2,015 research outputs found
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 NpO and CeB 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 and the phase IV of CeLaB are studied in
detail. Recent O NMR for polycrystalline samples of NpO are
discussed theoretically from our formulation. The observed feature of the
splitting of 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 O NMR spectrum gives a strong support to the model. The 4
O sites in the fcc NpO 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 CeLaB is also studied. It is
pointed out that there is a unique feature in the NMR spectra, if the
() AFO ordering is
realized in CeLaB. Namely, the hyperfine splitting of a B
atom pair on the sites crosses zero on the
plane when the magnetic field is rotated around the 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
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