广义零程粒子系统生成元预解算子的散逸性

Dissipative of the resolvent operator of the generator of a generalized infinite particle system with zero range interactions

具有零程相互作用的无穷粒子系统是粒子系统理论的主要研究对象之一,它描述了这样一种随机模型,在可列个位置上有无穷个不可辨粒子做随机移动,同一时刻任何位置上最多只能发生一个粒子转移,粒子转移的概率转移速率仅受该位置的粒子数影响.该文将上述模型作了推广,研究了在同一时刻任一位置上可以发生任意有限个粒子转移的情形,给出了系统预解算子的散逸性和生成元的可闭性.使用泛函分析方法给出了散逸性和可闭性的证明.

An infinite particle system with zero range interactions is one of the major research objects in particle system theory. It describes a stochastic model with infinite unrecognized particles moving at random at finite sites. At any time and at any site, there is only one particle moving from one site to another. The probabilistic transition speed depends only on the number of particles in a site. Here a more generalized situation is given, where, at any time and at any site, there may be finite particles moving from one site to another. The dissipative of the resolvent operator and the closability of the generator are given, wherein the main tool used is functional analysis.