2,373 research outputs found
On integration of the Kowalevski gyrostat and the Clebsch problems
For the Kowalevski gyrostat change of variables similar to that of the
Kowalevski top is done. We establish one to one correspondence between the
Kowalevski gyrostat and the Clebsch system and demonstrate that Kowalevski
variables for the gyrostat practically coincide with elliptic coordinates on
sphere for the Clebsch case. Equivalence of considered integrable systems
allows to construct two Lax matrices for the gyrostat using known rational and
elliptic Lax matrices for the Clebsch model. Associated with these matrices
solutions of the Clebsch system and, therefore, of the Kowalevski gyrostat
problem are discussed. The Kotter solution of the Clebsch system in modern
notation is presented in detail.Comment: LaTeX, 24 page
Wave Functions and Energy Terms of the SCHR\"Odinger Equation with Two-Center Coulomb Plus Harmonic Oscillator Potential
Schr\"odinger equation for two center Coulomb plus harmonic oscillator
potential is solved by the method of ethalon equation at large intercenter
separations. Asymptotical expansions for energy term and wave function are
obtained in the analytical form.Comment: 4 pages, no figures, LaTeX, submitted to PR
Polarization of Sunyaev-Zeldovich signal due to electron pressure anisotropy in galaxy clusters
We describe polarization of the Sunyaev-Zel'dovich (SZ) effect associated
with electron pressure anisotropy likely present in the intracluster medium
(ICM). The ICM is an astrophysical example of a weakly collisional plasma where
the Larmor frequencies of charged particles greatly exceed their collision
frequencies. This permits formation of pressure anisotropies, driven by
evolving magnetic fields via adiabatic invariance, or by heat fluxes. SZ
polarization arises in the process of Compton scattering of the cosmic
microwave background (CMB) photons off the thermal ICM electrons due to the
difference in the characteristic thermal velocities of the electrons along two
mutually orthogonal directions in the sky plane. The signal scales linearly
with the optical depth of the region containing large-scale correlated
anisotropy, and with the degree of anisotropy itself. It has the same spectral
dependence as the polarization induced by cluster motion with respect to the
CMB frame (kinematic SZ effect polarization), but can be distinguished by its
spatial pattern. { For the illustrative case of a galaxy cluster with a cold
front, where electron transport is mediated by Coulomb collisions, we estimate
the CMB polarization degree at the level of 10 ( nK). An
increase of the effective electron collisionality due to plasma instabilities
will reduce the effect. Such polarization, therefore, may be an independent
probe of the electron collisionality in the ICM, which is one of the key
properties of a high- weakly collisional plasma from the point of view
of both astrophysics and plasma theory.Comment: 13 pages, 5 figures, accepted for publication in MNRA
Quantum tops as examples of commuting differential operators
We study the quantum analogs of tops on Lie algebras and
represented by differential operators.Comment: 24 p
Relativistic dynamical polarizability of hydrogen-like atoms
Using the operator representation of the Dirac Coulomb Green function the
analytical method in perturbation theory is employed in obtaining solutions of
the Dirac equation for a hydrogen-like atom in a time-dependent electric field.
The relativistic dynamical polarizability of hydrogen-like atoms is calculated
and analysed.Comment: 15 pages, 3 figures (not included, but hard copies are available upon
request
Comparison of coupled and uncoupled thermo-elastic models in the range of low temperature below zero
Spectra of Doubly Heavy Quark Baryons
Baryons containing two heavy quarks are treated in the Born-Oppenheimer
approximation. Schr\"odinger equation for two center Coulomb plus harmonic
oscillator potential is solved by the method of ethalon equation at large
intercenter separations. Asymptotical expansions for energy term and wave
function are obtained in the analytical form. Using those formulas, the energy
spectra of doubly heavy baryons with various quark compositions are calculated
analytically.Comment: 19 pages, latex2e, published at PRC61(2000)04520
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