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

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

Scaling and the Metal-Insulator Transition in Si/SiGe Quantum Wells

The existence of a metal-insulator transition at zero magnetic field in two- dimensional electron systems has recently been confirmed in high mobility Si-MOSFETs. In this work, the temperature dependence of the resistivity of gated Si/SiGe/Si quantum well structures has revealed a similar metal- insulator transition as a function of carrier density at zero magnetic field. We also report evidence for a Coulomb gap in the temperature dependence of the resistivity of the dilute 2D hole gas confined in a SiGe quantum well. In addition, the resistivity in the insulating phase scales with a single parameter, and is sample independent. These results are consistent with the occurrence of a metal-insulator transition at zero magnetic field in SiGe square quantum wells driven by strong hole-hole interactions.Comment: 3 pages, 3 figures, LaTe

Addendum to "Coherent radio pulses from GEANT generated electromagnetic showers in ice"

We reevaluate our published calculations of electromagnetic showers generated by GEANT 3.21 and the radio frequency pulses they produce in ice. We are prompted by a recent report showing that GEANT 3.21-modeled showers are sensitive to internal settings in the electron tracking subroutine. We report the shower and pulse characteristics obtained with different settings of GEANT 3.21 and with GEANT 4. The default setting of electron tracking in GEANT 3.21 we used in previous work speeds up the shower simulation at the cost of information near the end of the tracks. We find that settings tracking electron and positron to lower energy yield a more accurate calculation, a more intense shower, and proportionately stronger radio pulses at low frequencies. At high frequencies the relation between shower tracking algorithm and pulse spectrum is more complex. We obtain radial distributions of shower particles and phase distributions of pulses from 100 GeV showers that are consistent with our published results.Comment: 4 pages, 3 figure

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

Metal-insulator transition in disordered 2DEG including temperature effects

We calculate self-consistently the mutual dependence of electron correlations and electron-defect scattering for a two dimensional electron gas at finite temperature. We employ an STLS approach to calculate the electron correlations while the electron scattering rate off Coulombic impurities and surface roughness is calculated using self-consistent current-relaxation theory. The methods are combined and self-consistently solved. We discuss a metal-insulator transition for a range of disorder levels and electron densities. Our results are in good agreement with recent experimental observations.Comment: 4 pages, RevTeX + epsf, 5 figure