Pakter Renato, Levin Yan
Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, Rio Grande do Sul, Brazil.
Phys Rev Lett. 2013 Apr 5;110(14):140601. doi: 10.1103/PhysRevLett.110.140601. Epub 2013 Apr 2.
Using extensive molecular dynamics simulations we explore the fine-grained phase space structure of systems with long-range interactions. We find that if the initial phase space particle distribution has no holes, the final stationary distribution will also contain a compact simply connected region. The microscopic holes created by the filamentation of the initial distribution function are always restricted to the outer regions of the phase space. In general, for complex multilevel distributions it is very difficult to a priori predict the final stationary state without solving the full dynamical evolution. However, we show that, for multilevel initial distributions satisfying a generalized virial condition, it is possible to predict the particle distribution in the final stationary state using Casimir invariants of the Vlasov dynamics.
通过广泛的分子动力学模拟，我们探索了具有长程相互作用的系统的细粒度相空间结构。我们发现，如果初始相空间粒子分布没有空洞，最终的稳态分布也将包含一个紧凑的单连通区域。由初始分布函数的丝状化产生的微观空洞总是局限于相空间的外部区域。一般来说，对于复杂的多级分布，在不求解完整动力学演化的情况下，很难先验地预测最终的稳态。然而，我们表明，对于满足广义维里条件的多级初始分布，可以使用弗拉索夫动力学的卡西米尔不变量来预测最终稳态下的粒子分布。
