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arXiv:2604.22421

Two flavor neutrino oscillations in presence of non-Hermitian dynamics

Kritika Rushiya, Gaurav Hajong, Bhabani Prasad Mandal, Poonam Mehta

quant-phhep-phhep-thSubmitted Apr 24, 2026• Announced Apr 27, 2026• 0 citations
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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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18 Pages, 4 Figures. Comments welcome

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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 G\mathcal{G}G and (b) the density matrix prescription by Brody and Graefe [Phys. Rev. Lett. 109, 230405 (2012)]. For the PT\mathcal{PT}PT-symmetric case, we show that the G\mathcal{G}G metric approach does not work well (probabilities are not conserved) both in PT\mathcal{PT}PT-unbroken as well as PT\mathcal{PT}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 1/21/21/2 thereby indicating non-Markovian behavior.
We show that the phase appearing in neutrino flavor oscillation formulae has a geometric and topological contribution. We identify a topological phase appearing in the two flavor neutrino oscillation formula using Pancharatnam's prescription of quantum collapses between nonorthogonal states. Such quantum collapses appear naturally in the expression for appearance and survival probabilities of neutrinos. Our analysis applies to neutrinos propagating in vacuum or through matter. For the minimal case of two flavors with CPCPCP conservation, our study shows for the first time that there is a geometric interpretation of the neutrino oscillation formulae for the detection probability of neutrino species.
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 νμ → νμ and νμ → ντ 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.
Abstract The burgeoning intersection of particle physics and quantum information science unveils significant connections, particularly in the context of neutrinos–fundamental particles that challenge our understanding of mass, mixing, and coherence at the quantum level. This work investigates the quantum informational aspects of two-flavor neutrino oscillations, treating neutrino flavor change as a dynamic carrier of quantum resources in addition to a fundamental lepton physics phenomenon. Employing realistic experimental parameters from the Daya Bay, KamLAND, and MINOS experiments, we systematically evaluate four key quantum metrics: quantum coherence, entanglement, local quantum Fisher information (LQFI), and Bell non-locality. Our formalism utilizes time-dependent density matrices, incorporating environmental interactions modeled by a correlated dephasing channel to capture both Markovian (memoryless) and non-Markovian (memory-retaining) regimes. In the Markovian regime, coherence and LQFI exhibit exponential decay, with MINOS demonstrating the highest persistence of quantum features attributed to its long baseline (735 km) and high energy range (0.5–50 GeV). KamLAND, with a medium baseline and moderate energy, shows intermediate behavior, while Daya Bay’s short baseline limits the survival of these quantum properties. Notably, Bell non-locality violation in the Markovian regime is exclusive to MINOS under high classical correlation strength, whereas Daya Bay and KamLAND remain within classical bounds. Across both regimes, particularly the non-Markovian where information backflow enhances coherence and entanglement, MINOS consistently emerges as the most robust setup for the preservation of quantum information.
In this report, we first briefly summarize Hermitian quantum mechanics before moving on to the non-Hermitian case. We then review PT-symmetric quantum mechanics with a focus on finite-dimensional systems, and include a novel generalization of a perturbative calculation of the C-operator. After briefly covering the basics of neutrino oscillations, we perturbatively examine a PT-symmetric addition to the neutrino oscillation Hamiltonian. We examine the effects of the addition with two different definitions of transition probabilities. However, probability is not conserved to first order with either definition. Further, we note that the effect of the chosen perturbation is to shift the transition probabilities by some phase, and to change the amplitudes of the transition probabilities.
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