Yamaguchi Yoshiyuki Y, Ogawa Shun
Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, 606-8501 Kyoto, Japan.
Aix-Marseille Université, Université de Toulon, CNRS, Centre de Physique Théorique UMR 7332, 13288 Marseille Cedex 9, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042131. doi: 10.1103/PhysRevE.92.042131. Epub 2015 Oct 14.
Predicting the long-lasting quasistationary state for a given initial state is one of central issues in Hamiltonian systems having long-range interaction. A recently proposed method is based on the Vlasov description and uniformly redistributes the initial distribution along contours of the asymptotic effective Hamiltonian, which is defined by the obtained quasistationary state and is determined self-consistently. The method, to which we refer as the rearrangement formula, was suggested to give precise prediction under limited situations. Restricting initial states consisting of a spatially homogeneous part and small perturbation, we numerically reveal two conditions that the rearrangement formula prefers: One is a no Landau damping condition for the unperturbed homogeneous part, and the other comes from the Casimir invariants. Mechanisms of these conditions are discussed. Clarifying these conditions, we validate to use the rearrangement formula as the response theory for an external field, and we shed light on improving the theory as a nonequilibrium statistical mechanics.
预测给定初始状态下的持久准静态是具有长程相互作用的哈密顿系统的核心问题之一。最近提出的一种方法基于弗拉索夫描述，并沿着渐近有效哈密顿量的等高线均匀地重新分布初始分布，该渐近有效哈密顿量由获得的准静态定义并自洽确定。我们将该方法称为重排公式，它被认为在有限情况下能给出精确预测。通过限制由空间均匀部分和小扰动组成的初始状态，我们在数值上揭示了重排公式所偏好的两个条件：一个是未扰动均匀部分的无朗道阻尼条件，另一个来自卡西米尔不变量。讨论了这些条件的机制。通过阐明这些条件，我们验证了将重排公式用作外场的响应理论，并为作为非平衡统计力学改进该理论提供了思路。
