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

Theory of Quark-Gluon Plasma and Phase Transition

Nonperturbative picture of strong interacting quark-gluon plasma is given based on the systematic Field Correlator Method. Equation of state, phase transition in density-temperature plane is derived and compared to lattice data as well as subsequent thermodynamical quantities of QGP.Comment: 6 pages,5 figures; talk given at "13th Lomonosov Conference on Elementary Particle Physics", Moscow, August 23 -- 29, 2007; new reference adde

Quantum tops as examples of commuting differential operators

We study the quantum analogs of tops on Lie algebras $so(4)$ and $e(3)$ represented by differential operators.Comment: 24 p

Ion Beam Synthesis of InAs Nanocrystals in Crystalline Silicon

The formation of nanodimensional InAs crystallites on Si wafers was studied by the method of high fluence implantation of As and In ions with subsequent high temperature treatment. It was found that the size and depth distributions of the crystallites depend on both the implantation temperature and the annealing conditions. A broad band in an energy range of 0.75–1.1 eV was recorded in the photolumines cence spectra of the samples

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