Decoherence from quantum spacetime noise: An open-systems framework with application to neutrino oscillations

Abstract

We present a general open-quantum-systems framework to model decoherence induced by stochastic Planck-scale fluctuations of spacetime, focusing on the kappa-Minkowski noncommutative geometry as a representative quantum-gravity scenario. Treating the deformation parameter as Gaussian white noise, we derive a Lindblad-type master equation applicable to arbitrary quantum systems and obtain a distinctive inverse-energy scaling of the decoherence rate, Gamma proportional to E^{-4}. As an illustrative example, we analyze a three-level system motivated by neutrino flavor oscillations and derive closed-form expressions for survival and transition probabilities with spacetime-induced damping. The E^{-4} scaling contrasts sharply with the positive power laws often invoked in quantum-gravity phenomenology and predicts negligible decoherence for high-energy neutrinos consistent with IceCube observations, while implying that the strongest effects arise in the extreme low-energy regime. In this context, the sub-eV-scale energies characteristic of the cosmic neutrino background provide a natural infrared benchmark for illustrating the enhanced sensitivity to quantum-spacetime fluctuations. Our results establish a unified formalism connecting quantum-information methods, open-system dynamics, and quantum-spacetime phenomenology, thereby offering a framework for exploring potential signatures of Planck-scale physics in future low-energy neutrino studies.

Figures (7)

• Figure 1: Coherence length $l_{\mathrm{ch}}^{ij}$ as a function of the parameter $\chi$ at $E = 10^{-6}\,\mathrm{eV}$. The three curves correspond to the three independent neutrino mass-squared differences: $l_{\mathrm{ch}}^{21}$ (blue), $l_{\mathrm{ch}}^{31}$ (red), and $l_{\mathrm{ch}}^{32}$ (green). Throughout the text, we use $l_{\mathrm{ch}}$ to denote the coherence length generically and $l_{\mathrm{ch}}^{ij}$ when referring to a specific mass-eigenstate pair $(i,j)$.
• Figure 2: Decoherence effect on standard survival and transition probabilities of C$\nu$B neutrinos for $\nu_{e} \rightarrow \nu_{e}$ (depicted in sky blue) and $\nu_{e} \rightarrow \nu_{\mu}$ (depicted in green), are plotted as a function of path length $L$ (in km) at a fixed neutrino energy $E = 10^{-6} \, \text{eV}$.
• Figure 3: Standard C$\nu$B neutrino survival probability for $\nu_{e} \rightarrow \nu_{e}$ (\ref{['l']}) plotted as a function of Energy $E$ (measured in eV) for a fixed $\chi = 10^{62}$ and path length $L \sim 10^{14} \, \text{km}$.
• Figure 4: Standard C$\nu$B neutrino transition probability for $\nu_{e} \rightarrow \nu_{\mu}$ (\ref{['l']}) plotted as a function of Energy $E$ (measured in eV) for a fixed $\chi = 10^{62}$ and path length $L \sim 10^{14} \, \text{km}$.
• Figure 5: Decoherence effect on standard survival and transition probabilities of C$\nu$B neutrinos for $\nu_{e} \rightarrow \nu_{e}$ (depicted in sky blue) and $\nu_{e} \rightarrow \nu_{\mu}$ (depicted in green), are plotted as a function of path length $L$ (in km) at a fixed neutrino energy $E = 10^{-6} \, \text{eV}$.