Integrable dynamics of a discrete curve and the Ablowitz-Ladik hierarchy

We show that the following elementary geometric properties of the motion of a discrete (i.e. piecewise linear) curve select the integrable dynamics of the Ablowitz-Ladik hierarchy of evolution equations: i) the set of points describing the discrete curve lie on the sphere S^3, ii) the distance between any two subsequant points does not vary in time, iii) the dynamics does not depend explicitly on the radius of the sphere. These results generalize to a discrete context our previous work on continuous curves.Comment: LaTeX file, 14 pages + 4 figure

Analysis of f-p model for octupole ordering in NpO2

In order to examine the origin of octupole ordering in NpO2, we propose a microscopic model constituted of neptunium 5f and oxygen 2p orbitals. To study multipole ordering, we derive effective multipole interactions from the f-p model by using the fourth-order perturbation theory in terms of p-f hopping integrals. Analyzing the effective model numerically, we find a tendency toward \Gamma_{5u} antiferro-octupole ordering.Comment: 4 pages, 3 figure

Microscopic theory of multipole ordering in NpO2

In order to examine the mysterious ordered phase of NpO2 from a microscopic viewpoint, we investigate an f-electron model on an fcc lattice constructed based on a j-j coupling scheme. First, an effective model with multipole interactions is derived in the strong-coupling limit. Numerical analysis of the model clearly indicates that the interactions for \Gamma_{4u} and \Gamma_{5u} moments are relevant to the ground state. Then, by applying mean-field theory to the simplified model including only such interactions, we conclude that longitudinal triple-q \Gamma_{5u} octupole order is realized in NpO2 through the combined effects of multipole interactions and anisotropy of the \Gamma_{5u} moment.Comment: 5 pages, 2 figure

Resonant x-ray scattering spectra from multipole orderings: Np M_{4,5} edges in NpO2

We study resonant x-ray scattering (RXS) at Np M_{4,5} edges in the triple-\textbf{k} multipole ordering phase in NpO_{2}, on the basis of a localized electron model. We derive an expression for RXS amplitudes to characterize the spectra under the assumption that a rotational invariance is preserved in the intermediate state of scattering process. This assumption is justified by the fact that energies of the crystal electric field and the intersite interaction is smaller than the energy of multiplet structures. This expression is found useful to calculate energy profiles with taking account of the intra-Coulomb and spin-orbit interactions. Assuming the \Gamma_{8}-quartet ground state, we construct the triple-\textbf{k} ground state, and analyze the RXS spectra. The energy profiles are calculated in good agreement with the experiment, providing a sound basis to previous phenomenological analyses.Comment: 10 pages, 7 figure

Triple-q octupolar ordering in NpO_2

We report the results of resonant X-ray scattering experiments performed at the Np M_4,5 edges in NpO_2. Below T_0 = 25 K, the development of long-range order of Np electric quadrupoles is revealed by the growth of superlattice Bragg peaks. The electronic transition is not accompanied by any measurable crystallographic distortion, either internal or external, so the symmetry of the system remains cubic. The polarization and azimuthal dependence of the intensity of the resonant peaks is well reproduced assuming Templeton scattering from a triple-q longitudinal antiferroquadrupolar structure. Electric quadrupole order in NpO_2 could be driven by the ordering at T_0 of magnetic octupoles of Gamma_5 symmetry, splitting the Np ground state quartet and leading to a singlet ground state with zero dipole magnetic moment.Comment: 4 Pages, 3 Figures, submitted to Phys. Rev. Lett. v2: resubmitted after referee report

Comparison of VLBI, TV and traveling clock techniques for time transfer

A three part experiment was conducted to develop and compare time transfer techniques. The experiment consisted of (1) a very long baseline interferometer (VLBI), (2) a high precision portable clock time transfer system between the two sites, and (3) a television time transfer. A comparison of the VLBI and traveling clock shows each technique can perform satisfactorily at the five nsec level. There was a systematic offset of 59 nsec between the two methods, which we attributed to a difference in epochs between VLBI formatter and station clock. The VLBI method had an internal random error of one nsec at the three sigma level for a two day period. Thus, the Mark II system performed well, and VLBI shows promise of being an accurate method of time transfer. The TV system, which had technical problems during the experiment, transferred time with a random error of about 50 nsec

Invariant Form of Hyperfine Interaction with Multipolar Moments - Observation of Octupolar Moments in NpO2_{2} and CeB6_{6} by NMR -

The invariant form of the hyperfine interaction between multipolar moments and the nuclear spin is derived, and applied to discuss possibilities to identify the antiferro-octupolar (AFO) moments by NMR experiments. The ordered phase of NpO$_{2}$ and the phase IV of Ce$_{1-x}$La$_{x}$B$_{6}$ are studied in detail. Recent $^{17}$O NMR for polycrystalline samples of NpO$_{2}$ are discussed theoretically from our formulation. The observed feature of the splitting of $^{17}$O NMR spectrum into a sharp line and a broad line, their intensity ratio, and the magnetic field dependence of the shift and of the width can be consistently explained on the basis of the triple \bq AFO ordering model proposed by Paix\~{a}o {\it et. al.} Thus, the present theory shows that the $^{17}$O NMR spectrum gives a strong support to the model. The 4 O sites in the fcc NpO$_2$ become inequivalent due to the secondary triple \bq ordering of AF-quadrupoles: one cubic and three non-cubic sites. It turns out that the hyperfine field due to the antiferro-dipole and AFO moments induced by the magnetic field, and the quadrupolar field at non-cubic sites are key ingredients to understand the observed spectrum. The controversial problem of the nature of phase IV in Ce$_{1-x}$La$_{x}$B$_{6}$ is also studied. It is pointed out that there is a unique feature in the NMR spectra, if the $\Gamma_{5}$($T^{\beta}_{x}=T^{\beta}_{y}=T^{\beta}_{z}$) AFO ordering is realized in Ce$_{1-x}$La$_{x}$B$_{6}$. Namely, the hyperfine splitting of a B atom pair on the $({1/2},{1/2},\pm u)$ sites crosses zero on the $(1\bar{1}0)$ plane when the magnetic field is rotated around the $[001]$ axis.Comment: 22 pages, 2 figure

Spin dynamics of heterometallic Cr7M wheels (M = Mn, Zn, Ni) probed by inelastic neutron scattering

Inelastic neutron scattering has been applied to the study of the spin dynamics of Cr-based antiferromagnetic octanuclear rings where a finite total spin of the ground state is obtained by substituting one Cr(III) ion (s = 3/2) with Zn (s = 0), Mn (s = 5/2) or Ni (s = 1) di-cations. Energy and intensity measurements for several intra-multiplet and inter-multiplet magnetic excitations allow us to determine the spin wavefunctions of the investigated clusters. Effects due to the mixing of different spin multiplets have been considered. Such effects proved to be important to correctly reproduce the energy and intensity of magnetic excitations in the neutron spectra. On the contrary to what is observed for the parent homonuclear Cr8 ring, the symmetry of the first excited spin states is such that anticrossing conditions with the ground state can be realized in the presence of an external magnetic field. Heterometallic Cr7M wheels are therefore good candidates for macroscopic observations of quantum effects.Comment: 9 pages, 11 figures, submitted to Phys. Rev. B, corrected typos and added references, one sentence change

Extension of Hereditary Symmetry Operators

Two models of candidates for hereditary symmetry operators are proposed and thus many nonlinear systems of evolution equations possessing infinitely many commutative symmetries may be generated. Some concrete structures of hereditary symmetry operators are carefully analyzed on the base of the resulting general conditions and several corresponding nonlinear systems are explicitly given out as illustrative examples.Comment: 13 pages, LaTe