8,325 research outputs found
On a factorization of second order elliptic operators and applications
We show that given a nonvanishing particular solution of the equation
(divpgrad+q)u=0 (1) the corresponding differential operator can be factorized
into a product of two first order operators. The factorization allows us to
reduce the equation (1) to a first order equation which in a two-dimensional
case is the Vekua equation of a special form. Under quite general conditions on
the coefficients p and q we obtain an algorithm which allows us to construct in
explicit form the positive formal powers (solutions of the Vekua equation
generalizing the usual powers of the variable z). This result means that under
quite general conditions one can construct an infinite system of exact
solutions of (1) explicitly, and moreover, at least when p and q are real
valued this system will be complete in ker(divpgrad+q) in the sense that any
solution of (1) in a simply connected domain can be represented as an infinite
series of obtained exact solutions which converges uniformly on any compact
subset of . Finally we give a similar factorization of the operator
(divpgrad+q) in a multidimensional case and obtain a natural generalization of
the Vekua equation which is related to second order operators in a similar way
as its two-dimensional prototype does
Influence of spin polarization on resistivity of a two-dimensional electron gas in Si MOSFET at metallic densities
Positive magnetoresistance (PMR) of a silicon MOSFET in parallel magnetic
fields B has been measured at high electron densities n >> n_c where n_c is the
critical density of the metal-insulator transition (MIT). It turns out that the
normalized PMR curves, R(B)/R(0), merge together when the field is scaled
according to B/B_c(n) where B_c is the field in which electrons become fully
spin polarized. The values of B_c have been calculated from the simple equality
between the Zeeman splitting energy and the Fermi energy taking into account
the experimentally measured dependence of the spin susceptibility on the
electron density. This extends the range of validity of the scaling all the way
to a deeply metallic regime far away from MIT. The subsequent analysis of PMR
for low n >~ n_c demonstrated that the merging of the initial parts of curves
can bee achieved only with taking into account the temperature dependence of
B_c. It is also shown that the shape of the PMR curves at strong magnetic
fields is affected by a crossover from a purely two-dimensional (2D) electron
transport to a regime where out-of-plane carrier motion becomes important
(quasi-three-dimensional regime).Comment: 5 pages, including 6 figures; misprints corrected; Europhys. Lett.
(in press
Thermodynamic Signature of a Two-Dimensional Metal-Insulator Transition
We present a study of the compressibility, K, of a two-dimensional hole
system which exhibits a metal-insulator phase transition at zero magnetic
field. It has been observed that dK/dp changes sign at the critical density for
the metal-insulator transition. Measurements also indicate that the insulating
phase is incompressible for all values of B. Finally, we show how the phase
transition evolves as the magnetic field is varied and construct a phase
diagram in the density-magnetic field plane for this system.Comment: 4 pages, 4 figures, submitted to Physical Review Letters; version 1
is identical to version 2 but didn't compile properl
Mesoscopic Behavior Near a Two-Dimensional Metal-Insulator Transition
We study conductance fluctuations in a two-dimensional electron gas as a
function of chemical potential (or gate voltage) from the strongly insulating
to the metallic regime. Power spectra of the fluctuations decay with two
distinct exponents (1/v_l and 1/v_h). For conductivity , we find a third exponent (1/v_i) in the shortest samples, and
non-monotonic dependence of v_i and v_l on \sigma. We study the dependence of
v_i, v_l, v_h, and the variances of corresponding fluctuations on \sigma,
sample size, and temperature. The anomalies near
indicate that the dielectric response and screening length are critically
behaved, i.e. that Coulomb correlations dominate the physics.Comment: Revised according to referee remark
Heavy Hadron Spectroscopy
I review recent theoretical advances in heavy hadron spectroscopy.Comment: Plenary talk at the XXXIII International Conference on High Energy
Physics (ICHEP 06), Moscow, Russia, July 26 - August 2, 2006; 11 page
IceCube-Plus: An Ultra-High Energy Neutrino Telescope
While the first kilometer-scale neutrino telescope, IceCube, is under
construction, alternative plans exist to build even larger detectors that will,
however, b e limited by a much higher neutrino energy threshold of 10 PeV or
higher rather than 10 to 100 GeV. These future projects detect radio and
acoustic pulses as w ell as air showers initiated by ultra-high energy
neutrinos. As an alternative, we here propose an expansion of IceCube, using
the same strings, placed on a gri d with a spacing of order 500 m. Unlike other
proposals, the expanded detector uses methods that are understood and
calibrated on atmospheric neutrinos. Atmosp heric neutrinos represent the only
background at the energies under consideratio n and is totally negligible.
Also, the cost of such a detector is understood. We conclude that supplementing
the 81 IceCube strings with a modest number of addi tional strings spaced at
large distances can almost double the effective volume of the detector.
Doubling the number of strings on a 800 m grid can deliver a d etector that
this a factor of 5 larger for horizontal muons at modest cost.Comment: Version to be published in JCA
On Lebesgue measure of integral self-affine sets
Let be an expanding integer matrix and be a finite subset
of . The self-affine set is the unique compact set satisfying
the equality . We present an effective algorithm to
compute the Lebesgue measure of the self-affine set , the measure of
intersection for , and the measure of intersection of
self-affine sets for different sets .Comment: 5 pages, 1 figur
Coulomb Drag at the Onset of Anderson Insulators
It is shown that the Coulomb drag between two identical layers in the
Anderson insulting state indicates a striking difference between the Mott and
Efros-Shklovskii (ES) insulators. In the former, the trans-resistance
is monotonically increasing with the localization length ; in the latter,
the presence of a Coulomb gap leads to an opposite result: is enhanced
with a decreasing , with the same exponential factor as the single layer
resistivity. This distinction reflects the relatively pronounced role of
excited density fluctuations in the ES state, implied by the enhancement in the
rate of hopping processes at low frequencies. The magnitude of drag is
estimated for typical experimental parameters in the different cases. It is
concluded that a measurement of drag can be used to distinguish between
interacting and non-interacting insulating state.Comment: 15 pages, revte
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