Two-beam Multiparticle Many-body simulations of Inhomogeneous FFI

TL;DR

The paper addresses the challenge of modeling nonlinear neutrino flavor evolution in dense astrophysical environments where many-body correlations exceed mean-field descriptions. It introduces a tensor-network framework based on matrix-product states to simulate two-beam, two-flavor fast flavor instabilities with spatial inhomogeneity, angular structure, and flexible boundary conditions, using a Hamiltonian $H[Z(t)]=H_{vac}+H_{SI}[Z(t)]$ and TEBD2 time evolution. The main findings show that many-body entanglement drives decoherence that suppresses FFIs and accelerates flavor equilibration relative to MF, with dynamics profoundly affected by inhomogeneity, boundary conditions, initial configurations, and bond-dimension convergence. This approach provides a scalable, physically faithful platform for benchmarking MB neutrino dynamics and informs astrophysical flavor transport and nucleosynthesis in core-collapse supernovae and neutron-star mergers, with clear pathways to extend to higher dimensions, multiple beams, and non-forward scattering terms. Overall, the work establishes a robust framework for systematically exploring MB effects in dense neutrino systems and for validating quantum simulators targeting entanglement-driven neutrino flavor dynamics.

Abstract

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.

Figures (14)

• Figure 1: Homogeneous two-flavor two-beam fast flavor instability prepared in an initially half muon and half electron flavor state. The upper panel shows occupation number of electron neutrinos in a mean-field (solid) vs full many-body picture (dashed). The lower panel shows the quantum coherence of electron and muon flavor states showing that the instability grows exponentially for the mean field case but does not for many-body. This growth rate of the flavor coherence matches the prediction from linear stability theory well. In contrast, many-body entanglement could erase homogeneous FFI.
• Figure 2: Inhomogeneous two-flavor, two-beam 20-particle system initially prepared with half muon and half electron neutrinos. Top panel: average of the density matrix component $\rho_{ee}$ over the first half of the sites. Bottom panel: quantum flavor coherence. Solid curves show MF results from setting BD=1 and dashed curves show MB results with full bond dimension. Black curves show results from using the inhomogeneous shape function and blue cuves show results from setting $\mathcal{S}=1$. Top extended panel: long-duration MF results using the Emu code using $10^5$ particles on a periodic domain of size $10^3$ cm. Inhomogeneity allows rapidly settling to an equilibrium without constant or periodic behavior for both the MF and MB simulations.
• Figure 3: Time evolution of the polarization vector components including their averages (solid constant lines) and the spread between their minimum and maximum values (shaded regions) for an all-sites 20-particle inhomogeneous system. Upper panel: Many-body simulation at infinite bond dimension. Lower panel: Mean-field simulation with bond dimension $=1$. In the many-body case, no exponential growth of transverse components is observed; instead, $\langle P_z \rangle$ undergoes sustained oscillations about zero, reflecting entanglement-driven decoherence. In contrast, the mean-field case shows each beam polarized fully in $\pm1 \langle P_z \rangle$ showed with a fill region between the poles until a sharp rise in $P_x$ and $P_y$ at $t \sim 170$ ps, signaling the onset of flavor conversion through collective coherence. In both cases, the polarization averages of all components remain centered near zero, preserving total spin.
• Figure 4: Evolution of the polarization vector components averaged over sites in the beam moving in the $+\hat{z}$ direction in terms of time scaled by $\mu=\sqrt{2}G_F n$. In the Symmetric simulations, there are seven sites in each neutrino beam. In Asymmetric simulations, there are seven sites in the $\nu_\mu$ beam and 14 sites in the $\nu_e$ beam. The many-body (MB) asymmetric system depolarizes faster than its symmetric counterpart and reaches the same asymptotic state as the mean-field (MF) simulations ($\langle P_z \rangle \approx 0.5$) significantly earlier. Fast flavor instability (FFI) also grows more rapidly under asymmetric conditions compared to the symmetric case.
• Figure 5: Time evolution for a 20-particle system under varying bond dimensions. Upper panel:$z$ component of the polarization vector at the first site. Lower panel: Von Neumann entanglement entropy averaged over all sites (solid curves) and the spread between the minimum and maximum values (shaded areas). Entanglement entropy saturates with average values reaching $S\approx \ln 2$, close to the expected thermal limit for BD = $\infty$. At low BD, the entropy spread across sites is broader and the average entropy remains lower. A sufficiently large BD is essential for capturing full many-body coherence and flavor dynamics.