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

Tommy Ohlsson, Shun Zhou

Published 2020-02-13Version 1

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 $t \to +\infty$. After making a connection between the PT-broken phase and the neutral-meson system in particle physics, we observe that the infinite-time behavior of the transition probabilities can be attributed to the negative decay width of one eigenstate of the non-Hermitian Hamiltonian. We also present some brief remarks on the situation at the so-called exceptional point, where both the eigenvalues and eigenvectors of the Hamiltonian coalesce.