Eigenvalues and eigenstates of the many-body collective neutrino oscillation problem
Eigenvalues and eigenstates of the many-body collective neutrino oscillation problem
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DOI：
10.1103/physrevd.99.123013
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发表时间：
2019-05
影响因子：
5
通讯作者：
A. Patwardhan;Michael J. Cervia;A. Balantekin
中科院分区：
文献类型：
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作者：
A. Patwardhan;Michael J. Cervia;A. Balantekin
我们展示了一种系统地获得描述集体中微子振荡的多体哈密顿量的本征值和本征态的方法。该方法源于Richardson-Gaudin框架，该框架将特征问题转化为一组耦合的非线性“Bethe Anatz方程”，其解可用于特征值和特征向量的参数化。本文概述的具体方法包括定义与Bethe-Anatz参数相关的辅助变量，从而将Bethe-Anatz方程转换为一组不同的方程，这些方程在数值上表现得更好，更容易处理。我们证明，不仅可以用这些辅助变量来表示本征值，而且可以用这些辅助变量来表示本征态，而不涉及Bethe Ansat z参数本身。
We demonstrate a method to systematically obtain eigenvalues and eigenstates of a many-body Hamiltonian describing collective neutrino oscillations. The method is derived from the Richardson-Gaudin framework, which involves casting the eigenproblem as a set of coupled nonlinear "Bethe Ansatz equations", the solutions of which can then be used to parametrize the eigenvalues and eigenvectors. The specific approach outlined in this paper consists of defining auxiliary variables that are related to the Bethe-Ansatz parameters, thereby transforming the Bethe-Ansatz equations into a different set of equations that are numerically better behaved and more tractable. We show that it is possible to express not only the eigenvalues, but also the eigenstates, directly in terms of these auxiliary variables without involving the Bethe Ansatz parameters themselves.