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arXiv:2404.16690 · Physical review. D/Physical review. D.

Neutrino many-body flavor evolution: The full Hamiltonian

Vincenzo Cirigliano, Srimoyee Sen, Yukari Yamauchi

Published Dec 20, 2024• 16 citations
arXivHTMLPDF

Abstract

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

DOI
10.1103/physrevd.110.123028

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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
Dense neutrino gases form in extreme astrophysical sites, and the flavor content of the neutrinos likely has an important impact on the subsequent dynamical evolution of their environment. Through coherent forward scattering among neutrinos, the flavor content of the gas evolves under a time-dependent potential which can be modeled in a quantum many-body formalism as an all-to-all coupled spin-spin interaction. This two-body potential generically introduces entanglement and greatly complicates the study of these systems. In this work we study the evolution of the quantum many-body problem as well as the typically employed mean-field approximation to it for a small number of neutrinos (N=16N = 16N=16). We consider randomly chosen one- and two-body couplings in the Hamiltonian, and the resulting evolution of several initial product states. We subsequently compare many-body and mean-field predictions for one-body observables, and we consider one- and two-body entanglement to assess under what conditions the many-body and mean-field predictions are likely to disagree. Except for a special category of prototypical initial conditions, we find that the typically employed mean-field approximation is insufficient to capture the evolution of one-body operators in the systems we consider. We also observe a loss of coherence in one- and two-body trace-reduced subsystems which suggests that the evolution may be well approximated as a classical mixture of separable states.
Neutrino evolution in dense astrophysical environments is typically described either within a quantum kinetic framework, which neglects the build-up of multi-body correlations, or through simplified many-body calculations that allow significant entanglement to develop. In this work, we compare these two approaches in a simple neutrino-gas configuration, with particular emphasis on the role of non-forward scattering processes. These effects are incorporated either through a collision term in the kinetic description, or by considering the full neutrino-neutrino many-body Hamiltonian. We highlight differences between the two descriptions in both their characteristic timescales and asymptotic behavior. Motivated by the natural suitability of quantum computing for many-body calculations, we further investigate the non-classicality of neutrino evolution, discussing Trotter error scaling, along with the associated costs of constructing quantum circuits in terms of entangling gates and non-Clifford gates. We find that the resources needed for neutrino many-body evolution are on the low end of typical high-energy physics problems and on the mid to high end with respect to quantum chemistry problems. For the full Hamiltonian, resource requirements increase relative to the truncated version. We emphasize the importance of efficient fermion-to-qubit encodings, which are essential for reducing the substantial computational resources required for such simulations.
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, ${t}_{{\mathcal{L}}_{\ifmmode\times\else\texttimes\fi{}}}$, are found to exhibit two distinct timescales that are exponentially separated. The second peak structure at longer times, effectively absent for N=4N=4N=4, develops with increasing NNN. 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.
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.
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.
The flavor evolution of neutrinos in environments with large neutrino number densities is an open problem at the nexus of astrophysics and neutrino flavor physics. Among the many unanswered questions pertaining to this problem, it remains to be determined whether neutrino-neutrino coherent scattering can give rise to nontrivial quantum entanglement among neutrinos, and whether this can affect the flavor evolution in a meaningful way. To gain further insight into this question, here we study a simple system of two interacting neutrino beams and obtain the exact phase space explored by this system using the Husimi quasiprobability distribution. We observe that the entanglement induced by the coupling leads to strong delocalization in phase-space with largely non-Gaussian quantum fluctuations. The link between the neutrino entanglement and quantum fluctuations is illustrated using the one- and two-neutrino entropy. In addition, we propose an approximate phase-space method to describe the interacting neutrinos problem, where the exact evolution is replaced by a set of independent mean-field evolutions with a statistical sampling of the initial conditions. The phase-space approach provides a simple and accurate method to describe the gross features of the neutrino entanglement problem. Applications are shown using time-independent and time-dependent Hamiltonians in the nonadiabatic regime.