Invariants of Collective Neutrino Oscillations
Invariants of Collective Neutrino Oscillations
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DOI：
10.1103/physrevd.84.065008
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发表时间：
2011-05
影响因子：
5
通讯作者：
Y. Pehlivan;A. Balantekin;T. Kajino;T. Yoshida
中科院分区：
文献类型：
--
作者：
Y. Pehlivan;A. Balantekin;T. Kajino;T. Yoshida
通过考虑真空振荡和中微子的自相互作用，我们考虑了致密中微子气体的风味演化。我们从多体的角度以及从有效的单体描述的角度来研究系统，该描述是根据中微子偏振矢量制定的。我们证明，在单角度近似下，多体图像和有效单粒子图像都具有几个运动常数。我们明确地用多体情况下的中微子同位旋算符和有效单体情况下的偏振矢量来表示这些运动常数。这些运动常数的存在是集体中微子振荡哈密顿量属于高丁哈密顿量这一事实的直接结果。这类哈密顿量还包括描述超导性的（简化的）BCS配对哈密顿量。我们指出了集体中微子振荡哈密顿量与BCS配对哈密顿量的相似性。运动常数表明系统的精确可解性。利用已建立的精确BCS谱计算技术，我们给出了描述集体中微子振荡的多体和有效单粒子哈密顿量的精确特征态和特征值。对于有效的单体情况，我们表明中微子的光谱分裂可以用一些准粒子自由度从高密度区域的绝热演化来理解，在高密度区域它们与味道本征态一致，在真空中它们与质量本征态一致。我们给出了有效的单体特征态所应满足的最一般的一致性方程，并证明了它们在适当的初始条件下可以简化为谱分裂一致性方程。
We consider the flavor evolution of a dense neutrino gas by taking into account both vacuum oscillations and self-interactions of neutrinos. We examine the system from a many-body perspective as well as from the point of view of an effective one-body description formulated in terms of the neutrino polarization vectors. We show that, in the single angle approximation, both the many-body picture and the effective one-particle picture possess several constants of motion. We write down these constants of motion explicitly in terms of the neutrino isospin operators for the many-body case and in terms of the polarization vectors for the effective one-body case. The existence of these constants of motion is a direct consequence of the fact that the collective neutrino oscillation Hamiltonian belongs to the class of Gaudin Hamiltonians. This class of Hamiltonians also includes the (reduced) BCS pairing Hamiltonian describing superconductivity. We point out the similarity between the collective neutrino oscillation Hamiltonian and the BCS pairing Hamiltonian. The constants of motion manifest the exact solvability of the system. Borrowing the well established techniques of calculating the exact BCS spectrum, we present exact eigenstates and eigenvalues of both the many-body and the effective one-particle Hamiltonians describing the collective neutrino oscillations. For the effective one-body case, we show that spectral splits of neutrinos can be understood in terms of the adiabatic evolution of some quasiparticle degrees of freedom from a high-density region where they coincide with flavor eigenstates to the vacuum where they coincide with mass eigenstates. We write down the most general consistency equations which should be satisfied by the effective one-body eigenstates and show that they reduce to the spectral split consistency equations for the appropriate initial conditions.