On the pseudo-Hermitian nondiagonalizable Hamiltonians
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Publication:4833125
DOI10.1063/1.1609031zbMATH Open1062.81049arXivquant-ph/0211161OpenAlexW2009568592MaRDI QIDQ4833125
Author name not available (Why is that?)
Publication date: 14 December 2004
Published in: (Search for Journal in Brave)
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 . Some consequences and applications are briefly discussed.
Full work available at URL: https://arxiv.org/abs/quant-ph/0211161
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