10,693 research outputs found
On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory
Elliptic pseudoanalytic function theory was considered independently by Bers
and Vekua decades ago. In this paper we develop a hyperbolic analogue of
pseudoanalytic function theory using the algebra of hyperbolic numbers. We
consider the Klein-Gordon equation with a potential. With the aid of one
particular solution we factorize the Klein-Gordon operator in terms of two
Vekua-type operators. We show that real parts of the solutions of one of these
Vekua-type operators are solutions of the considered Klein-Gordon equation.
Using hyperbolic pseudoanalytic function theory, we then obtain explicit
construction of infinite systems of solutions of the Klein-Gordon equation with
potential. Finally, we give some examples of application of the proposed
procedure
Test of scaling theory in two dimensions in the presence of valley splitting and intervalley scattering in Si-MOSFETs
We show that once the effects of valley splitting and intervalley scattering
are incorporated, renormalization group theory consistently describes the
metallic phase in silicon metal-oxide-semiconductor field-effect transistors
down to the lowest accessible temperatures
Weak Field Hall Resistance and Effective Carrier Density Through Metal-Insulator Transition in Si-MOS Structures
We studied the weak field Hall voltage in 2D electron layers in Si-MOS
structures with different mobilities, through the metal-insulator transition.
In the vicinity of the critical density on the metallic side of the transition,
we have found weak deviations (about 6-20 %) of the Hall voltage from its
classical value. The deviations do not correlate with the strong temperature
dependence of the diagonal resistivity rho_{xx}(T). The smallest deviation in
R_{xy} was found in the highest mobility sample exhibiting the largest
variation in the diagonal resistivity \rho_{xx} with temperature (by a factor
of 5).Comment: 4 pages, 4 figures, RevTe
Comment on "Theory of metal-insulator transitions in gated semiconductors" (B. L. Altshuler and D. L. Maslov, Phys. Rev. Lett. 82, 145 (1999))
In a recent Letter, Altshuler and Maslov propose a model which attributes the
anomalous temperature and field dependence of the resistivity of
two-dimensional electron (or hole) systems to the charging and discharging of
traps in the oxide (spacer), rather than to intrinsic behavior of interacting
particles associated with a conductor-insulator transition in two dimensions.
We argue against this model based on existing experimental evidence.Comment: 1 page; submitted to PR
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
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
Diassociative algebras and Milnor's invariants for tangles
We extend Milnor's mu-invariants of link homotopy to ordered (classical or
virtual) tangles. Simple combinatorial formulas for mu-invariants are given in
terms of counting trees in Gauss diagrams. Invariance under Reidemeister moves
corresponds to axioms of Loday's diassociative algebra. The relation of tangles
to diassociative algebras is formulated in terms of a morphism of corresponding
operads.Comment: 17 pages, many figures; v2: several typos correcte
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
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