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

Spin-flop transition in uniaxial antiferromagnets: magnetic phases, reorientation effects, multidomain states

The classical spin-flop is the field-driven first-order reorientation transition in easy-axis antiferromagnets. A comprehensive phenomenological theory of easy-axis antiferromagnets displaying spin-flops is developed. It is shown how the hierarchy of magnetic coupling strengths in these antiferromagnets causes a strongly pronounced two-scale character in their magnetic phase structure. In contrast to the major part of the magnetic phase diagram, these antiferromagnets near the spin-flop region are described by an effective model akin to uniaxial ferromagnets. For a consistent theoretical description both higher-order anisotropy contributions and dipolar stray-fields have to be taken into account near the spin-flop. In particular, thermodynamically stable multidomain states exist in the spin-flop region, owing to the phase coexistence at this first-order transition. For this region, equilibrium spin-configurations and parameters of the multidomain states are derived as functions of the external magnetic field. The components of the magnetic susceptibility tensor are calculated for homogeneous and multidomain states in the vicinity of the spin-flop. The remarkable anomalies in these measurable quantities provide an efficient method to investigate magnetic states and to determine materials parameters in bulk and confined antiferromagnets, as well as in nanoscale synthetic antiferromagnets. The method is demonstrated for experimental data on the magnetic properties near the spin-flop region in the orthorhombic layered antiferromagnet (C_2H_5NH_3)_2CuCl_4.Comment: (15 pages, 12 figures; 2nd version: improved notation and figures, correction of various typos

Evaluation of the current state of aquatic ecosystems and the problems of the protection of biological resources during development of kruzenshternskoye gcf

The results of studies of the current state of freshwater ecosystems and their biotic components in the western part of the Yamal Peninsula are presented in the article. Based on the evaluation of the structure of communities of phytoplankton, zooplankton, benthos, and whitefishes, the range of problems related to the protection of biological resources during the development of the Kruzenshternskoye gas field is defined. The data on species composition and quantitative indicators of hydrobionts of different types of waterbodies and watercourses in the lower reaches of the Mordyyakha and Naduyyakha Rivers basins is the basis for environmental monitoring of water objects during development and exploitation of the Kruzenshternskoye gas field. Estimation of the fish fauna state and their food base in the territory of the Kruzenshternskoye GCF according to the monitoring program is present. The river delta zones are the most important feeding areas of the salmonid and whitefishes valuable fish species in the territory of Kruzenshternskoye GCF. In cases where water bodies and watercourses are not completely demolished for the construction of GCF facilities, changes of quantitative and qualitative characteristics of communities of hydrobionts after the end of operations are reversible. River ecosystems are restored within a shorter period of time in comparison to lacustrine ones. Proposals for the protection of fisheries resources and monitoring of aquatic ecosystems on the basis of comprehensive studies are reported. Recommendations on reducing the anthropogenic impact on aquatic ecosystems in the development period are present. The results of the investigation were used in the development of the environmental protection part of the Kruzenshternskoye deposit project. Anthropogenic disturbances present now on the gas deposit territory of Kruzenshternskoye does not influence the aquatic ecosystems.The article have been prepared within the Project of the Presidium of the Russian Academy of Sciences № 12-P-47-2013 and "The Arctic" Project of the Presidium of the Ural Branch of the Russian Academy of Sciences № 12-4-3-012

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

Neutral skyrmion configurations in the low-energy effective theory of spinor condensate ferromagnets

We study the low-energy effective theory of spinor condensate ferromagnets for the superfluid velocity and magnetization degrees of freedom. This effective theory describes the competition between spin stiffness and a long-ranged interaction between skyrmions, topological objects familiar from the theory of ordinary ferromagnets. We find exact solutions to the non-linear equations of motion describing neutral configurations of skyrmions and anti-skyrmions. These analytical solutions provide a simple physical picture for the origin of crystalline magnetic order in spinor condensate ferromagnets with dipolar interactions. We also point out the connections to effective theories for quantum Hall ferromagnets.Comment: 13 pages, 7 figure

Global Defects in Field Theory with Applications to Condensed Matter

We review investigations on defects in systems described by real scalar fields in (D,1) space-time dimensions. We first work in one spatial dimension, with models described by one and two real scalar fields, and in higher dimensions. We show that when the potential assumes specific form, there are models which support stable global defects for D arbitrary. We also show how to find first-order differential equations that solve the equations of motion, and how to solve models in D dimensions via soluble problems in D=1. We illustrate the procedure examining specific models and showing how they may be used in applications in different contexts in condensed matter physics, and in other areas.Comment: 15 pages, 9 figure

Surface spin-flop transition in a uniaxial antiferromagnetic Fe/Cr superlattice induced by a magnetic field of arbitrary direction

We studied the transition between the antiferromagnetic and the surface spin-flop phases of a uniaxial antiferromagnetic [Fe(14 \AA)/Cr(11 \AA]$_{\rm x20}$ superlattice. For external fields applied parallel to the in-plane easy axis, the layer-by-layer configuration, calculated in the framework of a mean-field one-dimensional model, was benchmarked against published polarized neutron reflectivity data. For an in-plane field $H$ applied at an angle $\psi \ne 0$ with the easy axis, magnetometry shows that the magnetization $M$ vanishes at H=0, then increases slowly with increasing $H$. At a critical value of $H$, a finite jump in $M(H)$ is observed for $\psi<5^{\rm o}$, while a smooth increase of $M$ $vs$ $H$ is found for $\psi>5^{\rm o}$. A dramatic increase in the full width at half maximum of the magnetic susceptibility is observed for $\psi \ge 5^{\rm o}$. The phase diagram obtained from micromagnetic calculations displays a first-order transition to a surface spin-flop phase for low $\psi$ values, while the transition becomes continuous for $\psi$ greater than a critical angle, $\psi_{\rm max} \approx 4.75^{\rm o}$. This is in fair agreement with the experimentally observed results.Comment: 24 pages, 7 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