Boris Zhilinskií
Publications:
Dhont G., Iwai T., Zhilinskií B. I.
A Study of Energy Band Rearrangement in Isolated Molecules by Means of the Dirac Oscillator Approximation
2020, vol. 25, no. 5, pp. 424452
Abstract
Energy band rearrangement along a control parameter in isolated molecules
is studied through axially symmetric Hamiltonians describing the coupling of two angular
momenta $\mathbf{S}$ and $\mathbf{L}$ of fixed amplitude. We focus our attention on the case $S = 1$ which, albeit
nongeneric, describes the global rearrangement of a system of energy bands between two welldefined
limits corresponding to uncoupled and coupled momenta. The redistribution of energy
levels between bands is closely related to the degeneracy of the eigenvalues of the corresponding
semiquantum Hamiltonian at isolated points of the threedimensional Cartesian product of the
twodimensional phase space and the onedimensional control parameter space. The present
paper shows that the band rearrangement for the full quantum system can be quantitatively,
rather than qualitatively, reproduced with Dirac oscillator approximations. We also interpret
the energy band rearrangement by comparing the evolution of the joint spectra of commuting
observables (\emph{i.e.}, energy and axial angular momentum) with that of the image of the energymomentum
map of the completely classical limit of the Dirac oscillator approximations.
