Grassmannians Gr(N-1,N+1), closed differential N-1 forms and N-dimensional integrable systems

Integrable flows on the Grassmannians Gr(N-1,N+1) are defined by the requirement of closedness of the differential N-1 forms $\Omega_{N-1}$ of rank N-1 naturally associated with Gr(N-1,N+1). Gauge-invariant parts of these flows, given by the systems of the N-1 quasi-linear differential equations, describe coisotropic deformations of (N-1)-dimensional linear subspaces. For the class of solutions which are Laurent polynomials in one variable these systems coincide with N-dimensional integrable systems such as Liouville equation (N=2), dispersionless Kadomtsev-Petviashvili equation (N=3), dispersionless Toda equation (N=3), Plebanski second heavenly equation (N=4) and others. Gauge invariant part of the forms $\Omega_{N-1}$ provides us with the compact form of the corresponding hierarchies. Dual quasi-linear systems associated with the projectively dual Grassmannians Gr(2,N+1) are defined via the requirement of the closedness of the dual forms $\Omega_{N-1}^{\star}$. It is shown that at N=3 the self-dual quasi-linear system, which is associated with the harmonic (closed and co-closed) form $\Omega_{2}$, coincides with the Maxwell equations for orthogonal electric and magnetic fields.Comment: 26 pages, references adde

Current sheets at three-dimensional magnetic nulls:effect of compressibility

The nature of current sheet formation in the vicinity of three-dimensional (3D) magnetic null points is investigated. The particular focus is upon the effect of the compressibility of the plasma on the qualitative and quantitative properties of the current sheet. An initially potential 3D null is subjected to shearing perturbations, as in a previous paper [Pontin et al., Phys. Plasmas, in press (2007)]. It is found that as the incompressible limit is approached, the collapse of the null point is suppressed, and an approximately planar current sheet aligned to the fan plane is present instead. This is the case regardless of whether the spine or fan of the null is sheared. Both the peak current and peak reconnection rate are reduced. The results have a bearing on previous analytical solutions for steady-state reconnection in incompressible plasmas, implying that fan current sheet solutions are dynamically accessible, while spine current sheet solutions are not.Comment: to appear in Physics of Plasmas. This version contains updated figures and references, additional discussion, and typos are fixed. This is the second in a series of papers - the first of which (by the same authors) is located at astro-ph/0701462. A version with higher quality figures can be found at http://www.maths.dundee.ac.uk/~dpontin

Strongly Gapped Spin-Wave Excitation in the Insulating Phase of NaOsO3

NaOsO3 hosts a rare manifestation of a metal-insulator transition driven by magnetic correlations, placing the magnetic exchange interactions in a central role. We use resonant inelastic x-ray scattering to directly probe these magnetic exchange interactions. A dispersive and strongly gapped (58 meV) excitation is observed indicating appreciable spin-orbit coupling in this 5d3 system. The excitation is well described within a minimal model Hamiltonian with strong anisotropy and Heisenberg exchange (J1=J2=13.9 meV). The observed behavior places NaOsO3 on the boundary between localized and itinerant magnetism

Magnetic structures and reorientation transitions in noncentrosymmetric uniaxial antiferromagnets

A phenomenological theory of magnetic states in noncentrosymmetric tetragonal antiferromagnets is developed, which has to include homogeneous and inhomogeneous terms (Lifshitz-invariants) derived from Dzyaloshinskii-Moriya couplings. Magnetic properties of this class of antiferromagnets with low crystal symmetry are discussed in relation to its first known members, the recently detected compounds Ba2CuGe2O7 and K2V3O8. Crystallographic symmetry and magnetic ordering in these systems allow the simultaneous occurrence of chiral inhomogeneous magnetic structures and weak ferromagnetism. New types of incommensurate magnetic structures are possible, namely, chiral helices with rotation of staggered magnetization and oscillations of the total magnetization. Field-induced reorientation transitions into modulated states have been studied and corresponding phase diagrams are constructed. Structures of magnetic defects (domain-walls and vortices) are discussed. In particular, vortices, i.e. localized non-singular line defects, are stabilized by the inhomogeneous Dzyaloshinskii-Moriya interactions in uniaxial noncentrosymmetric antiferromagnets.Comment: 18 pages RevTeX4, 13 figure

On Preparing Entangled Pairs of Polarization Qubits in the Frequency Non-Degenerate Regime

The problems associated with practical implementation of the scheme proposed for preparation of arbitrary states of polarization ququarts based on biphotons are discussed. The influence of frequency dispersion effects are considered, and the necessity of group velocities dispersion compensation in the frequency non-degenerate case even for continuous pumping is demonstrated. A method for this compensation is proposed and implemented experimentally. Physical restrictions on the quality of prepared two-photon states are revealed.Comment: 9 pages, 6 figure

Atomic parity violation in 0-to-0 two-photon transitions

We present a method for measuring atomic parity violation in the absence of static external electric and magnetic fields. Such measurements can be achieved by observing the interference of parity conserving and parity violating two-photon transition amplitudes between energy eigenstates of zero electronic angular momentum. General expressions for induced two-photon transition amplitudes are derived. The signal-to-noise ratio of a two-photon scheme using the 6s^2 1S0 to 6s6p 3P0 transition in ytterbium is estimated.Comment: 8 pages, 2 figures, submitted to PR

Anomalous electronic structure and pseudogap effects in Nd_1.85Ce_0.15CuO_4

We report a high-resolution angle-resolved photoemission spectroscopic (ARPES) study of the electron-doped (n-type) cuprate superconductor Nd_1.85Ce_0.15CuO_4. We observe regions along the Fermi surface where the near-E_F intensity is suppressed and the spectral features are broad in a manner reminiscent of the high-energy ``pseudogap'' in the underdoped p-type (hole doped) cuprates. However, instead of occurring near the (pi, 0) region, as in the p-type materials, this pseudogap falls near the intersection of the underlying Fermi surface with the antiferromagnetic Brillouin zone boundary.Comment: 5 pages, 3 figures, RevTex, submitted Phys. Rev. Lett. December 21, 200

An angle-resolved photoemission spectral function analysis of the electron doped cuprate Nd_1.85Ce_0.15CuO_4

Using methods made possible by recent advances in photoemission technology, we perform an indepth line-shape analysis of the angle-resolved photoemission spectra of the electron doped (n-type) cuprate superconductor Nd_1.85Ce_0.15CuO_4. Unlike for the p-type materials, we only observe weak mass renormalizations near 50-70 meV. This may be indicative of smaller electron-phonon coupling or due to the masking effects of other interactions that make the electron-phonon coupling harder to detect. This latter scenario may suggest limitations of the spectral function analysis in extracting electronic self-energies when some of the interactions are highly momentum dependent.Comment: 8 pages, 5 figure