Stochastic phase space methods for non-equilibrium systems

目的是探索和扩大相空间方法的范围，以模拟多体量子系统的失平衡行为。作为初始项目，我将使用该系统的截断维格纳模拟的现有代码寻找半导体微腔中极化的OPO制度内的KPZ行为。这是为了达到双重目的，使我熟悉这些方法，以及它们是如何在计算上实现的，同时也回答了我的小组以前的研究提出的一个悬而未决的问题。进一步的项目将涉及探索相关的相空间方法，如正P，以超越截断维格纳近似的可及性，研究非平衡多体量子系统中的非经典效应，如极化晶格。

The aim is to explore and expand the scope of phase space methods for simulating the behaviour of many-body quantum systems out of equilibrium. As an initial project I will be looking for KPZ behaviour within the OPO regime of polaritons in semiconductor microcavities using existing code for the truncated Wigner simulation of this system. This is to serve the dual purpose of familiarising myself with the methods and how they are implemented computationally as well as answering an open question posed by my group's previous research. Further projects will then involve exploring related phase space methods, such as positive P, to go beyond what is accessible to the truncated Wigner approximation to study non-classical effects in non-equilibrium many-body quantum systems, such as polariton lattices.