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

Tommy Ohlsson, Shun Zhou

Jun 27, 2019
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Received Date: 13th June 19

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 $\nu^{}_\mu \to \nu^{}_\mu$ and $\nu^{}_\mu \to \nu^{}_\tau$ 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.

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This is an abstract of a preprint hosted on an independent third party site. It has not been peer reviewed but is currently under consideration at Nature Communications.

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