论文标题
弗拉索夫方程的哈密顿结构的严格推导
A rigorous derivation of the Hamiltonian structure for the Vlasov equation
论文作者
论文摘要
我们认为在任何空间维度中的弗拉索夫方程，长期以来一直被称为无限二维的哈密顿系统，其支架结构是lie-poisson型的。同时，经典的弗拉索夫方程是成对相互作用的牛顿系统的平均场限制。在这些知识的推动下，我们直接从多体问题直接提供了弗拉索夫方程的哈密顿结构的严格推导，包括汉密尔顿功能和泊松托。人们可以将这项工作视为与Arxiv：1908.03847的经典对应物，该作品从多体性问题中，从多体问题中，在某种无限粒子数量限制的多体问题中提供了对同类玻色子的多体问题的严格推导，这是其第一个结果。特别是，我们的工作解决了马斯登，莫里森和温斯坦的问题，为弗拉索夫方程的支架结构提供了“统计基础”。
We consider the Vlasov equation in any spatial dimension, which has long been known to be an infinite-dimensional Hamiltonian system whose bracket structure is of Lie-Poisson type. In parallel, it is classical that the Vlasov equation is a mean-field limit for a pairwise interacting Newtonian system. Motivated by this knowledge, we provide a rigorous derivation of the Hamiltonian structure of the Vlasov equation, both the Hamiltonian functional and Poisson bracket, directly from the many-body problem. One may view this work as a classical counterpart to arXiv:1908.03847, which provided a rigorous derivation of the Hamiltonian structure of the cubic nonlinear Schrödinger equation from the many-body problem for interacting bosons in a certain infinite particle number limit, the first result of its kind. In particular, our work settles a question of Marsden, Morrison, and Weinstein on providing a "statistical basis" for the bracket structure of the Vlasov equation.
