Ogawa Shun
Aix-Marseille Université, Université de Toulon, CNRS, CPT, Marseille, France.
Phys Rev E. 2017 Jul;96(1-1):012112. doi: 10.1103/PhysRevE.96.012112. Epub 2017 Jul 7.
Linear and nonlinear response formulas taking into account all Casimir invariants are derived without use of angle-action variables of a single-particle (mean-field) Hamiltonian. This article deals mainly with the Vlasov system in a spatially inhomogeneous quasistationary state whose associating single-particle Hamiltonian is not integrable and has only one integral of the motion, the Hamiltonian itself. The basic strategy is to restrict the form of perturbation so that it keeps Casimir invariants within a linear order, and the single particle's probabilistic density function is smooth with respect to the single particle's Hamiltonian. The theory is applied for a spatially two-dimensional system and is confirmed by numerical simulations. A nonlinear response formula is also derived in a similar manner.
在不使用单粒子（平均场）哈密顿量的角动量作用变量的情况下，推导了考虑所有卡西米尔不变量的线性和非线性响应公式。本文主要研究空间非均匀准稳态的弗拉索夫系统，其相关的单粒子哈密顿量不可积，且只有一个运动积分，即哈密顿量本身。基本策略是限制微扰的形式，使得卡西米尔不变量在一阶范围内保持不变，并且单粒子的概率密度函数相对于单粒子哈密顿量是光滑的。该理论应用于二维空间系统，并通过数值模拟得到了验证。还以类似的方式推导了一个非线性响应公式。
