Two flavor neutrino oscillations in presence of non-Hermitian dynamics

• URL: http://arxiv.org/abs/2604.22421v1
• Date: Fri, 24 Apr 2026 10:29:21 GMT
• Title: Two flavor neutrino oscillations in presence of non-Hermitian dynamics
• Abstract summary: We develop a consistent framework for studying two flavor neutrino oscillations in presence of non-Hermitian dynamics.<n>We consider two approaches : (a) bi-orthonormal inner product defined by a positive-definite metric operator $mathcalG$ and (b) the density matrix prescription by Brody and Graefe.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a consistent mathematical framework for studying two flavor neutrino oscillations in presence of non-Hermitian dynamics. We consider two approaches : (a) bi-orthonormal inner product defined by a positive-definite metric operator $\mathcal{G}$ and (b) the density matrix prescription by Brody and Graefe [Phys. Rev. Lett. 109, 230405 (2012)]. For the $\mathcal{PT}$-symmetric case, we show that the $\mathcal{G}$ metric approach does not work well (probabilities are not conserved) both in $\mathcal{PT}$-unbroken as well as $\mathcal{PT}$-broken regime. Hence, we adopt the density matrix prescription by Brody and Graefe which is a positive semi-definite map. In the density matrix prescription, we note that probability in the steady state limit is not necessarily $1/2$ thereby indicating non-Markovian behavior.

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