Non-Markovian speedup evolution of a center massive particle in two-dimensional environmental model

A two-dimensional ray model is introduced to realize the non-Markovian speedup evolution of a center massive particle gravitationally coupled to a controllable environment (multilayer arrangement of the massive particles). By controlling the environment, for instance by choosing a judicious mass of the environmental particles or by changing the separation distance of each massive particle, two dynamical crossover behaviors from Markovian to non-Markovian and from no-speedup to speedup are achieved due to the gravitational interactions between the system particle and environmental particles. It is obvious that the critical mass of the environmental particles or the critical separation distance for these two dynamical crossover behaviors restrict each other directly. The larger the value of the mass of the environmental particles is, the smaller the value of the critical separation distance should be requested. In addition, it should be emphasized that the non-Markovian dynamics is the principal physical reason for the speedup evolution of the system massive particle. Particularly, the non-Markovianity of the dynamics process of the system massive particle in the even ray case has better correspondence with the quantum speed limit time than that in the singular ray case.