Transition probabilities for flavor eigenstates of non-Hermitian Hamiltonians in the PT-broken phase

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 -> +infinity. 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.

Automated summary

The study focuses on the transition probabilities of flavor eigenstates in a two-level quantum system described by a non-Hermitian Hamiltonian with PT symmetry, particularly looking at the PT-broken phase and exceptional points. The investigation reveals attributes of unbounded transition probabilities and global decay effects in the system.