and metallic, while transport near the BZ axes is governed by a quantum critical point near doping $p\sim 0.22$ holes per CuO$_{2}$ plaquette. Important differences for La-214 are discussed. It is also shown that the $c-$ axis conductivity rise for $T\ll T_{c}$ is a consequence of partial conservation of in-plane momentum for out-of-plane transport.Comment: 16 pages, 8 Figures (3 pages added, new discussion on pseudogap and charge ordering in La214