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

Abstract

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.

23 pages, 1 figure. Final version published in J. Math. Phys

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• Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)$\mathcal{P}\mathcal{T}-$symmetric systems
• Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory
• Transition Probabilities for Flavor Eigenstates of Non-Hermitian Hamiltonians in the PT-Broken Phase
• Non-Hermiticity: a new paradigm for model building in particle physics
• Three perspectives on entropy dynamics in a non-Hermitian two-state system
• Witnessing criticality in non-Hermitian systems via entropic uncertainty relation
• Quantum Simulations of the Non-Unitary Time Evolution and Applications to Neutral-Kaon Oscillations
• Stronger sum uncertainty relations for non-Hermitian operators
• Decomposition of a system in pseudo-Hermitian quantum mechanics
• Oscillation probabilities for a PT-symmetric non-Hermitian two-state system