Critical processes on curved and dynamically evolving manifolds

在提出的项目中，我们希望研究非常规几何中的平衡，特别是非平衡临界现象。一个重点是研究具有曲率的背景几何的临界现象。这里的主要问题是曲率如何影响临界行为，这样的系统如何在数值上和解析上处理，以及如何适当地处理边界条件。此外，我们打算在动态变化的背景下研究各种临界现象。这里最简单的情况是一个自我膨胀或收缩的平坦空间。目的是找出关键性质是如何依赖于膨胀/收缩特性的。此外，在不能使用常规静态晶格的情况下，在数值上实现具有二阶相变的众所周知的模型是具有挑战性的。最后，发展合适的场理论方法来处理动态演变的背景几何上的关键现象将是有趣的。

With the proposed project we would like to investigate equilibrium and in particular non-equilibrium critical phenomena in non-conventional geometries. One focus is the study of critical phenomena on background geometries with curvature. Here the main questions are how the curvature affects the critical behavior, how such systems can be treated both numerically and analytically, and how boundary conditions can be handled appropriately. In addition we intend to study various critical phenomena on dynamically evolving backgrounds. Here the simplest scenario would be a self-inflating or contracting flat space. The aim is to find out how the critical properties depend on the expansion/contraction characteristics. Moreover, it is challenging to implement well-known models with second-order phase transitions numerically in a setup where a regular static lattice cannot be used. Finally, it would be interesting to develop suitable field-theoretical approaches to deal with critical phenomena on dynamically evolving background geometries.