Splitting the eigenvectors space for Kildal’s Hamiltonian
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’ de...
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| Published in: | Semiconductor Physics Quantum Electronics & Optoelectronics |
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| Date: | 2010 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/118570 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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.
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| ISSN: | 1560-8034 |