Multiple phases in stochastic dynamics: geometry and probabilities
统计力学
2007-11-08 v1 其他凝聚态物理
摘要
Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase transitions) of the underlying system become manifest as extremal points. This geometrical construction, which we call an \textit{observable-representation of state space}, can allow hierarchical structure to be observed. It also provides a method for the calculation of the probability that an initial points ends in one or another asymptotic state.
引用
@article{arxiv.cond-mat/0604159,
title = {Multiple phases in stochastic dynamics: geometry and probabilities},
author = {B. Gaveau and L. S. Schulman},
journal= {arXiv preprint arXiv:cond-mat/0604159},
year = {2007}
}