对稳定状态的超均性的方法 促进排除过程的稳定状态的超均性
S Goldstein1, J L Lebowitz1, E R Speer1
1Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, United States of America.
概括
保守格子气体模型中的粒子波动在临界密度附近表现出超均的行为. 随着密度接近这个临界点,差异缩放在不同的盒子大小中发生变化.
科学领域:
- 统计力学 统计力学
- 凝聚物质物理学 凝聚物质物理学
- 数学物理学的数学物理.
背景情况:
- 促进排除过程,或保存格子气体模型,是统计力学中研究的.
- 静态状态和粒子数的波动是这些系统的关键性质.
研究的目的:
- 分析保守格子气体模型中的粒子数波动.
- 为了描述这些波动的行为,随着系统密度接近临界值.
- 描述过渡到超均性的过程.
主要方法:
- 在无限体积的转换不变静态状态的分析.
- 从伯努利测量开始对系统的研究.
- 对d=1进行严格分析,对d>=2.2进行模拟.
主要成果:
- 对于低于临界密度的系统,系统接近"结"状态 (d=1,d>1的ρc=1/2和d=2的ρc<1/2).
- 在临界密度 (ρc) 时,系统变得超均,随着亚线性方差增长.
- 变量缩放表现出不同的模式:在大尺度上是正常的,在中间区域比正常快,在小尺度上是超均的,因为 ρ接近 ρc.
结论:
- 该研究详细描述了粒子波动在临界密度附近的不同长度尺度上扩展的细节.
- 过渡到超均的特点是异常行为交叉.
- 结果被严格证明为1D,并得到了更高维度的模拟的支持.
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