论文标题
几乎有周期性的哈密顿系统中绝热不变的一般公式
General formulas for adiabatic invariants in nearly-periodic Hamiltonian systems
论文作者
论文摘要
尽管众所周知，每个近乎周期的哈密顿系统都具有绝热的，现存的方法，用于计算绝热序列中的术语效率低下。最受欢迎的方法涉及对非唯一近乎身份坐标转换的大量中间计算，即使绝热不变本身是独特定义的标量。由S. omohundro开发的一种鲜为人知的方法避免了计算坐标转换的中间序列，但效率也很小，因为它涉及其自身的复杂中间计算序列。为了提高绝热不变的未来计算的效率，我们在绝热不变级数中的前几个术语中得出了通常可以适用的，易于计算的公式。为了证明这些公式的实用性，我们将它们应用于强磁场和磁场线动力学中的带电粒子动力学，当磁场线几乎封闭时。
While it is well-known that every nearly-periodic Hamiltonian system possesses an adiabatic invariant, extant methods for computing terms in the adiabatic invariant series are inefficient. The most popular method involves the heavy intermediate calculation of a non-unique near-identity coordinate transformation, even though the adiabatic invariant itself is a uniquely-defined scalar. A less well-known method, developed by S. Omohundro, avoids calculating intermediate sequences of coordinate transformations but is also inefficient as it involves its own sequence of complex intermediate calculations. In order to improve the efficiency of future calculations of adiabatic invariants, we derive generally-applicable, readily computable formulas for the first several terms in the adiabatic invariant series. To demonstrate the utility of these formulas, we apply them to charged particle dynamics in a strong magnetic field and magnetic field-line dynamics when the field lines are nearly closed.
