97 research outputs found
Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports
In this paper we present a survey about analytic properties of polynomials
orthogonal with respect to a weighted Sobolev inner product such that the
vector of measures has an unbounded support. In particular, we are focused in
the study of the asymptotic behaviour of such polynomials as well as in the
distribution of their zeros. Some open problems as well as some new directions
for a future research are formulated.Comment: Changed content; 34 pages, 41 reference
A novel superconducting glass state in disordered thin films in Clogston limit
A theory of mesoscopic fluctuations in disordered thin superconducting films
in a parallel magnetic field is developed. At zero temperature, the
superconducting state undergoes a phase transition into a state characterized
by superfluid densities of random signs, instead of a spin polarized disordered
Fermi liquid phase. Consequently, the ground state belongs to the same
universality class as the 2D XY spin glass. As the magnetic field increases
further, mesoscopic pairing states are nucleated in an otherwise homogeneous
spin polarized disordered Fermi liquid. The statistics of these pairing states
is universal depending on the sheet conductance of the 2D film.Comment: Latex, 39 pages, 2 figures included; to appear in Int. J. Mod. Phys.
Density of States of Disordered Two-Dimensional Crystals with Half-Filled Band
A diagrammatic method is applied to study the effects of commensurability in
two-dimensional disordered crystalline metals by using the particle-hole
symmetry with respect to the nesting vector P_0={\pm{\pi}/a, {\pi}/a} for a
half-filled electronic band. The density of electronic states (DoS) is shown to
have nontrivial quantum corrections due to both nesting and elastic impurity
scattering processes, as a result the van Hove singularity is preserved in the
center of the band. However, the energy dependence of the DoS is strongly
changed. A small offset from the middle of the band gives rise to disappearence
of quantum corrections to the DoS .Comment: to be published in Physical Review Letter
Strong asymptotics for Jacobi polynomials with varying nonstandard parameters
Strong asymptotics on the whole complex plane of a sequence of monic Jacobi
polynomials is studied, assuming that with and satisfying , , . The
asymptotic analysis is based on the non-Hermitian orthogonality of these
polynomials, and uses the Deift/Zhou steepest descent analysis for matrix
Riemann-Hilbert problems. As a corollary, asymptotic zero behavior is derived.
We show that in a generic case the zeros distribute on the set of critical
trajectories of a certain quadratic differential according to the
equilibrium measure on in an external field. However, when either
, or are geometrically close to ,
part of the zeros accumulate along a different trajectory of the same quadratic
differential.Comment: 31 pages, 12 figures. Some references added. To appear in Journal
D'Analyse Mathematiqu
Scaling of the Conductivity with Temperature and Uniaxial Stress in Si:B at the Metal-Insulator Transition
Using uniaxial stress to tune Si:B through the metal-insulator transition we
find the conductivity at low temperatures shows an excellent fit to scaling
with temperature and stress on both sides of the transition. The scaling
functions yield the conductivity in the metallic and insulating phases, and
allow a reliable determination of the temperature dependence in the critical
regions on both sides of the transition
Bulk Tunneling at Integer Quantum Hall Transitions
The tunneling into the {\em bulk} of a 2D electron system (2DES) in strong
magnetic field is studied near the integer quantum Hall transitions. We present
a nonperturbative calculation of the tunneling density of states (TDOS) for
both Coulomb and short-ranged electron-electron interactions. In the case of
Coulomb interaction, the TDOS exhibits a 2D quantum Coulomb gap behavior,
\nu(\ve)=C_Q\ave/e^4, with a nonuniversal coefficient of quantum
mechanical origin. For short-ranged interactions, we find that the TDOS at low
bias follows \nu(\ve)/\nu (0)=1+(\ave/\ve_0)^\gamma, where is a
universal exponent determined by the scaling dimension of short-ranged
interactions.Comment: 4 pages, revtex, final version to appear in Phys. Rev. Let
Новый подход к ВЭЖХ-анализу жидких витаминсодержащих лекарственных форм
A single-step HPLC method for the determination of fat-soluble vitamins and some additives in several liquid medicines by reverse phase in the isocratic mode was developed.Разработана методика одностадийного количественного анализа жирорастворимых витаминов и некоторых вспомогательных веществ ряда жидких лекарственных средств на обращенной фазе в изократическом режиме
Two-dimensional Anderson-Hubbard model in DMFT+Sigma approximation
Density of states, dynamic (optical) conductivity and phase diagram of
paramagnetic two-dimensional Anderson-Hubbard model with strong correlations
and disorder are analyzed within the generalized dynamical mean-field theory
(DMFT+Sigma approximation). Strong correlations are accounted by DMFT, while
disorder is taken into account via the appropriate generalization of the
self-consistent theory of localization. We consider the two-dimensional system
with the rectangular "bare" density of states (DOS). The DMFT effective single
impurity problem is solved by numerical renormalization group (NRG). Phases of
"correlated metal", Mott insulator and correlated Anderson insulator are
identified from the evolution of density of states, optical conductivity and
localization length, demonstrating both Mott-Hubbard and Anderson
metal-insulator transitions in two-dimensional systems of the finite size,
allowing us to construct the complete zero-temperature phase diagram of
paramagnetic Anderson-Hubbard model. Localization length in our approximation
is practically independent of the strength of Hubbard correlations. However,
the divergence of localization length in finite size two-dimensional system at
small disorder signifies the existence of an effective Anderson transition.Comment: 10 pages, 10 figures, improve phase diagra
Granulated superconductors:from the nonlinear sigma model to the Bose-Hubbard description
We modify a nonlinear sigma model (NLSM) for the description of a granulated
disordered system in the presence of both the Coulomb repulsion and the Cooper
pairing. We show that under certain controlled approximations this model is
reduced to the Bose-Hubbard (or ``dirty-boson'') model with renormalized
coupling constants. We obtain a more general effective action (which is still
simpler than the full NLSM action) which can be applied in the region of
parameters where the reduction to the Bose-Hubbard model is not justified. This
action may lead to a different picture of the superconductor-insulator
transition in 2D systems.Comment: 4 pages, revtex, no figure
Computation of the entropy of polynomials orthogonal on an interval.
We give an effective method to compute the entropy for polynomials orthogonal on a segment of the real axis that uses as input data only the coefficients of the recurrence relation satisfied by these polynomials. This algorithm is based on a series expression for the mutual energy of two probability measures naturally connected with the polynomials. The particular case of Gegenbauer polynomials is analyzed in detail. These results are applied also to the computation of the entropy of spherical harmonics, important for the study of the entropic uncertainty relations as well as the spatial complexity of physical systems in central potentials
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