非齐次拟stationary states长程系统的动力学稳定性判据
Dynamical stability criterion for inhomogeneous quasi-stationary states in long-range systems
摘要：
本文给出了哈密顿平均场（HMF）模型的非齐次Vlasov定态线性动力学稳定的一个充分必要条件。该条件表示为一个明确的不平等，必须满足的平稳状态，它推广了已知的不平等齐次平稳状态。此外，我们推导出类似的不等式，表示形式稳定的定态的必要和充分条件。从线性动力稳定性的观点来看，它们的用处在于它们更简单，尽管它们只提供了线性稳定性的充分判据。我们表明，对于齐次定态的关系变得平等，因此线性动力学稳定性和形式稳定性成为等价的。
英文摘要：
We derive a necessary and sufficient condition of linear dynamical stability for inhomogeneous Vlasov stationary states of the Hamiltonian Mean Field (HMF) model. The condition is expressed by an explicit disequality that has to be satisfied by the stationary state, and it generalizes the known disequality for homogeneous stationary states. In addition, we derive analogous disequalities that express necessary and sufficient conditions of formal stability for the stationary states. Their usefulness, from the point of view of linear dynamical stability, is that they are simpler, although they provide only sufficient criteria of linear stability. We show that for homogeneous stationary states the relations become equal, and therefore linear dynamical stability and formal stability become equivalent.
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