The yoga of commutators

In the present paper we discuss some recent versions of localisation methods for calculations in the groups of points of algebraic-like and classical-like groups. Namely, we describe relative localisation, universal localisation, and enhanced versions of localisation-completion. Apart from the general strategic description of these methods, we state some typical technical results of the conjugation calculus and the commutator calculus. Also, we state several recent results obtained therewith, such as relative standard commutator formulae, bounded width of commutators, with respect to the elementary generators, and nilpotent filtrations of congruence subgroups. Overall, this shows that localisation methods can be much more efficient, than expected

Excitonic Instability and Pseudogap Formation in Nodal Line Semimetal ZrSiS

Electron correlation effects are studied in ZrSiS using a combination of first-principles and model approaches. We show that basic electronic properties of ZrSiS can be described within a two-dimensional lattice model of two nested square lattices. High degree of electron-hole symmetry characteristic for ZrSiS is one of the key features of this model. Having determined model parameters from first-principles calculations, we then explicitly take electron-electron interactions into account and show that at moderately low temperatures ZrSiS exhibits excitonic instability, leading to the formation of a pseudogap in the electronic spectrum. The results can be understood in terms of Coulomb-interaction-assisted pairing of electrons and holes reminiscent to that of an excitonic insulator. Our finding allows us to provide a physical interpretation to the unusual mass enhancement of charge carriers in ZrSiS recently observed experimentally.Comment: 6 pages, 4 figures. Final versio

Langmuir wave linear evolution in inhomogeneous nonstationary anisotropic plasma

Equations describing the linear evolution of a non-dissipative Langmuir wave in inhomogeneous nonstationary anisotropic plasma without magnetic field are derived in the geometrical optics approximation. A continuity equation is obtained for the wave action density, and the conditions for the action conservation are formulated. In homogeneous plasma, the wave field E universally scales with the electron density N as E ~ N^{3/4}, whereas the wavevector evolution varies depending on the wave geometry

Electron-phonon relaxation in periodic granular films

We study the electron-phonon relaxation in the model of a granular metal film, where the grains are formed by regularly arranged potential barriers of arbitrary transparency. The relaxation rate of Debye acoustic phonons is calculated taking into account two mechanisms of electron-phonon scattering: the standard Frohlich interaction of the lattice deformation with the electron density and the interaction mediated by the displacement of grain boundaries dragged by the lattice vibration. At lowest temperatures, the electron-phonon cooling power follows the power-law temperature dependence typical for clean systems, but with the prefactor growing as the transparency of the grain boundaries decreases.Comment: 8 pages, 4 figure

Renormalized theory of the ion cyclotron turbulence in magnetic field--aligned plasma shear flow

The analytical treatment of nonlinear evolution of the shear-flow-modified current driven ion cyclotron instability and shear-flow-driven ion cyclotron kinetic instabilities of magnetic field--aligned plasma shear flow is presented. Analysis is performed on the base of the nonlinear dispersion equation, which accounts for a new combined effect of plasma turbulence and shear flow. It consists in turbulent scattering of ions across the shear flow with their convection by shear flow and results in enhanced nonlinear broadening of ion cyclotron resonances. This effect is found to lead to the saturation of ion cyclotron instabilities as well as to the development of nonlinear shear flow driven ion cyclotron instability. 52.35.RaComment: 21 page

Vacuum energy induced by an impenetrable flux tube of finite radius

We consider the effect of the magnetic field background in the form of a tube of the finite transverse size on the vacuum of the quantized charged massive scalar field which is subject to the Dirichlet boundary condition at the edge of the tube. The vacuum energy is induced, being periodic in the value of the magnetic flux enclosed in the tube. Our previous study in J. Phys. A: Vol.43, 175401 (2010) is extended to the case of smaller radius of the tube and larger distances from it. The dependence of the vacuum energy density on the distance from the tube and on the coupling to the space-time curvature scalar is comprehensively analyzed.Comment: 11 pages, 8 figures, journal version, abstract extended. arXiv admin note: substantial text overlap with arXiv:0911.287

Evidence for two-gap nodeless superconductivity in SmFeAsO0.8_{0.8}F0.2_{0.2} from point-contact Andreev-reflection spectroscopy

Point-contact Andreev-reflection measurements were performed in SmFeAsO_{0.8}F_{0.2} polycrystals with T_c \simeq 53 K. The experimental conductance curves reproducibly exhibit peaks around \pm 6 mV and shoulders at V \sim 16-20 mV, indicating the presence of two nodeless superconducting gaps. While the single-band Blonder-Tinkham-Klapwijk fit can only reproduce a small central portion of the conductance curve, the two-gap one accounts remarkably well for the shape of the whole experimental dI/dV. The fits of the normalized curves give Delta_1(0) = 6.15 \pm 0.45 meV and Delta_2(0) = 18 \pm 3 meV. Both gaps close at the same temperature and follow a BCS-like behavior.Comment: 4 pages, 4 eps color figure

Induced Scattering and Two-Photon Absorption of Alfven Waves with Arbitrary Propagation Angles

The equation for temporary evolution of spectral energy of collisionless Alfven waves is derived in framework of weak turbulence theory. The main nonlinear processes for such conditions are induced scattering and two quantum absorption of Alfven waves by thermal ions. The equation for velocity distribution of thermal particles is derived that describes diffusion in momentum space due to this nonlinear processes. Comparison is done with the results of another authors. Results obtained are qualitatively differ from the ones obtained for the case of Alfven waves propagation along mean magnetic field.Comment: 8 page