Interacting bosons in external traps: Theory, computational methods and applications beyond standard mean-field

玻色-爱因斯坦凝聚（BEC）在超冷囚禁气体中的实验实现激发了对囚禁相互作用玻色子基本物理的现代探索。俘获玻色-爱因斯坦凝聚最基本的理论和计算工具-- Gross-Pitaevskii（GP）方程，或所谓的标准平均场--已经成功地解释了许多观测结果。然而，需要超越GP是很好的理解（和记录）的科学界;有很多现象，它不能解释或发现。最近，利用我们的扩展，多轨道平均场的方法，我们已经预测了几个新的物理现象。这些包括宏观碎裂的存在性和一般性的基态和激发态的玻色-爱因斯坦凝聚体，一个动物园的量子相位和激发的玻色子在光学晶格中，和丰富的途径，从凝聚通过碎裂到费米化的被困冷玻色子系统。拟议的项目旨在：（1）继续发展我们的多轨道方法，在一维和更高的维度，并开发指定的多体工具[自洽的时间无关和时间相关的多构型方法]，这是我们的多轨道方法的自然扩展被困相互作用玻色子。(2)研究从捕获和操纵相互作用的玻色子中出现的丰富物理学，继续预测新的物理效应，刺激实验并解释其结果。一个主要目标是描述多体物理伴随着地面和激发态的碎片和量子相变的陷阱和多体动力学的凝聚体沉浸在不同的陷阱，并在其释放。

The experimental realizations of Bose-Einstein condensates (BECs) in ultracold trapped gases have stimulated a modern search for the fundamental physics governing trapped interacting bosons. The most basic theoretical and computational tool for trapped BECs - Gross-Pitaevskii (GP) equation, or, so-called standard mean-field - has been successful in explaining many observations. Yet, the need to go beyond GP is well understood (and documented) by the scientific community; There are many phenomena it cannot explain nor uncover.Recently, utilizing our extended, multi-orbital mean-field approach we have predicted several new physical phenomena. These include the existence and generality of macroscopic fragmentation in the ground and excited states of BECs, a zoo of quantum phases and excitations of bosons in optical lattices, and a rich pathway from condensation via fragmentation to fermionization of trapped cold bosonic systems. The proposed project is aimed at: (1) Continuing the development of our multi-orbital approach, in one- and in higher dimensions, and developing designated many-body tools [self-consistent timeindependent and time-dependent multiconfigurational methods] which are natural extensions of our multi-orbital approach for trapped interacting bosons. (2) Studying the rich physics emerging from the trapping of and manipulating interacting bosons, continuing to predict new physical effects, stimulating experiments and explaining their outcomes. A major goal is to describe the many-body physics accompanying ground and excited-state fragmentation and quantum phase transitions in traps and the many-body dynamics of condensates immersed in different traps and upon their release.