New and Old Results in Resultant Theory

Resultants are getting increasingly important in modern theoretical physics: they appear whenever one deals with non-linear (polynomial) equations, with non-quadratic forms or with non-Gaussian integrals. Being a subject of more than three-hundred-year research, resultants are of course rather well studied: a lot of explicit formulas, beautiful properties and intriguing relationships are known in this field. We present a brief overview of these results, including both recent and already classical. Emphasis is made on explicit formulas for resultants, which could be practically useful in a future physics research.Comment: 50 pages, 15 figure

SDiff(2) and uniqueness of the Pleba\'{n}ski equation

The group of area preserving diffeomorphisms showed importance in the problems of self-dual gravity and integrability theory. We discuss how representations of this infinite-dimensional Lie group can arise in mathematical physics from pure local considerations. Then using Lie algebra extensions and cohomology we derive the second Pleba\'{n}ski equation and its geometry. We do not use K\"ahler or other additional structures but obtain the equation solely from the geometry of area preserving transformations group. We conclude that the Pleba\'{n}ski equation is Lie remarkable

Anomalous Diffusion at Edge and Core of a Magnetized Cold Plasma

Progress in the theory of anomalous diffusion in weakly turbulent cold magnetized plasmas is explained. Several proposed models advanced in the literature are discussed. Emphasis is put on a new proposed mechanism for anomalous diffusion transport mechanism based on the coupled action of conductive walls (excluding electrodes) bounding the plasma drain current (edge diffusion) together with the magnetic field flux "cutting" the area traced by the charged particles in their orbital motion. The same reasoning is shown to apply to the plasma core anomalous diffusion. The proposed mechanism is expected to be valid in regimes when plasma diffusion scales as Bohm diffusion and at high $B/N$, when collisions are of secondary importance.Comment: 9 pages, 4 figure

Effect of Anode Dielectric Coating on Hall Thruster Operation

An interesting phenomenon observed in the near-anode region of a Hall thruster is that the anode fall changes from positive to negative upon removal of the dielectric coating, which is produced on the anode surface during the normal course of Hall thruster operation. The anode fall might affect the thruster lifetime and acceleration efficiency. The effect of the anode coating on the anode fall is studied experimentally using both biased and emissive probes. Measurements of discharge current oscillations indicate that thruster operation is more stable with the coated anode

Resistivity and Hall effect of LiFeAs: Evidence for electron-electron scattering

LiFeAs is unique among the broad family of FeAs-based superconductors, because it is superconducting with a rather large $T_c\simeq 18$ K under ambient conditions although it is a stoichiometric compound. We studied the electrical transport on a high-quality single crystal. The resistivity shows quadratic temperature dependence at low temperature giving evidence for strong electron-electron scattering and a tendency towards saturation around room temperature. The Hall constant is negative and changes with temperature, what most probably arises from a van Hove singularity close to the Fermi energy in one of the hole-like bands. Using band structure calculations based on angular resolved photoemission spectra we are able to reproduce all the basic features of both the resistivity as well as the Hall effect data.Comment: 6 pages, 3 figures included; V2 has been considerably revised and contain a more detailed analysis of the Hall effect dat

The superconducting gaps in LiFeAs: Joint study of specific heat and ARPES

We present specific heat, c_P, and ARPES data on single crystals of the stoichiometric superconductor LiFeAs. A pronounced anomaly is found in c_P at the superconducting transition. The electronic contribution can be described by two s-type energy gaps with magnitudes of approximately Delta1 = 1.2 meV and Delta2 = 2.6 meV and a normal-state gamma coefficient of 10 mJ/mol K^2. All these values are in remarkable agreement with ARPES results.Comment: 4 pages, 3 figure

On the interrelation between monopoles, vortices, topological charge and chiral symmetry breaking: an analysis using overlap fermions for SU(2)

We study the properties of configurations from which P-vortices on one hand or Abelian monopoles on the other hand have been removed. We find that the zero modes and the band of non-zero modes close to zero disappear from the spectrum of the overlap Dirac operator, confirming the absence of topological charge and quark condensate. The different behavior of the modified ensembles under smearing compared to the unmodified Monte Carlo ensemble corroborates these findings. The gluonic topological susceptibility rapidly approaches zero in accordance with Q_{index}=0. The remaining (ultraviolet) monopoles without vortices and -- to a less extent -- the remaining vortices without monopoles are unstable under smearing whereas smearing of the unmodified Monte Carlo ensemble effects the monopoles and vortices only by smoothing, reducing the density only slightly.Comment: 13 pages, 5 figures, strongly revised, results added, one figure added, accepted for publication, title changed

Theoretical model for the superconducting and magnetically ordered borocarbides

We present a theory of superconductivity in presence of a general magnetic structure in a form suitable for the description of complex magnetic phases encountered in borocarbides. The theory, complemented with some details of the band structure and with the magnetic phase diagram, may explain the nearly reentrant behaviour and the anisotropy of the upper critical field of HoNi2B2C. The onset of the helical magnetic order depresses superconductivity via the reduction of the interaction between phonons and electrons caused by the formation of magnetic Bloch states. At mean field level, no additional suppression of superconductivity is introduced by the incommensurability of the helical phase.Comment: 8 pages, 2 figures. Published version, one important reference adde