Spherical orbit closures in simple projective spaces and their normalizations

Let G be a simply connected semisimple algebraic group over an algebraically closed field k of characteristic 0 and let V be a rational simple G-module of finite dimension. If G/H \subset P(V) is a spherical orbit and if X is its closure, then we describe the orbits of X and those of its normalization. If moreover the wonderful completion of G/H is strict, then we give necessary and sufficient combinatorial conditions so that the normalization morphism is a homeomorphism. Such conditions are trivially fulfilled if G is simply laced or if H is a symmetric subgroup.Comment: 24 pages, LaTeX. v4: Final version, to appear in Transformation Groups. Simplified some proofs and corrected minor mistakes, added references. v3: major changes due to a mistake in previous version

Effect of magnesium doping on the orbital and magnetic order in LiNiO2

In LiNiO2, the Ni3+ ions, with S=1/2 and twofold orbital degeneracy, are arranged on a trian- gular lattice. Using muon spin relaxation (MuSR) and electron spin resonance (ESR), we show that magnesium doping does not stabilize any magnetic or orbital order, despite the absence of interplane Ni2+. A disordered, slowly fluctuating state develops below 12 K. In addition, we find that magnons are excited on the time scale of the ESR experiment. At the same time, a g factor anisotropy is observed, in agreement with $| 3z^{2}-r^{2}>$ orbital occupancy

K-orbit closures on G/B as universal degeneracy loci for flagged vector bundles with symmetric or skew-symmetric bilinear form

We use equivariant localization and divided difference operators to determine formulas for the torus-equivariant fundamental cohomology classes of $K$-orbit closures on the flag variety $G/B$, where G = GL(n,\C), and where $K$ is one of the symmetric subgroups O(n,\C) or Sp(n,\C). We realize these orbit closures as universal degeneracy loci for a vector bundle over a variety equipped with a single flag of subbundles and a nondegenerate symmetric or skew-symmetric bilinear form taking values in the trivial bundle. We describe how our equivariant formulas can be interpreted as giving formulas for the classes of such loci in terms of the Chern classes of the various bundles.Comment: Minor revisions and corrections suggested by referees. Final version, to appear in Transformation Group

Schubert calculus of Richardson varieties stable under spherical Levi subgroups

We observe that the expansion in the basis of Schubert cycles for $H^*(G/B)$ of the class of a Richardson variety stable under a spherical Levi subgroup is described by a theorem of Brion. Using this observation, along with a combinatorial model of the poset of certain symmetric subgroup orbit closures, we give positive combinatorial descriptions of certain Schubert structure constants on the full flag variety in type $A$. Namely, we describe $c_{u,v}^w$ when $u$ and $v$ are inverse to Grassmannian permutations with unique descents at $p$ and $q$, respectively. We offer some conjectures for similar rules in types $B$ and $D$, associated to Richardson varieties stable under spherical Levi subgroups of SO(2n+1,\C) and SO(2n,\C), respectively.Comment: Section 4 significantly shortened, and other minor changes made as suggested by referees. Final version, to appear in Journal of Algebraic Combinatoric

Validity of adiabaticity in Cavity QED

This paper deals with the concept of adiabaticity for fully quantum mechanically cavity QED models. The physically interesting cases of Gaussian and standing wave shapes of the cavity mode are considered. An analytical approximate measure for adiabaticity is given and compared with numerical wave packet simulations. Good agreement is obtained where the approximations are expected to be valid. Usually for cavity QED systems, the large atom-field detuning case is considered as the adiabatic limit. We, however, show that adiabaticity is also valid, for the Gaussian mode shape, in the opposite limit. Effective semiclassical time dependent models, which do not take into account the shape of the wave packet, are derived. Corrections to such an effective theory, which are purely quantum mechanical, are discussed. It is shown that many of the results presented can be applied to time dependent two-level systems.Comment: 10 pages, 9 figure

On spherical twisted conjugacy classes

Let G be a simple algebraic group over an algebraically closed field of good odd characteristic, and let theta be an automorphism of G arising from an involution of its Dynkin diagram. We show that the spherical theta-twisted conjugacy classes are precisely those intersecting only Bruhat cells corresponding to twisted involutions in the Weyl group. We show how the analogue of this statement fails in the triality case. We generalize to good odd characteristic J-H. Lu's dimension formula for spherical twisted conjugacy classes.Comment: proof of Lemma 6.4 polished. The journal version is available at http://www.springerlink.com/content/k573l88256753640

Phonons in the multiferroic langasite Ba_3\_3NbFe_3\_3Si_2\_2O_14\_{14} : evidences for symmetry breaking

The chiral langasite Ba$\_3$NbFe$\_3$Si$\_2$O$\_{14}$ is a multiferroic compound. While its magnetic order below T$\_N$=27 K is now well characterised, its polar order is still controversial. We thus looked at the phonon spectrum and its temperature dependence to unravel possible crystal symmetry breaking. We combined optical measurements (both infrared and Raman spectroscopy) with ab initio calculations and show that signatures of a polar state are clearly present in the phonon spectrum even at room temperature. An additional symmetry lowering occurs below 120~K as seen from emergence of softer phonon modes in the THz range. These results confirm the multiferroic nature of this langasite and open new routes to understand the origin of the polar state

Large phenotype jumps in biomolecular evolution

By defining the phenotype of a biopolymer by its active three-dimensional shape, and its genotype by its primary sequence, we propose a model that predicts and characterizes the statistical distribution of a population of biopolymers with a specific phenotype, that originated from a given genotypic sequence by a single mutational event. Depending on the ratio g0 that characterizes the spread of potential energies of the mutated population with respect to temperature, three different statistical regimes have been identified. We suggest that biopolymers found in nature are in a critical regime with g0 in the range 1-6, corresponding to a broad, but not too broad, phenotypic distribution resembling a truncated Levy flight. Thus the biopolymer phenotype can be considerably modified in just a few mutations. The proposed model is in good agreement with the experimental distribution of activities determined for a population of single mutants of a group I ribozyme.Comment: to appear in Phys. Rev. E; 7 pages, 6 figures; longer discussion in VII, new fig.

Early phrenic motor neuron loss and transient respiratory abnormalities following unilateral cervical spinal cord contusion

Contusion-type cervical spinal cord injury (SCI) is one of the most common forms of SCI observed in patients. In particular, injuries targeting the C3-C5 region affect the pool of phrenic motor neurons (PhMNs) that innervates the diaphragm, resulting in significant and often chronic respiratory dysfunction. Using a previously described rat model of unilateral midcervical C4 contusion with the Infinite Horizon Impactor, we have characterized the early time course of PhMN degeneration and consequent respiratory deficits following injury, as this knowledge is important for designing relevant treatment strategies targeting protection and plasticity of PhMN circuitry. PhMN loss (48% of the ipsilateral pool) occurred almost entirely during the first 24 h post-injury, resulting in persistent phrenic nerve axonal degeneration and denervation at the diaphragm neuromuscular junction (NMJ). Reduced diaphragm compound muscle action potential amplitudes following phrenic nerve stimulation were observed as early as the first day post-injury (30% of pre-injury maximum amplitude), with slow functional improvement over time that was associated with partial reinnervation at the diaphragm NMJ. Consistent with ipsilateral diaphragmatic compromise, the injury resulted in rapid, yet only transient, changes in overall ventilatory parameters measured via whole-body plethysmography, including increased respiratory rate, decreased tidal volume, and decreased peak inspiratory flow. Despite significant ipsilateral PhMN loss, the respiratory system has the capacity to quickly compensate for partially impaired hemidiaphragm function, suggesting that C4 hemicontusion in rats is a model of SCI that manifests subacute respiratory abnormalities. Collectively, these findings demonstrate significant and persistent diaphragm compromise in a clinically relevant model of midcervical contusion SCI; however, the therapeutic window for PhMN protection is restricted to early time points post-injury. On the contrary, preventing loss of innervation by PhMNs and/or inducing plasticity in spared PhMN axons at the diaphragm NMJ are relevant long-term targets