Moduli Spaces of Self-Dual Connections over Asymptotically Locally Flat Gravitational Instantons

We investigate Yang–Mills instanton theory over four dimensional asymptotically locally flat (ALF) geometries, including gravitational instantons of this type, by exploiting the existence of a natural smooth compactification of these spaces introduced by Hausel–Hunsicker–Mazzeo. First referring to the codimension 2 singularity removal theorem of Sibner–Sibner and R?de we prove that given a smooth, finite energy, self-dual SU(2) connection over a complete ALF space, its energy is congruent to a Chern–Simons invariant of the boundary three-manifold if the connection satisfies a certain holonomy condition at infinity and its curvature decays rapidly. Then we introduce framed moduli spaces of self-dual connections over Ricci flat ALF spaces. We prove that the moduli space of smooth, irreducible, rapidly decaying self-dual connections obeying the holonomy condition with fixed finite energy and prescribed asymptotic behaviour on a fixed bundle is a finite dimensional manifold. We calculate its dimension by a variant of the Gromov–Lawson relative index theorem. As an application, we study Yang–Mills instantons over the flat , the multi-Taub–NUT family, and the Riemannian Schwarzschild space.     

Non-Topological Solutions of the Relativistic SU(3) Chern–Simons Higgs Model

In this paper, we obtain non-topological solutions of the self-dual equations arising in the relativistic SU(3) Chern–Simons Higgs model. Received: 11 July 1998 / Accepted: 1 November 1998     

Self-dual Vortices in a Maxwell–Chern–Simons Model with Non-minimal Coupling

We study self-dual vortex solutions in a Maxwell – Chern – Simons model with anomalous magnetic moment. We establish the existence of multivortex solutions and obtain the quantized energy and the magnetic flux. We also prove the uniqueness of solutions when there is only one vortex point.      

The ADHM Construction and Non-local Symmetries of the Self-dual Yang–Mills Equations

We construct the most general reducible connection that satisfies the self-dual Yang–Mills equations on a simply-connected, open subset of flat \mathbbR⁴{\mathbb{R}^4}. We show how all such connections lie in the orbit of the flat connection on \mathbbR⁴{\mathbb{R}^4} under the action of non-local symmetries of the self-dual Yang–Mills equations. Such connections fit naturally inside a larger class of solutions to the self-dual Yang–Mills equations that are analogous to harmonic maps of finite type.     

Domain walls in a generalized Chern–Simons model

In this paper we study the structure of one dimensional topological solitons in a generalized Abelian-Higgs Chern–Simons model where the kinetic term is non-canonical. We present an example of an analytical self-dual electrically charged soliton solution which has a finite momentum per unit length along its direction. We compared the physical properties of our soliton with those for wall of Jackiw–Lee–Weinberg wall presented in Jackiw et al. (Phys. Rev. D 42:3488, 1990) to conclude that the non-canonical kinetic term can make the wall “thicker” redistributing uniformly the momentum flow along it.     

Parametric excitation of spin waves in ferromagnets by longitudinal pumping localized in space

The equations of motion for the slowly varying complex amplitudes of spin waves parametrically excited by a localized pumping magnetic field have been derived. A solution of these equations satisfying given boundary and initial conditions has been obtained. The energy dissipated by spin waves decreases with the pumping intensity beyond a certain pumping power, which can be termed the regeneration threshold. The losses vanish and change sign at the instability threshold. Both thresholds depend heavily on the linear dimension L of the pumping zone, increasing with decreasing L. Owing to the regeneration process, the dissipation length of spin waves increases without bound as the pumping power approaches the instability threshold. Consequently, perturbations of a uniform state due to the boundary penetrate throughout the pumping zone, regardless of the dimension L. As a result, the full pattern of parametric instability is strongly affected by the zone boundary: 1) the spatial distribution of wave amplitudes becomes nonuniform everywhere inside the zone; 2) the amplitude growth rate in the unstable regime decreases at all points when perturbations due to the boundary reach these points; 3) the instability threshold is independent of the spin-wave frequency offset from the parametric resonance frequency. The calculated minimum instability threshold as a function of the bias magnetic field (the “butterfly” curve) changes shape with L, in agreement with the available experimental data. Zh. éksp. Teor. Fiz. 111, 199–219 (January 1997)     

Cube–Root Boundary Fluctuations¶for Droplets in Random Cluster Models

For a family of bond percolation models on ℤ² that includes the Fortuin–Kasteleyn random cluster model, we consider properties of the “droplet” that results, in the percolating regime, from conditioning on the existence of an open dual circuit surrounding the origin and enclosing at least (or exactly) a given large area A. This droplet is a close surrogate for the one obtained by Dobrushin, Kotecky and Shlosman by conditioning the Ising model; it approximates an area-A Wulff shape. The local part of the deviation from the Wulff shape (the “local roughness”) is the inward deviation of the droplet boundary from the boundary of its own convex hull; the remaining part of the deviation, that of the convex hull of the droplet from the Wulff shape, is inherently long-range. We show that the local roughness is described by at most the exponent 1/3 predicted by nonrigorous theory; this same prediction has been made for a wide class of interfaces in two dimensions. Specifically, the average of the local roughness over the droplet surface is shown to be O(l ^1/3(log l)^2/3) in probability, where is the linear scale of the droplet. We also bound the maximum of the local roughness over the droplet surface and bound the long-range part of the deviation from a Wulff shape, and we establish the absense of “bottlenecks”, which are a form of self-approach by the droplet boundary, down to scale log l. Finally, if we condition instead on the event that the total area of all large droplets inside a finite box exceeds A, we show that with probability near 1 for large A, only a single large droplet is present. Received: 20 January 2000 / Accepted: 7 August 2001     

Vortex Condensates¶for the SU(3) Chern–Simons Theory

We investigate SU(3)-periodic vortices in the self-dual Chern–Simons theory proposed by Dunne in [13, 15]. At the first admissible non-zero energy level E= 2 π, and for each (broken and unbroken) vacuum state φ₍₀₎ of the system, we find a family of periodic vortices asymptotically gauge equivalent to φ₍₀₎, as the Chern–Simons coupling parameter k→ 0. At higher energy levels, we show the existence of multiple gauge distinct periodic vortices with at least one of them asymptotically gauge equivalent to the (broken) principal embedding vacuum, when k→ 0. Received: 23 October 1999 / Accepted: 14 March 2000     

Magnetic resonance of intrinsic defects in the spin-Peierls magnet CuGeO3

Magnetic resonance in pure single-crystal CuGeO₃ at frequencies 9–75 GHz in the temperature range 1.2–25 K is investigated. Splitting of the magnetic-resonance line into several spectral components is observed at temperatures below 5 K, where spin-Peierls dimerization suppresses the magnetic susceptibility and the ESR signal intensity. Analysis of the magnetic resonance spectra over a wide frequency range with different directions of the magnetic field at different temperatures makes it possible to identify among these components the ESR signals due to defects, having effective spin S=1/2 and spin S=1, in the spin-Peierls phase. The g factor corresponding to these ESR signals is the same and close to the value characteristic for the ion Cu²⁺. Another magnetic-resonance line is characterized by a strongly anisotropic g factor and an increase (at a threshold in the excitation power) in the susceptibility both at resonance and in the line wings. These signals are tentatively attributed to two possible types of planar defects arising on the walls of domains of the spin-Peierls state with different values of the dimerization phase. Zh. éksp. Teor. Fiz. 114, 1876–1896 (November 1998)     

Magnetic resonance in pure and diamagnetically diluted spin-Peierls CuGeO3

Magnetic resonance at frequencies 22–75 GHz is investigated in pure single-crystalline CuGeO₃ in the temperature range 1.2–25 K. At temperatures below 4 K the magnetic resonance line splits into four spectral components. The line close to the ESR of the paramagnetic phase is associated with impurities or defects. The other three lines have the same intensity in different samples and are apparently characteristic for pure single crystals at low temperature. An antiferromagnetic resonance with two resonance absorption branches and a spectrum characteristic for an antiferromagnet with easy, average, and hard anisotropy axes was observed and investigated in the Néel compound Cu_0.98Zn_0.02GeO₃ with diamagnetic dilution of the spin subsystem. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 4, 277–282 (25 August 1996)     

Multiple Instantons Representing Higher-Order Chern–Pontryagin Classes

It has been shown in the work of Chakrabarti, Sherry and Tchrakian that the chiral SO _±(4 p) Yang–Mills theory in the Euclidean 4 p (p≥ 2) dimensions allows an axially symmetric self-dual system of equations similar to Witten's instanton equations in the classical 4-dimensional SU(2)∼SO _±(4) theory and the solutions represent a new class of instantons. However the rigorous existence of these higher-dimensional instanton solutions has remained open except for the solution of unit charge representing a single instanton. In this paper we establish an existence and uniqueness theorem for multi-instantons of arbitrary charges in the case p≥ 2. These solutions are the first known instantons, with the Chern–Pontryagin index greater than one, of the Yang–Mills model in higher dimensions. Our approach is a study of a nonlinear variational equation defined on the Poincaré half plane. Received: 20 May 1996 / Accepted: 30 April 1997     

Growth parameters and shape specific synthesis of silicon nanowires by the VLS method

In this paper the effect of varying temperature, pressure and chemical precursors on the vapour–liquid–solid (VLS) growth of silicon nanowires (Si NWs) have been investigated. Some aspects of nucleation and growth mechanisms are discussed. Control on Si NW morphology by varying the choice of gaseous precursor (silane or dichlorosilane) at elevated temperatures is reported.     

Carbon nanotube grease with enhanced thermal and electrical conductivities

A stable and homogeneous grease based on carbon nanotubes (CNTs, single-wall and multi-wall) in polyalphaolefin oil has been produced without using a chemical surfactant. For example, for a 11 wt% (7 vol%) single-wall CNT (diameter 1–2 nm, length 0.5–40 μm) loading, the thermal conductivity (TC) of the grease shows a 60–70% increase compared to that for no nanotube loading. In addition, the grease is electrically conductive, has a high dropping point, good temperature resistance, and does not react with copper at temperatures up to 177 °C. The performance of carbon nanotube grease could be much better with the improvement of nanotube quality and purity. A possible explanation for these results is that of a high loading of CNTs (>10 wt%), they become associated with each other by van der Waals forces in the grease to form three-dimensional percolation networks. Time-dependent magnetic results demonstrate that, even under the influence of a strong outside magnetic field, the TC value remains constant. This phenomenon can be attributed to the existence of networks that makes magnetic alignment of nanotubes impossible.     

Magnetic Properties and Spin Crossover in Transition Metal Oxides with d 5 Ions at High Pressures

We analyze the influence of cooperative effects on the magnetic properties and spin crossover between the high-spin (HS) term S = 5/2 and low-spin (LS) term S = 1/2 in Mott–Hubbard dielectrics with 3d5 ions under high pressures. Two cooperation mechanisms (superexchange interaction and effective interaction via the elastic system) are considered. The sign of the exchange interaction changes because of the crossover from the antiferromagnetic in the HS state to the ferromagnetic in the LS state. In view of the large difference between the ionic radii of the HS and LS states, the systems with spin crossover acquire an additional strong coupling via the elastic system. Using the Hubbard operator representation and considering the electronic states of the two terms simultaneously, we obtain the effective Hamiltonian with allowance for the cooperative effects. The magnetic phase diagram and the spin crossover are investigated in the mean field approximation. It is shown that the inclusion of cooperative effects at low temperatures leads to a first-order phase transition between the antiferromagnetic HS state and the ferromagnetic LS state. At higher temperatures, more complicated sequences of phase transitions are possible upon an increase in pressure, including the HS paramagnet–HS antiferromagnet–LS paramagnet and HS antiferromagnet–LS paramagnet–LS ferromagnet transitions.     

Magnetoelectric response of the spin-Peierls compound CuGeO3

The effect of an electric field on the magnetic susceptibility in a pure CuGeO₃ single crystal at microwave frequencies is investigated. A quadratic effect of the electric field on the magnetic susceptibility, which increases with decreasing temperature, is observed in the spin-Peierls state at temperatures below 5 K. The observed effect is tentatively attributed to residual magnetism, due to distortions of the regular dimerized structure at domain walls with different values of the dimerization phase, and to the effect of the electric field on the interchain exchange interaction. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 9, 646–651 (10 November 1996)     

Magnetic vortices and thermoelectric effect in a hollow superconducting cylinder

The question of a surface barrier which determines the behavior of a vortex in a hollow superconducting cylinder of finite thickness in an external magnetic field is discussed, taking into account magnetic flux quantization in the cavity. The behavior of magnetic vortices in a hollow superconductor in the presence of a thermoelectric current is also considered. Pairs of magnetic vortices with opposite magnetic field orientations (vortex-antivortex pairs) are generated by this current near T _c. The thermoelectric current drives the antivortex (the vortex with oppositely directed field) out of the cylinder, whereas the vortex is ejected into the cavity and remains on the inside cylinder surface as a current. The number of magnetic flux quanta trapped inside the cylinder increases by one. The relation of this mechanism to the “giant” thermoelectric effect in hollow superconductors is discussed. Zh. éksp. Teor. Fiz. 111, 2175–2193 (June 1997)     

In situ observation of diffusion and reaction dynamics in gel microreactors by chemically resolved NMR microscopy

The enzymatically catalyzed esterification reaction of propionic acid+1-butanol ⇆ propionic-acid-butyl-ester+water inside an immobilizing hydrogel environment has been investigated by means of spectroscopically resolved nuclear magnetic resonance (NMR) imaging. The alginate hydrogel was in the shape of a 3–4 mm diameter bead, with both the gel-forming water and the solvent (cyclohexane) being fully deuterated to simplify the identification of small amounts of reactants. In the absence of enzymes, the self-diffusion process of the separate reactants (propionic acid and butanol) proved to be severely slowed down compared to pure Fickian self-diffusion, and the concentration buildup inside the gel bead was shown to depend strongly on the properties of the reactants. Two-dimensional, non-chemically resolved images revealed that the diffusion process is not radially symmetric as expected, thus complicating the modelling of the diffusion and reaction kinetics. The reaction itself has been observed with chemical resolution in a time series of up to 40 h, clearly demonstrating the reduction of 1-butanol and production of water inside the gel bead.     

Complex magnetism in ultra-thin films: atomic-scale spin structures and resolution by the spin-polarized scanning tunneling microscope

In this paper we present a density functional theory investigation of complex magnetic structures in ultra-thin films. The focus is on magnetically frustrated antiferromagnetic Cr and Mn monolayers deposited on a triangular lattice provided by a Ag (111) substrate. This involves non-collinear magnetic structures, which we treat by first-principles calculations on the basis of the vector spin-density formulation of the density functional theory. We find for Cr/Ag (111) a coplanar non-collinear periodic 120° Néel structure, for Mn/Ag (111) a row-wise antiferromagnetic structure, and for Fe/Ag (111) a ferromagnetic structure as magnetic ground states. The spin-polarized scanning tunneling microscope (SP–STM) operated in the constant-current mode is proposed as a powerful tool to investigate complex atomic-scale magnetic structures of otherwise chemically equivalent atoms. We discuss a recent application of this operation mode of the SP–STM on Mn/W (110), which led to the first observation of a two-dimensional antiferromagnet on a non-magnetic metal. The future potential of this approach is demonstrated by calculating SP–STM images for different magnetic structures of Cr/Ag (111). The results show that the predicted non-collinear magnetic ground state structure can clearly be discriminated from competing magnetic structures. A general discussion of the application of different operation modes of the SP–STM is presented on the basis of the model of Tersoff and Hamann. Received: 07 May 2001 / Accepted: 23 July 2001 / Published online: 3 April 2002     

Mixed conductivity of gadolinium titanate-based pyrochlore ceramics: The grain boundary effects

In order to reveal the role of grain boundaries on the ionic and electronic conduction processes, the transport properties of Gd_2−xGa_xTi₂O_7−δ (x=0.10–0.14) pyrochlore ceramics, pure and with SiO₂ additions, were studied at 700–950 °C by impedance spectroscopy and faradaic efficiency measurements. The oxygen ion transference numbers of “pure” materials in air vary in the range of 0.95–0.97, increasing when temperature decreases. For silica-containing ceramics having, as expected, highly resistive grain boundaries, the ion transference numbers were considerably lower, 0.76–0.88, and increase with temperature. This behavior suggests that grain boundaries in these oxygen ion-conducting ceramics have a larger limiting effect on ionic transport than on electronic conduction. Increasing boundary resistivity may increase the relative role of electronic conductivity in solid oxide electrolytes, thus preventing their potential use in electrochemical cells at low temperatures. Also, the presence of even small electronic contributions to the total conductivity may lead to significant errors in the grain-boundary resistance values estimated from impedance spectroscopy data. The evaluation of the grain boundary exact contribution should be based on a clear knowledge of the magnitude of transference numbers. Paper prestented at the 9th EuroConference on Ionics, Ixia, Rhodes, Greece, Sept. 15 – 21, 2002.     

Magnetically stabilized electron-hole liquid in indium antimonide

Luminescence spectra of sufficiently pure n-type indium antimonide crystals (N _D−N _A=(1–22)·10¹⁴ cm⁻³) in a magnetic field of up to 56 kOe, at temperatures of 1.8–2 K, and high optical pumping densities (more than 100 W/cm²) have been studied. More evidence of the existence of electron-hole liquid stabilized by magnetic field has been obtained, and its basic thermodynamic parameters as functions of magnetic field have been measured. When the magnetic field increases from 23 to 55.2 kOe, the liquid density increases from 3.2·10¹⁵ to 6.7·10¹⁵ cm⁻³, the binding energy per electron-hole pair rises from 3.0 to 5.2 meV, and the binding energy with respect to the ground exciton level (work function of an exciton in the liquid) rises from 0.43 to 1.2 meV. Zh. éksp. Teor. Fiz. 111, 737–758 (February 1997)