770 research outputs found
Method to solve integral equations of the first kind with an approximate input
Techniques are proposed for solving integral equations of the first kind with
an input known not precisely. The requirement that the solution sought for
includes a given number of maxima and minima is imposed. It is shown that when
the deviation of the approximate input from the true one is sufficiently small
and some additional conditions are fulfilled the method leads to an approximate
solution that is necessarily close to the true solution. No regularization is
required in the present approach. Requirements on features of the solution at
integration limits are also imposed. The problem is treated with the help of an
ansatz proposed for the derivative of the solution. The ansatz is the most
general one compatible with the above mentioned requirements. The techniques
are tested with exactly solvable examples. Inversions of the Lorentz, Stieltjes
and Laplace integral transforms are performed, and very satisfactory results
are obtained. The method is useful, in particular, for the calculation of
quantum-mechanical reaction amplitudes and inclusive spectra of
perturbation-induced reactions in the framework of the integral transform
approach.Comment: 28 pages, 1 figure; the presentation is somewhat improved; to be
published in Phys. Rev.
Electrostatics of Inhomogeneous Quantum Hall Liquid
The distribution of electron density in the quantum Hall liquid is considered
in the presence of macroscopic density gradient caused by side electrodes or
inhomogeneous doping. In this case different Landau levels are occupied in
different regions of a sample. These regions are separated by incompressible
liquid. It is shown that the applicability of the approach by Chklovskii et al.
is substantially restricted if the density gradient is not very large and
disorder is important. Due to the fluctuations of the remote donor's density
the liquid in the transition region can not be considered as completely
incompressible. In the typical situation, when the gap between Landau levels is
not much larger than the energy of disorder, the transition region is a wide
band where electron density, averaged over the fluctuations, is independent of
magnetic field. The band is a random mixture of regions occupied by electrons
of upper level, by holes of lower level and by incompressible liquid. The width
of this band is calculated and an analytical expression for the fraction of
incompressible liquid in different parts of this band is given.Comment: 12 pages, RevTe
Total 4He Photoabsorption Cross Section Revisited: Correlated HH versus Effective Interaction HH
Two conceptually different hyperspherical harmonics expansions are used for
the calculation of the total 4He photoabsorption cross section. Besides the
well known method of CHH the recently introduced effective interaction approach
for the hyperspherical formalism is applied. Semi-realistic NN potentials are
employed and final state interaction is fully taken into account via the
Lorentz integral transform method. The results show that the effective
interaction leads to a very good convergence, while the correlation method
exhibits a less rapid convergence in the giant dipole resonance region. The
rather strong discrepancy with the experimental photodisintegration cross
sections is confirmed by the present calculations.Comment: LaTeX, 7 pages, 3 ps figure
Statistics of the Charging Spectrum of a Two-Dimensional Coulomb Glass Island
The fluctuations of capacitance of a two-dimensional island are studied in
the regime of low electron concentration and strong disorder, when electrons
can be considered classical particles. The universal capacitance distribution
is found, with the dispersion being of the order of the average. This
distribution is shown to be closely related to the shape of the Coulomb gap in
the one-electron density of states of the island. Behavior of the the
capacitance fluctuations near the metal - insulator transition is discussed.Comment: 4 pages, LaTex, 4 Postscript figures are included Discussion of the
situation with screening by metallic gate is adde
Theory of Anisotropic Hopping Transport due to Spiral Correlations in the Spin-Glass Phase of Underdoped Cuprates
We study the in-plane resistivity anisotropy in the spin-glass phase of the
high- cuprates, on the basis of holes moving in a spiral spin
background. This picture follows from analysis of the extended model with
Coulomb impurities. In the variable-range hopping regime the resistivity
anisotropy is found to have a maximum value of around 90%, and it decreases
with temperature, in excellent agreement with experiments in
LaSrCuO. In our approach the transport anisotropy is due to the
non-collinearity of the spiral spin state, rather than an intrinsic tendency of
the charges to self-organize.Comment: 5 pages, 4 figures; expanded versio
Electromagnetic response functions of few-nucleon systems
Inclusive electromagnetic reactions in few-nucleon systems are studied basing
on accurate three- and four-body calculations. The longitudinal 4He(e,e')
response function obtained at q\le 600 MeV/c completely agrees with experiment.
The exact 4He spectral function obtained in a semirealistic potential model is
presented, and the accuracy of the quasielastic response calculated with its
help is assessed, as well as the accuracy of some simpler approximations for
the response. The photodisintegration cross section of 3He obtained with the
realistic AV14 NN force plus UrbanaVIII NNN force agrees with experiment. It is
shown that this cross section is very sensitive to underlying nuclear dynamics
in the E_\gamma\simeq 70-100 MeV region. In particular, the NNN nuclear force
clearly manifests itself in this region.Comment: 10 pages, Latex, style file is included, 7 ps figures, to appear in
Proc. of the 2nd Int. Conf. on Perspectives in Hadronic Physics, ITCP,
Triest, May 1999, World Sci., Singapor
The Lorentz Integral Transform (LIT) method and its applications to perturbation induced reactions
The LIT method has allowed ab initio calculations of electroweak cross
sections in light nuclear systems. This review presents a description of the
method from both a general and a more technical point of view, as well as a
summary of the results obtained by its application. The remarkable features of
the LIT approach, which make it particularly efficient in dealing with a
general reaction involving continuum states, are underlined. Emphasis is given
on the results obtained for electroweak cross sections of few--nucleon systems.
Their implications for the present understanding of microscopic nuclear
dynamics are discussed.Comment: 83 pages, 31 figures. Topical review. Corrected typo
Frequency Scaling of Microwave Conductivity in the Integer Quantum Hall Effect Minima
We measure the longitudinal conductivity at frequencies GHz over a range of temperatures K with particular emphasis on the Quantum Hall plateaus. We find that
scales linearly with frequency for a range of magnetic field
around the center of the plateaus, i.e. where . The width of this scaling region decreases with higher
temperature and vanishes by 1.2 K altogether. Comparison between localization
length determined from and DC measurements on the same
wafer show good agreement.Comment: latex 4 pages, 4 figure
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