Transition probabilities in the two-level quantum system with PT-symmetric non-Hermitian Hamiltonians

摘要

We investigate how to define in a consistent way the probabilities of the transitions between the "flavor" states of the two-level quantum system, which is described by a non-Hermitian but parity and time-reversal (PT) symmetric Hamiltonian. Explicit calculations are carried out to demonstrate the conservation of probability if a proper definition of the final state is adopted. Finally, this formalism is applied to two-flavor neutrino oscillations nu(mu) -> nu(mu) and nu(mu) -> nu(tau) in vacuum, where the exact PT symmetry requires the vacuum mixing angle to be maximal, which is compatible with current neutrino oscillation experiments. A possible generalization to the three-flavor case is briefly discussed.