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Transition probabilities for flavor eigenstates of non-Hermitian Hamiltonians in the PT-broken phase.
- Source :
-
Journal of Mathematical Physics . Apr2021, Vol. 62 Issue 4, p1-14. 14p. - Publication Year :
- 2021
-
Abstract
- We investigate the transition probabilities for the "flavor" eigenstates in the two-level quantum system, which is described by a non-Hermitian Hamiltonian with the parity and time-reversal (PT) symmetry. Particularly, we concentrate on the so-called PT-broken phase, where two eigenvalues of the non-Hermitian Hamiltonian turn out to be a complex-conjugate pair. In this case, we find that the transition probabilities will be unbounded in the limit of infinite time t → +∞. However, after performing a connection between a non-Hermitian system, which exhibits passive PT symmetry and global decay, and the neutral-meson system in particle physics, we observe that the diverging behavior of the transition probabilities is actually applicable to the gauge-transformed neutral-meson states, whereas the transition probabilities for physical states are exponentially suppressed by the global decay. We also present a brief review on the situation at the so-called exceptional point, where both the eigenvalues and eigenvectors of the Hamiltonian coalesce. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 62
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 150105686
- Full Text :
- https://doi.org/10.1063/5.0012050