2,256 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
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
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
Angle Dependence of Landau Level Spectrum in Twisted Bilayer Graphene
In the context of the low energy effective theory, the exact Landau level
spectrum of quasiparticles in twisted bilayer graphene with small twist angle
is analytically obtained by spheroidal eigenvalues. We analyze the dependence
of the Landau levels on the twist angle to find the points, where the two-fold
degeneracy for twist angles is lifted in the nonzero modes and below/above
which massive/massless fermion pictures become valid. In the perpendicular
magnetic field of 10\,T, the degeneracy is removed at %angles around 3 degrees for a few low levels, specifically,
for the first pair of nonzero levels and
for the next pair. Massive quasiparticle
appears at in 10\,T, %angles less
than 1.17 degrees. which match perfectly with the recent experimental results.
Since our analysis is applicable to the cases of arbitrary constant magnetic
fields, we make predictions for the same experiment performed in arbitrary
constant magnetic fields, e.g., for B=40\,T we get and the sequence of angles for the pairs of nonzero energy levels. The symmetry restoration
mechanism behind the massive/massless transition is conjectured to be a
tunneling (instanton) in momentum space.Comment: 8 pages, 7 figures, version to appear in PR
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
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
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
Operator method in solving non-linear equations of the Hartree-Fock type
The operator method is used to construct the solutions of the problem of the
polaron in the strong coupling limit and of the helium atom on the basis of the
Hartree-Fock equation. is obtained for the polaron
ground-state energy. Energies for 2s- and 3s-states are also calculated. The
other excited states are briefly discussed.Comment: 7 page
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