玻色-爱因斯坦凝聚的有限温度模型
Finite Temperature Models of Bose-Einstein Condensation
摘要：
对囚禁的弱相互作用玻色-爱因斯坦凝聚体的理论描述的特点是，随着时间的推移，由具有非常不同背景的研究人员开发了大量看似非常不同的方法。这个领域的新来者，实验家和年轻的研究人员都面临着相当大的挑战，在丰富的理论模型的“迷宫”中导航，现有方法之间的简单对应关系并不总是非常透明的。这篇文章对这些理论作了一般性的介绍，试图挑出某些“类别的方法”的共同特点和不足之处，这些“类别的方法”是按其物理内容而不是按其特定的数学实施方式确定的。这本书的结构是以一种非专业人士可以访问的方式，具有良好的量子力学工作知识。虽然一些熟悉的概念，量子场论将是一个优势，关键的概念，如占领数表示的第二次量子化仍然简要回顾。在一般性介绍之后，从Gross-Pitaevskii方程的基本零温度形式主义开始，逐渐建立模型的复杂性。这种结构使读者能够根据他们的特殊需要探索不同层次的理论发展（平均场，数量守恒和随机）。除了它的“培训元素”，我们希望，这将证明是有用的，积极的研究人员在这一领域，无论是在不同的理论模型之间的对应关系，并作为现有的和发展中的有限温度理论模型的参考来源。
英文摘要：
The theoretical description of trapped weakly-interacting Bose-Einstein condensates is characterized by a large number of seemingly very different approaches which have been developed over the course of time by researchers with very distinct backgrounds. Newcomers to this field, experimentalists and young researchers all face a considerable challenge in navigating through the `maze' of abundant theoretical models, and simple correspondences between existing approaches are not always very transparent. This Tutorial provides a generic introduction to such theories, in an attempt to single out common features and deficiencies of certain `classes of approaches' identified by their physical content, rather than their particular mathematical implementation. This Tutorial is structured in a manner accessible to a non-specialist with a good working knowledge of quantum mechanics. Although some familiarity with concepts of quantum field theory would be an advantage, key notions such as the occupation number representation of second quantization are nonetheless briefly reviewed. Following a general introduction, the complexity of models is gradually built up, starting from the basic zero-temperature formalism of the Gross-Pitaevskii equation. This structure enables readers to probe different levels of theoretical developments (mean-field, number-conserving and stochastic) according to their particular needs. In addition to its `training element', we hope that this Tutorial will prove useful to active researchers in this field, both in terms of the correspondences made between different theoretical models, and as a source of reference for existing and developing finite-temperature theoretical models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
