5,085 research outputs found
On irreducible partials of Ricci tensor traceless part in finite space-time region in GR
Riemann tensor irreducible part constructed from metric tensor
and traceless part of Ricci tensor
is expanded into bilinear combinations of bivectorial fields being
eigenfunctions of . Field equations for the bivectors induced by Bianchi
identities are studied and it is shown that in general case it will be
3-parametric local symmetry group Yang-Mills field.Comment: LaTeX2e, 13 pages, to be published in Ukrainian Physical Journa
Electron spin relaxation in semiconductors and semiconductor structures
We suggest an approach to the problem of free electron spin evolution in a
semiconductor with arbitrary anisotropy or quantum structure in a magnetic
field. The developed approach utilizes quantum kinetic equations for average
spin components. These equations represent the relaxation in terms of
correlation functions for fluctuating effective fields responsible for spin
relaxation. In a particular case when autocorrelation functions are dominant,
the kinetic equations reduce to the Bloch equations. The developed formalism is
applied to the problem of electron spin relaxation due to exchange scattering
in a semimagnetic quantum well (QW) as well as to the spin relaxation in a QW
due to Dyakonov-Perel mechanism.Comment: 9 pages, 1 postscript figur
PET Detectors with 0.4-mm Depth-of-Interaction Resolution
Presice measurements of the photons conversion points in the scintillators
are required to achieve a high spatial resolution of the PET system. I have
developed a new method of reconstruction of the depth-of-interaction
information for PET detectors with dual-side readout. The depth-of-interaction
and energy resolutions from Monte-Carlo simulations are presented in this
paper. The new method allows to reach depth-of-interaction resolution that is
about 0.4~mm ()
[or about 1.0~mm (FWHM)] for 10-mm long LYSO scintillator. If the precise
measurement of the primary photon energy is not a high priority, the new method
can be tuned to achieve even better results for the DOI resolution that is
better than 0.3~mm () [or better than 0.7~mm (FWHM)].Comment: 13 pages, 15 figures, 1 tabl
On the theory of the Kolmogorov operator in the spaces and I
We obtain the basic results concerning the problem of constructing operator
realizations of the formal differential expression with measurable matrix and vector field having
critical-order singularities as the generators of Markov semigroups in
and .Comment: 61
regularity of solutions to Kolmogorov equation with Gilbarg-Serrin matrix
In , , consider the divergence and the non-divergence
form operators \begin{equation} \tag{} -\Delta - \nabla \cdot (a-I) \cdot
\nabla + b \cdot \nabla, \end{equation} \begin{equation} \tag{} - \Delta -
(a-I) \cdot \nabla^2 + b \cdot \nabla, \end{equation} where the second order
perturbations are given by the matrix
The vector field is form-bounded with
the form-bound (this includes a sub-critical class , as well as vector fields having critical-order singularities). We
characterize quantitative dependence on and of the regularity of the resolvents of the operator
realizations of (), () in , as (minus)
generators of positivity preserving contraction semigroups.Comment: 35
Brownian motion with general drift
We construct and study the weak solution to stochastic differential equation
, , for every , , with in the class of weakly form-bounded vector fields,
containing, as proper subclasses, a sub-critical class , as
well as critical classes such as weak class, Kato class, Campanato-Morrey
class, Chang-Wilson-T. Wolff class
Stochastic differential equations with singular (form-bounded) drift
We consider the problem of constructing weak solutions to the It\^{o} and to
the Stratonovich stochastic differential equations having critical-order
singularities in the drift and critical-order discontinuities in the dispersion
matrix
Two-sided weighted bounds on fundamental solution to fractional Schr\"odinger operator
We establish sharp two-sided weighted bounds on the fundamental solution to
the fractional Schr\"{o}dinger operator using the method of desingularizing
weights.Comment: Added a comment on the critical case of relative bound \delta=
A hybrid method without extrapolation step for solving variational inequality problems
In this paper, we introduce a new method for solving variational inequality
problems with monotone and Lipschitz-continuous mapping in Hilbert space. The
iterative process is based on two well-known projection method and the hybrid
(or outer approximation) method. However we do not use an extrapolation step in
the projection method. The absence of one projection in our method is explained
by slightly different choice of sets in hybrid method. We prove a strong
convergence of the sequences generated by our method
Anisotropy of heavy hole spin splitting and interference effects of optical polarization in semiconductor quantum wells subjected to an in-plane magnetic field
Strong effects of optical polarization anisotropy observed previously in the
quantum wells subjected to the in-plane magnetic field arrive at complete
description within microscopic approach. Theory we develop involves two sources
of optical polarization. First source is due to correlations between electron
and heavy hole (HH) phases of -functions arising due to electron Zeeman
spin splitting and joint manifestation of low-symmetry and Zeeman interactions
of HH in an in-plane magnetic field. In this case, four possible
phase-controlled electron-HH transitions constitute the polarization effect,
which can reach its maximal amount (1) at low temperatures when only one
transition survives. Other polarization source stems from the admixture of
excited light-holes (LH) states to HH by low-symmetry interactions. The
contribution of this mechanism to total polarization is relatively small but it
can be independent of temperature and magnetic field. Analysis of different
mechanisms of HH splitting exhibits their strong polarization anisotropy. Joint
action of these mechanisms can result in new peculiarities, which should be
taken into account for explanation of different experimental situations.Comment: 8 pages, 5 postscript figure
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