对于2d弱自我排斥的布朗聚合物的一种不变性原理
Giuseppe Cannizzaro1, Harry Giles1
1University of Warwick, Coventry, CV4 7AL UK.
概括
我们在两个维度中研究了自排斥布朗聚合物 (SRBP). 我们的发现表明,它的平均平方位移增长为t ((log t) ^1/2,表明扩散增强,并提供了特定扩展指数的证据.
科学领域:
- 统计物理学的统计物理.
- 随机过程是指随机的过程.
- 聚合物物理 聚合物物理
背景情况:
- 自排斥布朗聚合物 (SRBP) 通过随机微分方程模型自排斥运动.
- 它的离散对应物,真正的自我避开步行 (TSAW),据推测是对数超扩散的.
- 在临界维度d=2中SRBP的行为仍然是一个悬而未决的问题.
研究的目的:
- 在临界维度d=2.2中研究SRBP的大规模行为.
- 在弱合扩展下为SRBP建立一个不变性原理.
- 确定环境过程的缩放极限及其与增强扩散性的关系.
主要方法:
- 对控制SRBP的随机微分方程的分析.
- 在聚合物模型中应用弱合缩放.
- 对粒子和环境过程的缩放极限的推导.
- 解决一个非线性奇数随机局部微分方程 (SPDE).
主要成果:
- 在弱合扩展下建立了SRBP的不变性原理.
- 限制布朗运动的显式扩散性表明,平均平方位移中的指数β是1/2.
- 环境过程的缩放极限被证明是一个线性传输方程,具有增强的扩散性.
结论:
- 这项研究提供了强有力的证据,即d=2中的SRBP表现出对数超扩散,指数为1/2.
- 弱合缩放显示了向不同的扩散行为过渡.
- 环境过程的缩放极限证实了增强的扩散性,为复杂的粒子动态提供了洞察力.
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