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arXiv:2312.16212 · Physical Review C

Timescales in many-body fast-neutrino-flavor conversion

Ramya Bhaskar, Alessandro Roggero, Martin J. Savage A

Published Oct 1, 2024• 8 citations
arXivHTMLPDF

Abstract

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, ${t}_{{\mathcal{L}}_{\ifmmode\times\else\texttimes\fi{}}}$, 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 $ln{t}_{{\mathcal{L}}_{\ifmmode\times\else\texttimes\fi{}}}$, 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.

DOI
10.1103/physrevc.110.045801

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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 NNN neutrinos, with N/2N/2N/2 electron type and N/2N/2N/2 heavy type, with uniform angular distributions, the Loschmidt echo crossing times, tL\ifmmode×\else\texttimes\fi{t}_{{\mathcal{L}}_{\ifmmode\times\else\texttimes\fi{}}}tL\ifmmode×\else\texttimes\fi​​, are found to exhibit two distinct timescales that are exponentially separated. The second peak structure at longer times, effectively absent for N=4N=4N=4, develops with increasing NNN. When rescaled in terms of lntL\ifmmode×\else\texttimes\filn{t}_{{\mathcal{L}}_{\ifmmode\times\else\texttimes\fi{}}}lntL\ifmmode×\else\texttimes\fi​​, 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.
We study neutrino flavor evolution in the quantum many-body approach using the full neutrino-neutrino Hamiltonian, including the usually neglected terms that mediate nonforward scattering processes. Working in the occupation number representation with plane waves as single-particle states, we explore the time evolution of simple initial states with up to N = 10 neutrinos. We discuss the time evolution of the Loschmidt echo, one body flavor and kinetic observables, and the one-body entanglement entropy. For the small systems considered, we observe “thermalization” of both flavor and momentum degrees of freedom on comparable time scales, with results converging towards expectation values computed within a microcanonical ensemble. We also observe that the inclusion of nonforward processes generates a faster flavor evolution compared to the one induced by the truncated (forward) Hamiltonian. Published by the American Physical Society 2024
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 timescales much shorter 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.
Collective neutrino flavor oscillations are of primary importance in understanding the dynamic evolution of core-collapse supernovae and subsequent terrestrial detection, but also among the most challenging aspects of numerical simulations. This situation is complicated by the quantum many-body nature of the problem due to neutrino-neutrino interactions which demands a quantum treatment. An additional complication is the presence of three flavors, which often is approximated by the electron flavor and a heavy lepton flavor. In this work, we provide both qubit and qutrit encodings for all three flavors, and develop optimized quantum circuits for the time evolution and analyze the Trotter error. We conclude our study with a hardware experiment of a system of two neutrinos with superconducting hardware: the IBM Torino device for qubits and AQT device for qutrits. We find that error mitigation greatly helps in obtaining a signal consistent with simulations. While hardware results are comparable at this stage, we expect the qutrit setup to be more convenient for large-scale simulations since it does not suffer from probability leakage into nonphsycial qubit space, unlike the qubit setup.
Dense-neutrino flavor evolution is a quantum many-body problem whose fully correlated treatment becomes rapidly more expensive with increasing particle number and spatial structure. We develop a \texttt{QCNO} quantum simulation code that maps a inhomogeneous forward-scattering neutrino Hamiltonian with advection and finite-range interactions to TEBD2 product-formula quantum circuits, and connects ideal many-body simulation, backend-aware execution, and fault-tolerant resource estimation within the same physical model. We reproduce the exact many-body evolution of the suppressed mean-field-like transverse fast flavor instability through N=30N=30N=30 and show that even a single open-boundary interaction generates Rënyi entanglement and non-stabilizer magic, although noisy backends still produce polarization RMSEs of order 0.10.10.1--0.30.30.3. The restricted active interaction graph of this problem allows us to estimate the circuit depth and TTT gate cost through N=50N=50N=50 for both NISQ and fault-tolerant approaches. The measured TEBD2 error in our fiducial ideal simulation of order 10−310^{-3}10−3 motivates a synthesis tolerance εsyn∼10−7\varepsilon_{\rm syn}\sim10^{-7}εsyn​∼10−7, corresponding to about 707070 TTT gates per RZR_ZRZ​ rotation. The generated circuit contains 1.4×1041.4\times10^41.4×104 TTT gates per qubit for open boundaries (twice that for closed boundaries), requiring an application-level logical-TTT error target of order 10−710^{-7}10−7 for early fault-tolerant architectures.
Neutrino flavor evolution in dense astrophysical environments is inherently nonlinear and sensitive to many-body (MB) quantum effects beyond the mean-field (MF) approximation. Existing MB studies are constrained by small system sizes, closed boundaries, and highly idealized symmetry assumptions. We present a unified tensor-network framework that enables simulations of inhomogeneous and anisotropic flavor evolution under conditions relevant to core-collapse supernovae and neutron-star mergers. Within this framework, we examine the effects of inhomogeneity, boundary conditions, and convergence with resolution for multiple neutrino distributions, allowing direct comparison of these setups under one consistent formulation. In our simulations, many-body systems equilibrate earlier than their mean-field counterparts while approaching similar final flavor states. Enlarging the interaction region allows open boundaries to reproduce closed-system behavior, but only when the beams begin superimposed and interact continuously. By contrast, initially separated configurations develop entanglement more slowly, interact over longer times, and equilibrate to a flavor content that differs from that obtained from initially superimposed calculations.
If a system of flavor-oscillating neutrinos is at high enough densities that neutrino-neutrino coherent forward scatterings are non-negligible, the system becomes a time-dependent many-body problem. An important and open question is whether the flavor evolution is sufficiently described by a mean-field approach or can be strongly affected by correlations arising from two-body interactions in the neutrino Hamiltonian, as measured by nontrivial quantum entanglement. Numerical computations of the time evolution of many-body quantum systems are challenging because the size of the Hilbert space scales exponentially with the number of particles NNN in the system. Thus, it is important to investigate approximate but beyond-mean-field numerical treatments at larger values of NNN. Here we investigate the efficacy of tensor network methods to calculate the time evolution of interacting neutrinos at larger values of NNN than are possible with conventional methods. In particular, we introduce the use of time-dependent variational principle methods to address the long-range (in momentum space) interactions of the neutrino Hamiltonian when including many distinct vacuum oscillation frequencies. We also define new error measures based upon the instantaneously conserved charge operators known for this Hamiltonian to determine validity of large-NNN tensor network calculations.