Splitting the eigenvectors space for Kildal’s Hamiltonian

• Published in: Semiconductor Physics Quantum Electronics & Optoelectronics
• Date: 2010
• Main Authors: Chuiko, G.P., Don, N.L.
• Format: Article
• Language: English
• Published: Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/118570
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Splitting the eigenvectors space for Kildal’s Hamiltonian / G.P. Chuiko, N.L. Don // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 4. — С. 366-368. — Бібліогр.: 6 назв. — англ.

The rational canonical form of Kildal’s Hamiltonian has been obtained as a
 matrix with two identical diagonal blocks. It allowed to formulate and strictly prove few
 common assertions. Each of the eigenvalues of Kildal’s Hamiltonian is twice
 degenerated everywhere, and it is well-known Kramers’ degeneration, firstly. However,
 there is neither degeneration with except for Kramers’, secondly. The symmetry of
 Kildal’s Hamiltonian forcedly includes the operation of inversion (i.e. the center of
 symmetry), thirdly. Consequently this form of Hamiltonian is evidently not able to
 describe the specific properties of crystals without the center of symmetry. The
 Frobenius form (alias “the rational canonical form”) of Hamiltonian should consist of
 two non-identical diagonal blocks to remove Kramers’ degeneration.