Transition Probabilities in the Two-Level Quantum System with PT-Symmetric Non-Hermitian Hamiltonians

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 $ν^{}_μ\to ν^{}_μ$ and $ν^{}_μ\to ν^{}_τ$ 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.

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