9,724 research outputs found
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
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