Critical Properties of Bose-Einstein Condensates

该项目的目的是通过应用多体物理的场论方法，了解均匀玻色-爱因斯坦凝聚体在临界点以上，特别是在临界点以下的临界性质。在这两种情况下，我们将分析任意弱排斥性两粒子相互作用对临界温度和比热的影响。此外，在过渡下，我们想研究相波动对均匀玻色-爱因斯坦凝聚体超流体性质的影响。同样的场论方法将被应用于光晶格中的玻色-爱因斯坦凝聚体。在那里，由于布洛赫定理，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，从而导致具有不相关相的状态，其行为类似于莫特绝缘子。在这些跃迁的邻域中，物理量的微扰展开受到无处不在的红外散度的影响，使得有效展开参数变得无限大。我们借助变分摄动理论来解决这个问题，变分摄动理论是我们小组最近发展的一种确定发散弱耦合展开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.