3,518 research outputs found
Arak Inequalities for Concentration Functions and the Littlewood--Offord Problem: a shortened version
Let be independent identically distributed random
variables. In this paper we study the behavior of concentration functions of
weighted sums with respect to the arithmetic structure
of coefficients~ in the context of the Littlewood--Offord problem.
Concentration results of this type received renewed interest in connection with
distributions of singular values of random matrices. Recently, Tao and Vu
proposed an Inverse Principle in the Littlewood--Offord problem. We discuss the
relations between the Inverse Principle of Tao and Vu as well as that of Nguyen
and Vu and a similar principle formulated for sums of arbitrary independent
random variables in the work of Arak from the 1980's. This paper is a shortened
and edited version of the preprint arXiv:1506.09034. Here we present the
results without proofs.Comment: 9 pages. shortened version of arXiv:1506.0903
Experimental evidence of ageing and slow restoration of the weak-contact configuration in tilted 3D granular packings
Granular packings slowly driven towards their instability threshold are
studied using a digital imaging technique as well as a nonlinear acoustic
method. The former method allows us to study grain rearrangements on the
surface during the tilting and the latter enables to selectively probe the
modifications of the weak-contact fraction in the material bulk. Gradual ageing
of both the surface activity and the weak-contact reconfigurations is observed
as a result of repeated tilt cycles up to a given angle smaller than the angle
of avalanche. For an aged configuration reached after several consecutive tilt
cycles, abrupt resumption of the on-surface activity and of the weak-contact
rearrangements occurs when the packing is subsequently inclined beyond the
previous maximal tilting angle. This behavior is compared with literature
results from numerical simulations of inclined 2D packings. It is also found
that the aged weak-contact configurations exhibit spontaneous restoration
towards the initial state if the packing remains at rest for tens of minutes.
When the packing is titled forth and back between zero and near-critical
angles, instead of ageing, the weak-contact configuration exhibits "internal
weak-contact avalanches" in the vicinity of both the near-critical and zero
angles. By contrast, the stronger-contact skeleton remains stable
NN potentials from inverse scattering in the J-matrix approach
An approximate inverse scattering method [7,8] has been used to construct
separable potentials with the Laguerre form factors. As an application, we
invert the phase shifts of proton-proton in the and
channels and neutron-proton in the channel elastic scattering. In
the latter case the deuteron wave function of a realistic potential was
used as input.Comment: LaTex2e, 17 pages, 3 Postscript figures; corrected typo
Anatomy of point-contact Andreev reflection spectroscopy from the experimental point of view (review)
We review application of point-contact Andreev-reflection spectroscopy to
study elemental superconductors, where theoretical conditions for the smallness
of the point-contact size with respect to the characteristic lengths in the
superconductor can be satisfied. We discuss existing theoretical models and
identify new issues that have to be solved, especially when applying this
method to investigate more complex superconductors. We will also demonstrate
that some aspects of point-contact Andreev-reflection spectroscopy still need
to be addressed even when investigating ordinary metals.Comment: 20 pages, 18 figs. V2: Ref.60 and footnote 3 are added, a number of
minor fixe
Quasiparticle states of the Hubbard model near the Fermi level
The spectra of the t-U and t-t'-U Hubbard models are investigated in the
one-loop approximation for different values of the electron filling. It is
shown that the four-band structure which is inherent in the case of
half-filling and low temperatures persists also for some excess or deficiency
of electrons. Besides, with some departure from half-filling an additional
narrow band of quasiparticle states arises near the Fermi level. The dispersion
of the band, its bandwidth and the variation with filling are close to those of
the spin-polaron band of the t-J model. For moderate doping spectral
intensities in the new band and in one of the inner bands of the four-band
structure decrease as the Fermi level is approached which leads to the
appearance of a pseudogap in the spectrum.Comment: 8 pages, 7 figure
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