Two flavor neutrino oscillations in presence of non-Hermitian dynamics
Kritika Rushiya, Gaurav Hajong, Bhabani Prasad Mandal, Poonam Mehta
TLDR
This paper develops a consistent framework for two-flavor neutrino oscillations with non-Hermitian dynamics, finding the density matrix approach superior.
Key contributions
- Developed a mathematical framework for two-flavor neutrino oscillations under non-Hermitian dynamics.
- Compared bi-orthonormal inner product (G-metric) and density matrix approaches.
- Found the G-metric approach fails for PT-symmetric cases, as probabilities are not conserved.
- Adopted the density matrix method, revealing non-Markovian behavior in steady-state probabilities.
Why it matters
This paper provides a robust mathematical framework for studying neutrino oscillations in non-Hermitian systems, which are increasingly relevant in quantum mechanics. By identifying flaws in a common approach and successfully applying an alternative, it offers a more accurate method. This work deepens our understanding of fundamental particle behavior.
Original 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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