Timescales in many-body fast-neutrino-flavor conversion

Timescales 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 timescales obtained from a linear stability analysis and from the distributions of Loschmidt echo crossing times (intimately connected to dynamical phase transitions in nonequilibrium 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, 𝑡ℒ×, are found to exhibit two distinct timescales that are exponentially separated. The second peak structure at longer times, effectively absent for 𝑁=4, develops with increasing 𝑁. When rescaled in terms of ln⁡𝑡ℒ×, 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 timescale.