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

Electronic structure and spectroscopy of O2 and O2+

We carried out a comprehensive SCF MRD--CI ab initio study of the electronic structure of O$_2$ and O$_2^+$. Potential energy curves (PECs) of about 150 electronic states of O$_2$ and about 100 of O$_2^+$, as well as a number of states of O$_2^{++}$ were computed. The cc--pVQZ basis set augmented with diffuse functions was employed. Spectroscopic parameters ($T_e, T_v, \omega_e, \omega_ex_e, B_e,$ $D_e, D_0$, $\mu$, IP, etc.) are reported. A preliminary sample of the results will be presented. The electronic absorption spectrum of O$_2$ has proved difficult to analyze/interpret due to the unusually large number of electronic states which arise from the peculiar open--shell structure of both the oxygen atomic fragments and the O$_2$ molecule. For instance, there are 62 valence molecular electronic states which correlate to the six lowest dissociation limits resulting from the three valence O atom fragment states ($^3$P, $^1$D, $^1$S). In addition, there are several $nl\lambda$ Rydberg series converging to the X$^2\Pi_g$ ground ionic state and to the lowest two excited states of the cation, a$^4\Pi_u$$_i$ and A$^2\Pi_u$. Furthermore, a number of interactions of various types among several electronic states result in rovibronic perturbations which manifest themselves, e.g., as irregular vibronic structure, hence severely complicating the assignment of the absorption features and the analysis and interpretation of the spectrum. An overview of the electronic states and spectroscopy of O$_2$ will be presented. A chief motivation of this study of O$_2$ was to try to provide a theoretical insight on the nature, energetic position, shape, and dissociation asymptotes, of electronic states located in the 4 eV energy region encompassed between the O$_2^+$ ground state X$^2\Pi_g$ (IP$=12.07$ eV) and the first excited state of the cation a$^4\Pi_u$$_i$ (IP$=16.10$ eV). This in order to aid in the interpretation of experimental data related to the mechanism(s) of the neutral dissociation of the O$_2^{**}$ (Rydberg) superexcited states, which competes with autoionization. We are currently striving to compute PECs of relatively highly excited states of O$_2$ located in the 12--16 eV energy region which might help to visualize possible pathways for the neutral XUV photodissociation of the I, I$^{\prime}$ and I$^{\prime\prime}$ $^3\Pi_u$ superexcited states of O$_2$ leading to the O($^3$P) + O$^{*}$($^3$S, $^5$S) dissociation limits.Ope

Zero kinetic energy-pulsed field ionization and resonance enhanced multiphoton ionization photoelectron spectroscopy: Ionization dynamics of Rydberg states in HBr

The results of rotationally resolved resonance enhanced multiphoton ionization photoelectron spectroscopy and zero kinetic energy‐pulsed field ionization studies on HBr via various rotational levels of the F^ 1Δ_2 and f^ 3Δ_2 Rydberg states are reported. These studies lead to an accurate determination of the lowest ionization threshold as 94 098.9±1 cm^(−1). Observed rotational and spin–orbit branching ratios are compared to the results of ab initio calculations. The differences between theory and experiment highlight the dominant role of rotational and spin–orbit interactions for the dynamic properties of the high‐n Rydberg states involved in the pulsed field ionization process

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.

Observation of Feshbach resonances in an ultracold gas of 52{}^{52}Cr

We have observed Feshbach resonances in elastic collisions between ultracold ${}^{52}$Cr atoms. This is the first observation of collisional Feshbach resonances in an atomic species with more than one valence electron. The zero nuclear spin of ${}^{52}$Cr and thus the absence of a Fermi-contact interaction leads to regularly-spaced resonance sequences. By comparing resonance positions with multi-channel scattering calculations we determine the s-wave scattering length of the lowest $^{2S+1}\Sigma_{g}^{+}$ potentials to be \unit[112(14)]{a_0}, \unit[58(6)]{a_0} and -\unit[7(20)]{a_0} for S=6, 4, and 2, respectively, where a_{0}=\unit[0.0529]{nm}.Comment: 4 pages, 2 figures, 1 tabl

Standard monomial theory for wonderful varieties

A general setting for a standard monomial theory on a multiset is introduced and applied to the Cox ring of a wonderful variety. This gives a degeneration result of the Cox ring to a multicone over a partial flag variety. Further, we deduce that the Cox ring has rational singularities.Comment: v3: 20 pages, final version to appear on Algebras and Representation Theory. The final publication is available at Springer via http://dx.doi.org/10.1007/s10468-015-9586-z. v2: 20 pages, examples added in Section 3 and in Section

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

Formation of collective spins in frustrated clusters

Using magnetization, specific heat and neutron scattering measurements, as well as exact calculations on realistic models, the magnetic properties of the \lacuvo compound are characterized on a wide temperature range. At high temperature, this oxide is well described by strongly correlated atomic $S$=1/2 spins while decreasing the temperature it switches to a set of weakly interacting and randomly distributed entangled pseudo spins $\tilde S=1/2$ and $\tilde S=0$. These pseudo-spins are built over frustrated clusters, similar to the kagom\'e building block, at the vertices of a triangular superlattice, the geometrical frustration intervening then at different scales.Comment: 10 page

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