中微子快味摆。第2部分：碰撞阻尼
Neutrino Fast Flavor Pendulum. Part 2: Collisional Damping
摘要：
在致密天体中，中微子密度可能很高，以至于中微子-中微子折射可以导致快速的味道转换，这种转换是$ν_e \barν_e \leftrightarrow ν_x \barν_x$与$x=μ,τ$，取决于中微子的角度分布。以前，我们已经表明，在一个均匀的，轴对称的两味系统，这些集体的解决方案演变类似于一个陀螺摆。在味空间中，其偏离弱相互作用方向的量化变量$\cos\vartheta$之间移动$+1$和$\cos\vartheta_{\rm min}$，后者从线性模式分析。作为下一步，我们包括味相干性的碰撞阻尼，假设所有模式的共同阻尼率$Γ$。根据经验，我们发现阻尼摆动运动达到对转换$f=A+(1-A)\cos\vartheta_{\rm min}$（数值$A\simeq 0.370$）的渐近水平，不依赖于角分布的细节（除了固定$\cos\vartheta_{\rm min}$），初始种子，也不$Γ$。另一方面，即使中微子和反中微子阻尼率之间的微小不对称也会强烈改变这一图景，甚至可能使原本稳定的系统出现味不稳定性。
英文摘要：
In compact astrophysical objects, the neutrino density can be so high that neutrino-neutrino refraction can lead to fast flavor conversion of the kind $ν_e \barν_e \leftrightarrow ν_x \barν_x$ with $x=μ,τ$, depending on the neutrino angle distribution. Previously, we have shown that in a homogeneous, axisymmetric two-flavor system, these collective solutions evolve in analogy to a gyroscopic pendulum. In flavor space, its deviation from the weak-interaction direction is quantified by a variable $\cos\vartheta$ that moves between $+1$ and $\cos\vartheta_{\rm min}$, the latter following from a linear mode analysis. As a next step, we include collisional damping of flavor coherence, assuming a common damping rate $Γ$ for all modes. Empirically we find that the damped pendular motion reaches an asymptotic level of pair conversion $f=A+(1-A)\cos\vartheta_{\rm min}$ (numerically $A\simeq 0.370$) that does not depend on details of the angular distribution (except for fixing $\cos\vartheta_{\rm min}$), the initial seed, nor $Γ$. On the other hand, even a small asymmetry between the neutrino and antineutrino damping rates strongly changes this picture and can even enable flavor instabilities in otherwise stable systems.
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