论文标题
在动力中微子振荡的动力学方法中考虑海森堡和保利原则
Accounting for the Heisenberg and Pauli principles in the kinetic approach to neutrino oscillations
论文作者
论文摘要
虽然通常使用单粒子量子力学方法研究太阳中微子的振荡，但通常使用动力学方程来分析超新星中微子的风味转化，以使其密度矩阵的矩阵，因为还需要包括散射过程。使用量子力学的Wigner公式，我们显示了量子力学和动力学方法在无碰撞中微子传播极限（在背景介质中）的等效性。基于这一观察结果，我们还认为，动力学方程的解决方案解释了海森堡的不确定性原理和波数据包分离的相关效果（对于单个中微子）以及保利排除原理，如果初始条件与这些基本量子原理一致。可以构建这样的初始条件，例如通过识别使用中微子波函数的初始条件计算的（还原的）单粒子Wigner函数的密度的矩阵。因此，中微子动量不确定性是密度矩阵矩阵初始条件的组成部分，这可能会通过波包分离的影响对超新星中微子的现象产生影响。
While oscillations of solar neutrinos are usually studied using the single-particle quantum-mechanical approach, flavor conversions of supernovae neutrinos are typically analyzed using the kinetic equation for the matrix of densities due to the necessity of including also the scattering processes. Using the Wigner formulation of quantum mechanics we show the equivalence of the quantum-mechanical and kinetic approaches in the limit of collisionless neutrino propagation (in a background medium). Based on this observation we also argue that solutions of the kinetic equation account for the Heisenberg uncertainty principle and the related effect of wave packet separation (for single neutrinos), as well as the Pauli exclusion principle, if the initial conditions are consistent with these fundamental quantum principles. Such initial conditions can be constructed e.g. by identifying the matrix of densities with the (reduced) single-particle Wigner function computed using initial conditions for the neutrino wave function. Hence the neutrino momentum uncertainty is an integral part of the initial conditions for the matrix of densities, that may have an impact on the phenomenology of supernovae neutrinos via the effect of wave packet separation.
