Equilibrium and ageing in glassy systems

这些项目旨在研究自旋玻璃等高度无序系统的平衡和动力学性质。在这样的系统中，平衡的特征在于热力学极限中吉布斯状态的复杂结构，而动力学的特征在于朝向局部响应的缓慢瞬变。导致“老龄化”现象的全球平衡。我们计划研究一类具有层次相关性的高斯自旋玻璃（即所谓的广义随机能量模型）中这些特征之间的关系。在这些模型中，我们期望得到吉布斯测度的完整描述。在此基础上，我们计划研究更难的问题，相关的随机动力学。这个问题已经解决了以前在最简单的例子，随机能量模型，我们希望在这种情况下开发的方法提供了一个基础，在更复杂的情况下进行分析。

The projects aims at the investigation of equilibrium and dynamical properties of highly disordered systems such as spin glasses. In such systems the equilibrium is characterized by a complex structure of the Gibbs states in the thermodynamic limit, while the dynamics are characterized by slow transients towards local resp. global equilibria that give rise to the `ageing' phenomenon. We plan to investigate the relation between these features within a class of Gaussian spin glasses with hierarchical correlations, the so-called Generalised Random Energy Models. In these models we expect to obtain a full description of the Gibbs measures. On this basis we then plan to investigate the much harder problem of the associated stochastic dynamics. This problem has been solved previously in the simplest example, the Random Energy Model, and we expect the methods developed in this context to provide a basis for the analysis in more complex situations.