配对涨落理论的守恒近似及其对超冷费米子气体的应用

Recently, one of the important topics of condensed matter theory is the study of the ultra-cold Fermi gases in the strong correlated limit. Since the traditional perturbation theory is invalid for the strong correlated system, the understanding of strong correlation becomes a very difficult problem and therefore stimulated a lot of new concept and theoretical model, such as the BCS-BEC crossover theory etc. This project aims to develop a conserved approximation for the BCS-BEC crossover theory with pair fluctuations, which satisfies the conservation laws of U(1) gauge current and stress tensor. Under the transition temperature, we also have to take into account the vertex correction due to the Nambu-Goldstone boson caused by spontaneously symmetry breaking. This will allow us to establish the Ward identity for stress tensor and generalized the conserved approximation of pair fluctuation theory to all finite temperature range and the whole BCS-BEC crossover interaction range. This provides the basis for the reliable understanding the transport property of pseudogap phase of Fermi gases.

超冷原子费米子气体在强关联相互作用下的物理性质是目前凝聚态理论研究的热点。由于传统的微扰方法对于强关联体系失效，因此强关联成为理论研究的难点，并且由此产生了很多新的理论方法和概念如BCS-BEC过渡理论等。本项目的主要研究目标是发展包含配对涨落的BCS-BEC过渡理论的守恒近似，使得理论满足U(1)规范流守恒和能量-动量张量守恒。在转变温度之下，我们考虑对称性破缺导致的Nambu-Goldstone玻色子对相作用顶角的修正，从而证明推广的Ward恒等式，进一步得到在整个有限温度和整个BCS-BEC过渡区域都符合守恒律的配对涨落理论的守恒近似,并且对超冷原子的赝能隙相的输运性质做定量描述。

我们发展了一种基于包含配对涨落的BCS-BEC过渡理论的线性响应理论。在该理论中，我们通过引入完全修正的顶角，使得规范流和能量-动量张量的响应函数满足一般的Ward恒等式，从而使理论具有更高的自洽性。所得到的理论形式可以应用于描述强关联费米子气体的外场响应。目前由于理论形式相当复杂，应用该理论做具体数值计算还有相当的困难。