Two flavor neutrino oscillations in presence of non-Hermitian dynamics
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914504643706880 |
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| author | Rushiya, Kritika Hajong, Gaurav Mandal, Bhabani Prasad Mehta, Poonam |
| author_facet | Rushiya, Kritika Hajong, Gaurav Mandal, Bhabani Prasad Mehta, Poonam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22421 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two flavor neutrino oscillations in presence of non-Hermitian dynamics Rushiya, Kritika Hajong, Gaurav Mandal, Bhabani Prasad Mehta, Poonam Quantum Physics High Energy Physics - Phenomenology High Energy Physics - Theory 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. |
| title | Two flavor neutrino oscillations in presence of non-Hermitian dynamics |
| topic | Quantum Physics High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.22421 |