零程过程的临界密度的数值模拟

The Numeral Simulation of the Critical Density in Zero-Range Process Model

零程过程(Zero-Range Process以下简称ZRP)的临界密度是我们所关注的,在随机动力学规则下已经能解析得出,但在其他的动力学规则下还不能解析求解。我们引入了一个新的参量局域化系数来度量系统粒子分布的局域性,数值模拟了在随机动力学规则下的局域化系数随粒子密度的变化关系,得到临界密度,结果与解析得到的系统临界密度相符。这样我们可以通过数值来得出其他动力学规则下的临界密度。

The critical density of Zero - Range Process （ZRP） has gained much attention. It can be solved with random updating rule, but when it comes to other updating rule, there is no way to be solved. A new parameter is introduced here to measure the locality of particle distribution. The relationship between local coefficient and particle density is simulated with random updating rule and critical density is measured, which is in conformity with the critical density of the system. In this way, we can calculate the critical density with other updating rule.