Abstract
Collective neutrino oscillations play a crucial role in transporting lepton flavor in astrophysical settings, such as supernovae, where the neutrino density is large. In this regime, neutrino-neutrino interactions are important and simulations in the mean-field approximation show evidence for collective oscillations occurring at time scales much larger than those associated with vacuum oscillations. In this work, we study the out-of-equilibrium dynamics of a corresponding spin model using Matrix Product States and show how collective bipolar oscillations can be triggered by many-body correlations if appropriate initial conditions are present. We find entanglement entropies scaling at most logarithmically in the system size suggesting that classical tensor network methods could be efficient in describing collective neutrino dynamics more generally. These observation provide a clear path forward, not only to increase the accuracy of current simulations, but also to elucidate the mechanism behind collective flavor oscillations without resorting to the mean field approximation.
Highlights
Neutrinos play a pivotal role in extreme astrophysical events like core-collapse supernovae and neutron star mergers, where they are responsible for both reinvigorating a stalled shock wave and controlling the conditions for nucleosynthesis in the ejected material [1,2,3,4]
In these environments with a large neutrino density ρν, neutrino flavor evolution is substantially modified by neutrinoneutrino scattering processes which can lead to self-sustained collective flavor oscillations [5,6,7,8,9,10,11,12,13,14]
Since neutrinos in supernovae are emitted with fluxes and spectra that are strongly flavor dependent [2], the presence of collective flavor oscillations could lead to important effects [15,16,17]
Summary
Neutrinos play a pivotal role in extreme astrophysical events like core-collapse supernovae and neutron star mergers, where they are responsible for both reinvigorating a stalled shock wave and controlling the conditions for nucleosynthesis in the ejected material [1,2,3,4]. We study the model equation (1) for large systems with up to N 1⁄4 128 neutrino amplitudes in a simplifying limit and show how coherent flavor oscillations at the fast scale τF can occur even without vacuum mixing These first-principle simulations, obtained without resorting to the mean-field approximation or exploiting the symmetries present in the model, are made possible by using a matrix product state (MPS) [38] representation of the many-body neutrino state. This technique (described in detail in Sec. III below) allows for efficient simulation of the real-time dynamics in situations where the entanglement entropy (which provides a measure of quantum correlations) is relatively small and growing only as the logarithm of the system size. The Appendices contain a direct comparison with the mean-field approach and a discussion of the numerical accuracy of our implementation
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