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

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

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

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

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 Droplet State in an Interacting Two-Dimensional Electron System

It is well known that the dielectric constant of two-dimensional (2D) electron system goes negative at low electron densities. A consequence of the negative dielectric constant could be the formation of the droplet state. The droplet state is a two-phase coexistence region of high density liquid and low density "gas". In this paper, we carry out energetic calculations to study the stability of the droplet ground state. The possible relevance of the droplet state to recently observed 2D metal-insulator transition is also discussed.Comment: 4 pages, 4 figures. To appear in Phys. Rev. B (Rapid Communications

Flow diagram of the metal-insulator transition in two dimensions

The discovery of the metal-insulator transition (MIT) in two-dimensional (2D) electron systems challenged the veracity of one of the most influential conjectures in the physics of disordered electrons, which states that `in two dimensions, there is no true metallic behaviour'; no matter how weak the disorder, electrons would be trapped and unable to conduct a current. However, that theory did not account for interactions between the electrons. Here we investigate the interplay between the electron-electron interactions and disorder near the MIT using simultaneous measurements of electrical resistivity and magnetoconductance. We show that both the resistance and interaction amplitude exhibit a fan-like spread as the MIT is crossed. From these data we construct a resistance-interaction flow diagram of the MIT that clearly reveals a quantum critical point, as predicted by the two-parameter scaling theory (Punnoose and Finkel'stein, Science 310, 289 (2005)). The metallic side of this diagram is accurately described by the renormalization group theory without any fitting parameters. In particular, the metallic temperature dependence of the resistance sets in when the interaction amplitude reaches gamma_2 = 0.45 - a value in remarkable agreement with the one predicted by the theory.Comment: as publishe

Magnetic Field Suppression of the Conducting Phase in Two Dimensions

The anomalous conducting phase that has been shown to exist in zero field in dilute two-dimensional electron systems in silicon MOSFETs is driven into a strongly insulating state by a magnetic field of about 20 kOe applied parallel to the plane. The data suggest that in the limit of T -> 0 the conducting phase is suppressed by an arbitrarily weak magnetic field. We call attention to striking similarities to magnetic field-induced superconductor-insulator transitions