Quaternionic factorization of the Schroedinger operator and its applications to some first order systems of mathematical physics

We consider the following first order systems of mathematical physics. 1.The Dirac equation with scalar potential. 2.The Dirac equation with electric potential. 3.The Dirac equation with pseudoscalar potential. 4.The system describing non-linear force free magnetic fields or Beltrami fields with nonconstant proportionality factor. 5.The Maxwell equations for slowly changing media. 6.The static Maxwell system. We show that all this variety of first order systems reduces to a single quaternionic equation the analysis of which in its turn reduces to the solution of a Schroedinger equation with biquaternionic potential. In some important situations the biquaternionic potential can be diagonalized and converted into scalar potentials

On a complex differential Riccati equation

We consider a nonlinear partial differential equation for complex-valued functions which is related to the two-dimensional stationary Schrodinger equation and enjoys many properties similar to those of the ordinary differential Riccati equation as, e.g., the famous Euler theorems, the Picard theorem and others. Besides these generalizations of the classical "one-dimensional" results we discuss new features of the considered equation like, e.g., an analogue of the Cauchy integral theorem

Multi-wavelength observations of the gamma-ray flaring quasar S4 1030+61 in 2009-2014

We present a study of the parsec-scale multi-frequency properties of the quasar S4 1030+61 during a prolonged radio and gamma-ray activity. Observations were performed within Fermi gamma-ray telescope, OVRO 40-m telescope and MOJAVE VLBA monitoring programs, covering five years from 2009. The data are supplemented by four-epoch VLBA observations at 5, 8, 15, 24, and 43 GHz, which were triggered by the bright gamma-ray flare, registered in the quasar in 2010. The S4 1030+61 jet exhibits an apparent superluminal velocity of (6.4+-0.4)c and does not show ejections of new components in the observed period, while decomposition of the radio light curve reveals nine prominent flares. The measured variability parameters of the source show values typical for Fermi-detected quasars. Combined analysis of radio and gamma-ray emission implies a spatial separation between emitting regions at these bands of about 12 pc and locates the gamma-ray emission within a parsec from the central engine. We detected changes in the value and direction of the linear polarization and the Faraday rotation measure. The value of the intrinsic brightness temperature of the core is above the equipartition state, while its value as a function of distance from the core is well approximated by the power-law. Altogether these results show that the radio flaring activity of the quasar is accompanied by injection of relativistic particles and energy losses at the jet base, while S4 1030+61 has a stable, straight jet well described by standard conical jet theories.Comment: accepted by MNRAS, 16 pages, 14 figures, 8 tables, 5 pages of supplementary materia

Instability of the Two-Dimensional Metallic Phase to Parallel Magnetic Field

We report on magnetotransport studies of the unusual two-dimensional metallic phase in high mobility Si-MOS structures. We have observed that the magnetic field applied in the 2D plane suppresses the metallic state, causing the resistivity to increase dramatically by more than 30 times. Over the total existence range of the metallic state, we have found three distinct types of the magnetoresistance, related to the corresponding quantum corrections to the conductivity. Our data suggest that the unusual metallic state is a consequence of both spin- and Coulomb-interaction effects.Comment: 6 pages, Latex, 4 ps fig

Formation of three-particle clusters in hetero-junctions and MOSFET structures

A novel interaction mechanism in MOSFET structures and $GaAs/AlGaAs$ hetero-junctions between the zone electrons of the two-dimensional (2D) gas and the charged traps on the insulator side is considered. By applying a canonical transformation, off-diagonal terms in the Hamiltonian due to the trapped level subsystem are excluded. This yields an effective three-particle attractive interaction as well as a pairing interaction inside the 2D electronic band. A type of Bethe- Goldstone equation for three particles is studied to clarify the character of the binding and the energy of the three-particle bound states. The results are used to offer a possible explanation of the Metal-Insulator transition recently observed in MOSFET and hetero-junctions.Comment: 4 page

Comment on "Interaction Effects in Conductivity of Si Inversion Layers at Intermediate Temperatures"

We show that the comparison between theory and experiment, performed by Pudalov et al. in PRL 91, 126403 (2003), is not valid.Comment: comment on PRL 91, 126403 (2003) by Pudalov et a

A New Liquid Phase and Metal-Insulator Transition in Si MOSFETs

We argue that there is a new liquid phase in the two-dimensional electron system in Si MOSFETs at low enough electron densities. The recently observed metal-insulator transition results as a crossover from the percolation transition of the liquid phase through the disorder landscape in the system below the liquid-gas critical temperature. The consequences of our theory are discussed for variety of physical properties relevant to the recent experiments.Comment: 12 pages of RevTeX with 3 postscript figure