Critical Properties of Bose-Einstein Condensates

该项目的目标是通过应用多体物理的场论方法，了解高于临界点，特别是低于临界点的均匀玻色-爱因斯坦凝聚体的临界性质。在这两种情况下，我们将分析任意弱排斥两粒子相互作用对临界温度和比热的影响。此外，在跃迁下面，我们想要研究相位涨落对均匀玻色-爱因斯坦凝聚体超流体性质的影响。然后，同样的场论方法将被应用于捕获在光学晶格中的玻色-爱因斯坦凝聚体。在这里，由于布洛赫的S定理，周期性导致了准自由行为。在晶格系统中，人们可以增加玻色子之间的有效排斥相互作用，从而导致相位不相关的状态表现为Mott绝缘体。在这些跃迁附近，物理量的微扰展开会受到无处不在的红外发散的影响，因此有效展开参数变得无限大。我们借助于变分微扰理论掌握了这个问题，这是我们课题组最近发展起来的一种确定发散弱耦合展开式的强耦合极限的方法。

The goal of the project is to understand the critical properties of homogeneous Bose-Einstein condensates above and, especially, below the critical point by applying field-theoretic methods of many-body physics. In both regimes we shall analyze the effect of an arbitrarily weak repulsive two-particle interaction on the critical temperature and the specific heat. Furthermore, below the transition, we want to investigate the influence of phase fluctuations upon the superfluid properties of homogeneous Bose-Einstein condensates. The same field-theoretic methods will then be applied to Bose-Einstein condensates trapped in optical lattices. There the periodicity leads to a quasi-free behavior due to Bloch´s theorem. In the lattice systems one can increase the effective repulsive interaction between the bosons which leads to a state with uncorrelated phases behaving like a Mott insulator. In the neighborhood of any of these transitions, perturbation expansions of physical quantities suffer from ubiquitous infrared divergencies so that the effective expansion parameter becomes infinite. We master this problem with the help of variational perturbation theory, a method developed recently in our group to determine the strong-coupling limit of divergent weak-coupling expansions.