On the tau-functions of the Degasperis-Procesi equation

The DP equation is investigated from the point of view of determinant-pfaffian identities. The reciprocal link between the Degasperis-Procesi (DP) equation and the pseudo 3-reduction of the $C_{\infty}$ two-dimensional Toda system is used to construct the N-soliton solution of the DP equation. The N-soliton solution of the DP equation is presented in the form of pfaffian through a hodograph (reciprocal) transformation. The bilinear equations, the identities between determinants and pfaffians, and the $\tau$-functions of the DP equation are obtained from the pseudo 3-reduction of the $C_{\infty}$ two-dimensional Toda system.Comment: 27 pages, 4 figures, Journal of Physics A: Mathematical and Theoretical, to be publishe

Graphitic-BN Based Metal-free Molecular Magnets From A First Principle Study

We perform a first principle calculation on the electronic properties of carbon doped graphitic boron nitride graphitic BN. It was found that carbon substitution for either boron or nitrogen atom in graphitic BN can induce spontaneous magnetization. Calculations based on density functional theory with the local spin density approximation on the electronic band structure revealed a spin polarized, dispersionless band near the Fermi energy. Spin density contours showed that the magnetization density originates from the carbon atom. The magnetization can be attributed to the carbon 2p electron. Charge density distribution shows that the carbon atom forms covalent bonds with its three nearest neighbourhood. The spontaneous magnetization survives the curvature effect in BN nanotubes, suggesting the possibility of molecular magnets made from BN. Compared to other theoretical models of light-element or metal-free magnetic materials, the carbon-doped BN are more experimentally accessible and can be potentially useful.Comment: 8 pages, 4 figure

Generally Covariant Conservative Energy-Momentum for Gravitational Anyons

We obtain a generally covariant conservation law of energy-momentum for gravitational anyons by the general displacement transform. The energy-momentum currents have also superpotentials and are therefore identically conserved. It is shown that for Deser's solution and Clement's solution, the energy vanishes. The reasonableness of the definition of energy-momentum may be confirmed by the solution for pure Einstein gravity which is a limit of vanishing Chern-Simons coulping of gravitational anyons.Comment: 12 pages, Latex, no figure

Insulator-metal transition shift related to magnetic polarons in La0.67-xYxCa0.33MnO3

The magnetic transport properties have been measured for La0.67-xYxCa0.33MnO3 (0 <= x <= 0.14) system. It was found that the transition temperature Tp almost linearly moves to higher temperature as H increases. Electron spin resonance confirms that above Tp, there exist ferromagnetic clusters. From the magnetic polaron point of view, the shift of Tp vs. H was understood, and it was estimated that the size of the magnetic polaron is of 9.7~15.4 angstrom which is consistent with the magnetic correlation length revealed by the small-angle neutron-scattering technique. The transport properties at temperatures higher than Tp conform to the variable-range hopping mechanism.Comment: 22 pages, 6 figures, pdf, to be published in Euro. Phys. J.

Deterministically entangling distant nitrogen-vacancy centers by a nanomechanical cantilever

We present a practical scheme by global addressing to deterministically entangle negatively charged nitrogen-vacancy (N-V) centers in distant diamonds using a nano-mechanical cantilever with the magnetic tips strongly coupled to the N-V electron spins. Symmetric Dicke states are generated as an example, and the experimental feasibility and challenge of our scheme are discussed.Comment: 5 pages, 4 figure