Linearizing neutrino evolution equations including νν̄ pairing correlations
Linearizing neutrino evolution equations including νν̄ pairing correlations
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线性化中微子演化方程，包括 νν̄ 配对相关性
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
C. Volpe
中科院分区：
文献类型：
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作者：
D. Vaananen;C. Volpe
我们线性化的中微子平均场演化方程描述的中微子在物质和中微子的背景下的传播，使用多体微观方法的技术。该程序导致的本征值方程，允许识别不稳定性的演变，与中微子能量密度表面的曲率的变化。我们的结果包括了中微子哈密顿量的所有贡献，并且可以推广到在演化的任意点线性化运动方程。然后，我们考虑的扩展方程，包括正常的平均场以及异常的平均场，是与中微子-反中微子配对相关。我们首先重新推导出扩展的中微子哈密顿量，并表明，这样的哈密顿量可以对角化通过引入一个广义Bogoliubov-Valatin变换与准粒子运营商，混合中微子和反中微子。给出了确定准粒子本征态能量的本征方程。最后，我们推导出的本征值方程的扩展运动方程，在小振幅近似有效。我们的结果适用于任意数量的中微子家庭。
We linearize the neutrino mean-field evolution equations describing the neutrino propagation in a background of matter and of neutrinos, using techniques from many-body microscopic approaches. The procedure leads to an eigenvalue equation that allows to identify instabilities in the evolution, associated with a change of the curvature of the neutrino energy-density surface. Our result includes all contributions from the neutrino Hamiltonian and is generalizable to linearize the equations of motion at an arbitrary point of the evolution. We then consider the extended equations that comprise the normal mean field as well as the abnormal mean field that is associated with neutrino-antineutrino pairing correlations. We first re-derive the extended neutrino Hamiltonian and show that such a Hamiltonian can be diagonalized by introducing a generalized Bogoliubov-Valatin transformation with quasi-particle operators that mix neutrinos and antineutrinos. We give the eigenvalue equations that determine the energies of the quasi-particles eigenstates. Finally we derive the eigenvalue equation of the extended equations of motion, valid in the small amplitude approximation. Our results apply to an arbitrary number of neutrino families.