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"Classical" instabilities and "quantum" speed-up in the evolution of neutrino clouds
High Energy Physics - Phenomenology · Submitted 24 Aug 2004
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Turning to the more complete case in which we do not assume the classical factorization, but instead solve for the evolution under the influence of the full "forward" Hamiltonian, we find the possibility of rapid evolution, under our definition, even when there is no seeding from conventional neutrino mixing.
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The abstract, sentence by sentence
We study some examples of collective behavior in neutrino clouds governed by the neutral-current neutrino-neutrino interaction. The standard equations for analyzing such systems are rederived in a two-step process: first, a replacement of the full interaction Hamiltonian with a "forward" Hamiltonian that contains only the momentum states that were initially occupied by a neutrino of one flavor or another; second, a factorization assumption that reduces the time evolution problem to the solution of coupled equations for the expectations of various bilinear forms in the neutrino fields. We designate the latter as the "classical" equations. We analyze some solutions of these equations in cases in which the initial momentum and flavor distributions of neutrinos are strongly anisotropic in space. In some cases we find an instability that leads to rapid evolution of the flavor-angle distribution, even when it is seeded by a very small initial flavor mixing (or alternatively by a very small neutrino mass$^2$ term). Turning to the more complete case in which we do not assume the classical factorization, but instead solve for the evolution under the influence of the full "forward" Hamiltonian, we find the possibility of rapid evolution, under our definition, even when there is no seeding from conventional neutrino mixing.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study some examples of collective behavior in neutrino clouds governed by the neutral-current neutrino-neutrino interaction. | contribution 0.89 | 0.90 | 0.04 | asserted 0.94 |
| s1 | The standard equations for analyzing such systems are rederived in a two-step process: first, a replacement of the full interaction Hamiltonian with a "forward" Hamiltonian that contains only the momentum states that were initially occupied by a neutrino of one flavor or another; second, a factorization assumption that reduces the time evolution problem to the solution of coupled equations for the expectations of various bilinear forms in the neutrino fields. | method 0.97 | 0.85 | 0.05 | asserted 0.99 |
| s2 | We designate the latter as the "classical" equations. | method 0.91 | 0.82 | 0.04 | asserted 0.97 |
| s3 | We analyze some solutions of these equations in cases in which the initial momentum and flavor distributions of neutrinos are strongly anisotropic in space. | contribution 0.50 | 0.87 | 0.05 | asserted 0.81 |
| s4 | In some cases we find an instability that leads to rapid evolution of the flavor-angle distribution, even when it is seeded by a very small initial flavor mixing (or alternatively by a very small neutrino mass$^2$ term). | result 1.00 | 0.95 | 0.23 | asserted 0.99 |
| s5 | Turning to the more complete case in which we do not assume the classical factorization, but instead solve for the evolution under the influence of the full "forward" Hamiltonian, we find the possibility of rapid evolution, under our definition, even when there is no seeding from conventional neutrino mixing. | result 0.99 | 0.95 | 0.43 | hedged possibility 0.87 |
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Original abstract
We study some examples of collective behavior in neutrino clouds governed by the neutral-current neutrino-neutrino interaction. The standard equations for analyzing such systems are rederived in a two-step process: first, a replacement of the full interaction Hamiltonian with a "forward" Hamiltonian that contains only the momentum states that were initially occupied by a neutrino of one flavor or another; second, a factorization assumption that reduces the time evolution problem to the solution of coupled equations for the expectations of various bilinear forms in the neutrino fields. We designate the latter as the "classical" equations. We analyze some solutions of these equations in cases in which the initial momentum and flavor distributions of neutrinos are strongly anisotropic in space. In some cases we find an instability that leads to rapid evolution of the flavor-angle distribution, even when it is seeded by a very small initial flavor mixing (or alternatively by a very small neutrino mass$^2$ term). Turning to the more complete case in which we do not assume the classical factorization, but instead solve for the evolution under the influence of the full "forward" Hamiltonian, we find the possibility of rapid evolution, under our definition, even when there is no seeding from conventional neutrino mixing.
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References
How the literature uses it
24 arXiv papers cite this in 43 sentences
Papers citing it · 26 sentences without a confident label
Contests it 1 paper
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The models considered in [ref] , and described in more detail in Sec. [ref] below, give rise to fast oscillations with times scaling as $τ_F$ by introducing however an unphysical perturbation that breaks the $SU(2)$ invariance of the neutrino Hamiltonian in Eq. [ref].
Dynamical Phase Transitions in models of Collective Neutrino Oscillations · Introduction · contest 0.73
Compares with it 1 paper
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This simulation strategy is used here with two main goals, the first one was to validate the early small scale simulations by Sawyer et al. [ref] which, correctly, predicted flavor evolution to occur (in their model) at a fast time-scale $τ_F≈μ^-1log(N)$.
Dynamical Phase Transitions in models of Collective Neutrino Oscillations · Summary and Conclusions · 0.86
Cites it as background 14 papers
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In this work, we will study the flavor evolution of such a neutrino gas in the limit that the potential generated by coherent $ν-ν$ forward scattering is the dominant effect; this is a regime known in the literature as the “fast" flavor oscillation limit [ref] .
Equilibration of quantum many-body fast neutrino flavor oscillations · Introduction · 0.93
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We here focus on fast flavor evolution [ref] , corresponding to massless neutrinos, the purest form of collective flavor evolution.
Single-wave solutions of the neutrino fast flavor system. Part II. Weak instabilities and their resonant behavior · Introduction · 0.91
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The role of entanglement and quantum effects in the out-of-equilibrium dynamics [ref] of neutrinos has received renewed interest recently [ref] but is still not well understood, with seemingly conflicting results in the past predicting either a vanishingly small contribution in the large system size limit [ref] or substantial flavor evolution over time scales $τ_F=μ^-1log(N)$, which can remain relevant for large systems [ref] .
Entanglement and Many-Body effects in Collective Neutrino Oscillations · Introduction · 0.80
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