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  • Open Access

Three-flavor neutrino oscillations using the phase space approach

Mariane Mangin-Brinet*

Angel Bauge and Denis Lacroix†

  • *Contact author: mariane@lpsc.in2p3.fr
  • †Contact author: lacroix@ijclab.in2p3.fr
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Phys. Rev. D 113, 036026 – Published 26 February, 2026

DOI: https://doi.org/10.1103/yr2g-1g2g

Abstract

The phase-space approximation (PSA) approach, originally applied in [Phys. Rev. D 106, 123006 (2022)] to describe neutrino oscillations from a dense astrophysical source such as a core-collapse supernova in the two-flavor limit, is extended here to describe the more realistic case where neutrinos can oscillate between three different flavors. The approach is successfully validated against the exact solutions up to eight neutrinos. In all cases where the exact solution is feasible, the PSA provides excellent reproduction of the neutrino oscillation dynamics. By replacing the full problem with a set of simple mean-field equations, the PSA offers a versatile, predictive, and easily parallelizable approach for tackling three-flavor problems. This enables the simulation of large-scale neutrino oscillations, as illustrated here with simulations involving up to 300 neutrinos. Even if direct comparison to exact solutions is only feasible for small systems (up to eight neutrinos), where PSA shows excellent agreement, its applicability in the large-N regime appears promising, although a full quantitative validation remains beyond current computational capabilities. Additionally, the method also provides insight into the system’s equilibration properties.

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References (57)

  1. G. M. Fuller, R. W. Mayle, J. R. Wilson, and D. N. Schramm, Resonant neutrino oscillations and stellar collapse, Astrophys. J. 322, 795 (1987).
  2. D. Notzold and G. Raffelt, Neutrino dispersion at finite temperature and density, Nucl. Phys. B307, 924 (1988).
  3. G. Sigl and G. Raffelt, General kinetic description of relativistic mixed neutrinos, Nucl. Phys. B406, 423 (1993).
  4. H. Duan, G. M. Fuller, J. Carlson, and Y.-Z. Qian, Simulation of coherent nonlinear neutrino flavor transformation in the supernova environment: Correlated neutrino trajectories, Phys. Rev. D 74, 105014 (2006).
  5. A. B. Balantekin and Y. Pehlivan, Neutrino–neutrino interactions and flavor mixing in dense matter, J. Phys. G 34, 47 (2007).
  6. M. Cristina Volpe, Neutrinos from dense environments: Flavor mechanisms, theoretical approaches, observations, and new directions, Rev. Mod. Phys. 96, 025004 (2024).
  7. Y. Pehlivan, A. B. Balantekin, Toshitaka Kajino, and Takashi Yoshida, Invariants of collective neutrino oscillations, Phys. Rev. D 84, 065008 (2011).
  8. Savas Birol, Y. Pehlivan, A. B. Balantekin, and T. Kajino, Neutrino spectral split in the exact many-body formalism, Phys. Rev. D 98, 083002 (2018).
  9. Amol V. Patwardhan, Michael J. Cervia, and A. Baha Balantekin, Eigenvalues and eigenstates of the many-body collective neutrino oscillation problem, Phys. Rev. D 99, 123013 (2019).
  10. Ermal Rrapaj, Exact solution of multi-angle quantum many-body collective neutrino flavor oscillations, Phys. Rev. C 101, 065805 (2020).
  11. Michael J. Cervia, Amol V. Patwardhan, A. B. Balantekin, S. N. Coppersmith, and Calvin W. Johnson, Entanglement and collective flavor oscillations in a dense neutrino gas, Phys. Rev. D 100, 083001 (2019).
  12. Amol V. Patwardhan, Michael J. Cervia, and A. B. Balantekin, Spectral splits and entanglement entropy in collective neutrino oscillations, Phys. Rev. D 104, 123035 (2021).
  13. Joshua D. Martin, A. Roggero, Huaiyu Duan, J. Carlson, and V. Cirigliano, Classical and quantum evolution in a simple coherent neutrino problem, Phys. Rev. D 105, 083020 (2022).
  14. Alessandro Roggero, Entanglement and many-body effects in collective neutrino oscillations, Phys. Rev. D 104, 103016 (2021).
  15. Michael J. Cervia, Pooja Siwach, Amol V. Patwardhan, A. B. Balantekin, S. N. Coppersmith, and Calvin W. Johnson, Collective neutrino oscillations with tensor networks using a time-dependent variational principle, Phys. Rev. D 105, 123025 (2022).
  16. A. B. Balantekin, Quantum entanglement and neutrino many-body systems, J. Phys. Conf. Ser. 2191, 012004 (2022).
  17. Zewei Xiong, Many-body effects of collective neutrino oscillations, Phys. Rev. D 105, 103002 (2022).
  18. Denis Lacroix, A. B. Balantekin, Michael J. Cervia, Amol V. Patwardhan, and Pooja Siwach, Role of non-Gaussian quantum fluctuations in neutrino entanglement, Phys. Rev. D 106, 123006 (2022).
  19. Alessandro Roggero, Ermal Rrapaj, and Zewei Xiong, Entanglement and correlations in fast collective neutrino flavor oscillations, Phys. Rev. D 106, 043022 (2022).
  20. Joshua D. Martin, A. Roggero, Huaiyu Duan, and J. Carlson, Many-body neutrino flavor entanglement in a simple dynamic model, arXiv:2301.07049.
  21. Joshua D. Martin, Duff Neill, A. Roggero, Huaiyu Duan, and J. Carlson, Equilibration of quantum many-body fast neutrino flavor oscillations, Phys. Rev. D 108, 123010 (2023).
  22. Ramya Bhaskar, Alessandro Roggero, and Martin J. Savage, Time scales in many-body fast neutrino flavor conversion, Phys. Rev. C 110, 045801 (2024).
  23. Denis Lacroix, Angel Bauge, Bulent Yilmaz, Mariane Mangin-Brinet, Alessandro Roggero, and A. Baha Balantekin, Phase-space methods for neutrino oscillations: Extension to multi-beams, Phys. Rev. D 110, 103027 (2024).
  24. Benjamin Hall, Alessandro Roggero, Alessandro Baroni, and Joseph Carlson, Simulation of collective neutrino oscillations on a quantum computer, Phys. Rev. D 104, 063009 (2021).
  25. Kübra Yeter-Aydeniz, Shikha Bangar, George Siopsis, and Raphael C. Pooser, Collective neutrino oscillations on a quantum computer, Quantum Inf. Process. 21, 84 (2022).
  26. Abhishek Kumar Jha and Akshay Chatla, Quantum studies of neutrinos on IBMQ processors, Eur. Phys. J. Spec. Top. 231, 141 (2022).
  27. Marc Illa and Martin J. Savage, Multi-neutrino entanglement and correlations in dense neutrino systems, Phys. Rev. Lett. 130, 221003 (2023).
  28. Marc Illa and Martin J. Savage, Basic elements for simulations of standard model physics with quantum annealers: Multigrid and clock states, Phys. Rev. A 106, 052605 (2022).
  29. Valentina Amitrano, Alessandro Roggero, Piero Luchi, Francesco Turro, Luca Vespucci, and Francesco Pederiva, Trapped-ion quantum simulation of collective neutrino oscillations, Phys. Rev. D 107, 023007 (2023).
  30. P. Siwach, K. Harrison, and A. B. Balantekin, Collective neutrino oscillations on a quantum computer with hybrid quantum-classical algorithm, Phys. Rev. D 108, 083039 (2023).
  31. Francesco Turro, Ivan A. Chernyshev, Ramya Bhaskar, and Marc Illa, Qutrit and qubit circuits for three-flavor collective neutrino oscillations, Phys. Rev. D 111, 043038 (2025).
  32. I. A. Chernyshev, Three-flavor collective neutrino oscillation simulations on a qubit quantum annealer, Phys. Rev. D 111, 043017 (2025).
  33. Luca Spagnoli, , , , , , , , , , , and , Collective neutrino oscillations in three flavors on qubit and qutrit processors, Phys. Rev. D 111, 103054 (2025).
  34. Pooja Siwach, Anna M. Suliga, and A. Baha Balantekin, Entanglement in three-flavor collective neutrino oscillations, Phys. Rev. D 107, 023019 (2023).
  35. Pooja Siwach, A. Baha Balantekin, Amol V. Patwardhan, and Anna M. Suliga, Exploring entanglement and spectral split correlations in three-flavor collective neutrino oscillations, Phys. Rev. D 111, 063038 (2025).
  36. Ivan Chernyshev, Caroline E. P. Robin, and Martin J. Savage, Quantum magic and computational complexity in the neutrino sector, Phys. Rev. Res. 7, 023228 (2025).
  37. S. Ayik, A stochastic mean-field approach for nuclear dynamics, Phys. Lett. B 658, 174 (2008).
  38. Denis Lacroix, Sakir Ayik, and Bulent Yilmaz, Symmetry breaking and fluctuations within stochastic mean-field dynamics: Importance of initial quantum fluctuations, Phys. Rev. C 85, 041602(R) (2012).
  39. Denis Lacroix, Danilo Gambacurta, and Sakir Ayik, Quantal corrections to mean-field dynamics including pairing, Phys. Rev. C 87, 061302(R) (2013).
  40. D. Lacroix and S. Ayik, Stochastic quantum dynamics beyond mean field, Eur. Phys. J. A 50, 95 (2014).
  41. Bulent Yilmaz, Denis Lacroix, and Resul Curebal, Importance of realistic phase-space representations of initial quantum fluctuations using the stochastic mean-field approach for fermions, Phys. Rev. C 90, 054617 (2014).
  42. Denis Lacroix, S. Hermanns, C. M. Hinz, and M. Bonitz, Ultrafast dynamics of finite Hubbard clusters: A stochastic mean-field approach, Phys. Rev. B 90, 125112 (2014).
  43. D. Lacroix, Y. Tanimura, S. Ayik, and B. Yilmaz, A simplified BBGKY hierarchy for correlated fermions from a stochastic mean-field approach, Eur. Phys. J. A 52, 94 (2016).
  44. Ibrahim Ulgen, Bulent Yilmaz, and Denis Lacroix, Impact of initial fluctuations on the dissipative dynamics of interacting Fermi systems: A model case study, Phys. Rev. C 100, 054603 (2019).
  45. David Regnier, Denis Lacroix, Guillaume Scamps, and Yukio Hashimoto, Microscopic description of pair transfer between two superfluid Fermi systems: Combining phase-space averaging and combinatorial techniques, Phys. Rev. C 97, 034627 (2018).
  46. Thomas Czuba, Denis Lacroix, David Regnier, Ibrahim Ulgen, and Bulent Yilmaz, Combining phase-space and time-dependent reduced density matrix approach to describe the dynamics of interacting fermions, Eur. Phys. J. A 56, 111 (2020).
  47. I. Esteban, M. C. González-García, M. Maltoni, T. Schwetz, and A. Zhou, The fate of hints: Updated global analysis of three-flavor neutrino oscillations, J. High Energy Phys. 09 (2020) 178.
  48. Nufit 5.3 (2024), http://www.nu-fit.org/.
  49. Basudeb Dasgupta and Amol Dighe, Collective three-flavor oscillations of supernova neutrinos, Phys. Rev. D 77, 113002 (2008).
  50. Ali Javadi-Abhari, Matthew Treinish, Kevin Krsulich, Christopher J. Wood, Jake Lishman, Julien Gacon, Simon Martiel, Paul D. Nation, Lev S. Bishop, Andrew W. Cross et al., Quantum computing with Qiskit, arXiv:2405.08810.
  51. M. H. Quenouille, Notes on bias in estimation Biometrika 43, 353 (1956).
  52. Hideo Aoki, Naoto Tsuji, Martin Eckstein, Marcus Kollar, Takashi Oka, and Philipp Werner, Nonequilibrium dynamical mean-field theory and its applications Rev. Mod. Phys. 86, 779 (2014).
  53. L. Wolfenstein, Neutrino oscillations in matter, Phys. Rev. D 17, 2369 (1978).
  54. S. P. Mikheyev and A. Yu. Smirnov, Resonant amplification of ν oscillations in matter and solar-neutrino spectroscopy, Il Nuovo Cimento C 9, 17 (1986).
  55. L. Johns, Neutrino many-body correlations, Int. J. Mod. Phys. A 39, 2450122 (2024).
  56. Anson Kost, Lucas Johns, and Huaiyu Duan, Once-in-a-lifetime encounter models for neutrino media: From coherent oscillations to flavor equilibration, Phys. Rev. D 109, 103037 (2024).
  57. https://www.hqi.fr/.

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Phys. Rev. D 113, 036026– Published 26 February, 2026
  • Received 25 July 2025
  • Accepted 23 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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