Time Scales in Many-Body Fast Neutrino Flavor Conversion
arxiv(2023)
摘要
Time scales associated with many-body fast neutrino flavor conversions in
core-collapse supernova are explored in the context of an effective two-flavor
model with axial symmetry. We present a preliminary study of time scales
obtained from a linear stability analysis and from the distributions of
Loschmidt echo crossing times (intimately connected to dynamical phase
transitions in non-equilibrium systems) determined by time evolution with the
exact many-body Hamiltonian. Starting from a tensor-product initial state
describing systems of N neutrinos, with N/2 electron-type and N/2
heavy-type, with uniform angular distributions, the Loschmidt echo crossing
times, t_ℒ_×, are found to exhibit two distinct time
scales that are exponentially separated. The second peak structure at longer
times, effectively absent for N=4, develops with increasing N. When
re-scaled in terms of log t_ℒ_×, the distributions are
found to become increasingly well described by the sum of two stable
distributions. The distribution of Loschmidt echo crossing times differs
somewhat from the results of the (numerical) linear stability analysis, which
exhibits a peak at finite frequency and a second peak consistent with zero
frequency. The exact analysis suggests that the zero-frequency instability
manifests itself as a modest flavor-conversion time scale.
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