Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies

We study exact multi-soliton solutions of integrable hierarchies on noncommutative space-times which are represented in terms of quasi-determinants of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic behavior of the multi-soliton solutions and found that the asymptotic configurations in soliton scattering process can be all the same as commutative ones, that is, the configuration of N-soliton solution has N isolated localized energy densities and the each solitary wave-packet preserves its shape and velocity in the scattering process. The phase shifts are also the same as commutative ones. Furthermore noncommutative toroidal Gelfand-Dickey hierarchy is introduced and the exact multi-soliton solutions are given.Comment: 18 pages, v3: references added, version to appear in JHE

Quasideterminant solutions of a non-Abelian Hirota-Miwa equation

A non-Abelian version of the Hirota-Miwa equation is considered. In an earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. \textbf{39}, 5053-5065] it was shown how solutions expressed as quasideterminants could be constructed for this system by means of Darboux transformations. In this paper we discuss these solutions from a different perspective and show that the solutions are quasi-Pl\"{u}cker coordinates and that the non-Abelian Hirota-Miwa equation may be written as a quasi-Pl\"{u}cker relation. The special case of the matrix Hirota-Miwa equation is also considered using a more traditional, bilinear approach and the techniques are compared

Lattice Distortion and Octupole Ordering Model in CexLa1-xB6

Possible order parameters of the phase IV in CexLa1-xB6 are discussed with special attention to the lattice distortion recently observed. A \Gamma_{5u}-type octupole order with finite wave number is proposed as the origin of the distortion along the [111] direction. The \Gamma_8 crystalline electric field (CEF) level splits into three levels by a mean field with the \Gamma_{5u} symmetry. The ground and highest singlets have the same quadrupole moment, while the intermediate doublet has an opposite sign. It is shown that any collinear order of \Gamma_{5u}-type octupole moment accompanies the \Gamma_{5g}-type ferro-quadrupole order, and the coupling of the quadrupole moment with the lattice induces the distortion. The cusp in the magnetization at the phase transition is reproduced, but the internal magnetic field due to the octupole moment is smaller than the observed one by an order of magnitude.Comment: 5 pages, 4 figures, submitted to J. Phys. Soc. Jp

Influence of apical oxygen on the extent of in-plane exchange interaction in cuprate superconductors

In high Tc superconductors the magnetic and electronic properties are determined by the probability that valence electrons virtually jump from site to site in the CuO2 planes, a mechanism opposed by on-site Coulomb repulsion and favored by hopping integrals. The spatial extent of the latter is related to transport properties, including superconductivity, and to the dispersion relation of spin excitations (magnons). Here, for three antiferromagnetic parent compounds (single-layer Bi2Sr0.99La1.1CuO6+delta, double-layer Nd1.2Ba1.8Cu3O6 and infinite-layer CaCuO2) differing by the number of apical atoms, we compare the magnetic spectra measured by resonant inelastic x-ray scattering over a significant portion of the reciprocal space and with unprecedented accuracy. We observe that the absence of apical oxygens increases the in-plane hopping range and, in CaCuO2, it leads to a genuine 3D exchange-bond network. These results establish a corresponding relation between the exchange interactions and the crystal structure, and provide fresh insight into the materials dependence of the superconducting transition temperature.Comment: 9 pages, 4 figures, 1 Table, 42 reference

Low Temperature Specific Heat of Dy2_2Ti2_2O7_7 in the Kagome Ice State

We report the specific heat of single crystals of the spin ice compound Dy$_2$Ti$_2$O$_7$ at temperatures down to 100 mK in the so-called Kagome ice state. In our previous paper, we showed the anisotropic release of residual entropy in different magnetic field directions and reported new residual entropy associated with spin frustration in the Kagome slab for field in the [111] direction. In this paper, we confirm the first-order phase transition line in the field-temperature phase diagram and the presence of a critical point at (0.98 T, 400 mK), previously reported from the magnetization and specific-heat data. We newly found another peak in the specific heat at 1.25 T below 0.3 K. One possible explanation for the state between 1 T and 1.25 T is the coexistence of states with different spin configurations including the 2-in 2-out one (Kagome ice state), the 1-in 3-out state (ordered state) and paramagnetic one (free-spin state).Comment: 14 pages, 7 figure

Factorization methods for Noncommutative KP and Toda hierarchy

We show that the solution space of the noncommutative KP hierarchy is the same as that of the commutative KP hierarchy owing to the Birkhoff decomposition of groups over the noncommutative algebra. The noncommutative Toda hierarchy is introduced. We derive the bilinear identities for the Baker--Akhiezer functions and calculate the $N$-soliton solutions of the noncommutative Toda hierarchy.Comment: 7 pages, no figures, AMS-LaTeX, minor corrections, final version to appear in Journal of Physics

On a direct approach to quasideterminant solutions of a noncommutative KP equation

A noncommutative version of the KP equation and two families of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux and binary Darboux transformations. Additionally, it is shown that these solutions may also be verified directly. This approach is reminiscent of the wronskian technique used for the Hirota bilinear form of the regular, commutative KP equation but, in the noncommutative case, no bilinearising transformation is available.Comment: 11 page

Bryostatin enhancement of memory in Hermissenda

Author Posting. © Marine Biological Laboratory, 2006. This article is posted here by permission of Marine Biological Laboratory for personal use, not for redistribution. The definitive version was published in Biological Bulletin 210 (2006): 201-214.Bryostatin, a potent agonist of protein kinase C (PKC), when administered to Hermissenda was found to affect acquisition of an associative learning paradigm. Low bryostatin concentrations (0.1 to 0.5 ng/ml) enhanced memory acquisition, while concentrations higher than 1.0 ng/ml down-regulated the pathway and no recall of the associative training was exhibited. The extent of enhancement depended upon the conditioning regime used and the memory stage normally fostered by that regime. The effects of two training events (TEs) with paired conditioned and unconditioned stimuli, which standardly evoked only short-term memory (STM) lasting 7 min, were—when bryostatin was added concurrently—enhanced to a long-term memory (LTM) that lasted about 20 h. The effects of both 4- and 6-paired TEs (which by themselves did not generate LTM), were also enhanced by bryostatin to induce a consolidated memory (CM) that lasted at least 5 days. The standard positive 9-TE regime typically produced a CM lasting at least 6 days. Low concentrations of bryostatin (<0.5 ng/ml) elicited no demonstrable enhancement of CM from 9-TEs. However, animals exposed to bryostatin concentrations higher than 1.0 ng/ml exhibited no behavioral learning. Sharp-electrode intracellular recordings of type-B photoreceptors in the eyes from animals conditioned in vivo with bryostatin revealed changes in input resistance and an enhanced long-lasting depolarization (LLD) in response to light. Likewise, quantitative immunocytochemical measurements using an antibody specific for the PKC-activated Ca2+/GTP-binding protein calexcitin showed enhanced antibody labeling with bryostatin. Animals exposed to the PKC inhibitor bisindolylmaleimide-XI (Ro-32-0432) administered by immersion prior to 9-TE conditioning showed no training-induced changes with or without bryostatin exposure. However, if animals received bryostatin before Ro-32, the enhanced acquisition and demonstrated recall still occurred. Therefore, pathways responsible for the enhancement effects induced by bryostatin were putatively mediated by PKC. Overall, the data indicated that PKC activation occurred and calexcitin levels were raised during the acquisition phases of associative conditioning and memory initiation, and subsequently returned to baseline levels within 24 and 48 h, respectively. Therefore, the protracted recall measured by the testing regime used was probably due to bryostatin-induced changes during the acquisition and facilitated storage of memory, and not necessarily to enhanced recall of the stored memory when tested many days after training.AMK and HTE acknowledge the support of the Marine Biological Laboratory and Blanchette Rockefeller Neurosciences Institutes for these initial studies

Effect of Pressure on Tiny Antiferromagnetic Moment in the Heavy-Electron Compound URu_2Si_2

We have performed elastic neutron-scattering experiments on the heavy-electron compound URu_2Si_2 for pressure P up to 2.8 GPa. We have found that the antiferrmagnetic (100) Bragg reflection below T_m ~ 17.5 K is strongly enhanced by applying pressure. For P < 1.1 GPa, the staggered moment mu_o at 1.4 K increases linearly from ~ 0.017(3) mu_B to ~ 0.25(2) mu_B, while T_m increases slightly at a rate ~ 1 K/GPa, roughly following the transition temperature T_o determined from macroscopic anomalies. We have also observed a sharp phase transition at P_c ~ 1.5 GPa, above which a 3D-Ising type of antiferromagnetic phase (mu_o ~ 0.4 mu_B) appears with a slightly reduced lattice constant.Comment: RevTeX, 4 pages, 4 eps figures, accepted for publication in Phys. Rev. Let

Electromagnetic Form Factors of a Massive Neutrino

Electromagnetic form factors of a massive neutrino are studied in a minimally extended standard model in an arbitrary $R_{\xi}$ gauge and taking into account the dependence on the masses of all interacting particles. The contribution from all Feynman diagrams to the charge, magnetic, and anapole form factors, in which the dependence on the masses of all particles as well as on gauge parameters is accounted for exactly, are obtained for the first time in explicit form. The asymptotic behavior of the magnetic form factor for large negative squares of the momentum of an external photon is analyzed and expression for the anapole moment of a massive neutrino is derived. The results are generalized to the case of mixing between various generations of the neutrino. Explicit expressions are obtained for the charge, magnetic, and electric dipole and anapole transition form factors as well as for the transition electric dipole moment.Comment: 16 pares with 5 figures in pdf forma