dorsal/arxiv
View SchemaOn the pseudo-Hermitian nondiagonalizable Hamiltonians
| Authors | G. Scolarici, L. Solombrino |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0211161 |
| URL | https://arxiv.org/abs/quant-ph/0211161 |
| DOI | 10.1063/1.1609031 |
Abstract
We consider a class of (possibly nondiagonalizable) pseudo-Hermitian operators with discrete spectrum, showing that in no case (unless they are diagonalizable and have a real spectrum) they are Hermitian with respect to a semidefinite inner product, and that the pseudo-Hermiticity property is equivalent to the existence of an antilinear involutory symmetry. Moreover, we show that a typical degeneracy of the real eigenvalues (which reduces to the well known Kramers degeneracy in the Hermitian case) occurs whenever a fermionic (possibly nondiagonalizable) pseudo-Hermitian Hamiltonian admits an antilinear symmetry like the time-reversal operator $T$. Some consequences and applications are briefly discussed.
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"abstract": "We consider a class of (possibly nondiagonalizable) pseudo-Hermitian\noperators with discrete spectrum, showing that in no case (unless they are\ndiagonalizable and have a real spectrum) they are Hermitian with respect to a\nsemidefinite inner product, and that the pseudo-Hermiticity property is\nequivalent to the existence of an antilinear involutory symmetry. Moreover, we\nshow that a typical degeneracy of the real eigenvalues (which reduces to the\nwell known Kramers degeneracy in the Hermitian case) occurs whenever a\nfermionic (possibly nondiagonalizable) pseudo-Hermitian Hamiltonian admits an\nantilinear symmetry like the time-reversal operator $T$. Some consequences and\napplications are briefly discussed.",
"arxiv_id": "quant-ph/0211161",
"authors": [
"G. Scolarici",
"L. Solombrino"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1609031",
"title": "On the pseudo-Hermitian nondiagonalizable Hamiltonians",
"url": "https://arxiv.org/abs/quant-ph/0211161"
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