Transition Probabilities for Flavor Eigenstates of Non-Hermitian Hamiltonians in the PT-Broken Phase

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 $t\to +\infty$. 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.

21 pages, 1 figure. Final version published in J. Math. Phys

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• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
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Cited by in corpus (3)

• Density Matrix Formalism for PT-Symmetric Non-Hermitian Hamiltonians with the Lindblad Equation
• Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory
• Witnessing criticality in non-Hermitian systems via entropic uncertainty relation