214 research outputs found
Towards investigation of evolution of dynamical systems with independence of time accuracy: more classes of systems
The recently developed method (Paper 1) enabling one to investigate the
evolution of dynamical systems with an accuracy not dependent on time is
developed further. The classes of dynamical systems which can be studied by
that method are much extended, now including systems that are; (1)
non-Hamiltonian, conservative; (2) Hamiltonian with time-dependent
perturbation; (3) non-conservative (with dissipation). These systems cover
various types of N-body gravitating systems of astrophysical and cosmological
interest, such as the orbital evolution of planets, minor planets, artificial
satellites due to tidal, non-tidal perturbations and thermal thrust, evolving
close binary stellar systems, and the dynamics of accretion disks.Comment: Eur. Phys. Journ. C (in press), to match the published version, 4
page
A principal possibility for computer investigation of evolution of dynamical systems with independent on time accuracy
Extensive N-body simulations are among the key means for the study of
numerous astrophysical and cosmological phenomena, so various schemes are
developed for possibly higher accuracy computations. We demonstrate the
principal possibility for revealing the evolution of a perturbed Hamiltonian
system with an accuracy independent on time. The method is based on the Laplace
transform and the derivation and analytical solution of an evolution equation
in the phase space for the resolvent and using computer algebra.Comment: Eur Phys Journ C (in press), to match the version to appear, 7 pages,
3 fig
Superexchange in Dilute Magnetic Dielectrics: Application to (Ti,Co)O_2
We extend the model of ferromagnetic superexchange in dilute magnetic
semiconductors to the ferromagnetically ordered highly insulating compounds
(dilute magnetic dielectrics). The intrinsic ferromagnetism without free
carriers is observed in oxygen-deficient films of anatase TiO_2 doped with
transition metal impurities in cation sublattice. We suppose that ferromagnetic
order arises due to superexchange between complexes [oxygen vacancies +
magnetic impurities], which are stabilized by charge transfer from vacancies to
impurities. The Hund rule controls the superexchange via empty vacancy related
levels so that it becomes possible only for the parallel orientation of
impurity magnetic moments. The percolation threshold for magnetic ordering is
determined by the radius of vacancy levels, but the exchange mechanism does not
require free carriers. The crucial role of the non-stoichiometry in formation
of the ferromagnetism makes the Curie temperatures extremely sensitive to the
methods of sample preparation.Comment: 18 pages, 2 figure
Slave boson theory of the extended Falicov-Kimball model
The extended Falicov-Kimball model, with both an on-site hybridization
potential and dispersive narrow band, is examined within the saddle-point
approximation to the Kotliar-Ruckenstein slave boson theory. We first set the
hybridization potential to zero and find that the phase diagram depends
strongly upon the orbital structure: for degenerate orbitals, a
correlated-insulating state is found at sufficiently strong interaction
strengths, whereas a finite orbital energy difference can lead to discontinuous
valence transitions. The obtained phase diagram is very sensitive to the
presence of a finite hybridization potential. As in Hartree-Fock theory, we
find an enhancement of the hybridization by the inter-orbital Coulomb
repulsion. The more precise treatment of correlation effects, however, leads to
large deviations from the Hartree-Fock results. In the limit of vanishing
hybridization an excitonic insulator state is only found when the orbitals are
degenerate, which restricts this phase to a much smaller parameter space than
in other available mean-field theories.Comment: 23 pages, 10 figure
A weakly random Universe?
The cosmic microwave background (CMB) radiation is characterized by
well-established scales, the 2.7 K temperature of the Planckian spectrum and
the amplitude of the temperature anisotropy. These features were
instrumental in indicating the hot and equilibrium phases of the early history
of the Universe and its large scale isotropy, respectively. We now reveal one
more intrinsic scale in CMB properties. We introduce a method developed
originally by Kolmogorov, that quantifies a degree of randomness (chaos) in a
set of numbers, such as measurements of the CMB temperature in some region.
Considering CMB as a composition of random and regular signals, we solve the
inverse problem of recovering of their mutual fractions from the temperature
sky maps. Deriving the empirical Kolmogorov's function in the Wilkinson
Microwave Anisotropy Probe's maps, we obtain the fraction of the random signal
to be about 20 per cent, i.e. the cosmological sky is a weakly random one. The
paper is dedicated to the memory of Vladimir Arnold (1937-2010).Comment: 4 pages, 3 figs, A & A (Lett) in press; to match the published
versio
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