冷气体中的热点问题
Hot Topics in Cold Gases
摘要：
自1995年首次在实验上实现冷原子气体中的玻色-爱因斯坦凝聚以来，这一领域的活动激增。巧妙的实验使我们能够探测接近零温度的物质，并揭示量子力学赋予自然界的一些迷人效应。对于数学物理学家来说，从第一原理（即从基础的多体薛定谔方程开始）理解这些各种现象是一个挑战。这方面的最新进展主要是关于稀冷量子气体的平衡性质。我们将在这篇文章中解释一些结果，并描述理解这些现象所涉及的数学。内容包括正温度下的基态能量和自由能，粒子间相互作用对玻色-爱因斯坦凝聚临界温度的影响，以及快速旋转气体中超流和量子化涡旋的出现。
英文摘要：
Since the first experimental realization of Bose-Einstein condensation in cold atomic gases in 1995 there has been a surge of activity in this field. Ingenious experiments have allowed us to probe matter close to zero temperature and reveal some of the fascinating effects quantum mechanics has bestowed on nature. It is a challenge for mathematical physicists to understand these various phenomena from first principles, that is, starting from the underlying many-body Schrödinger equation. Recent progress in this direction concerns mainly equilibrium properties of dilute, cold quantum gases. We shall explain some of the results in this article, and describe the mathematics involved in understanding these phenomena. Topics include the ground state energy and the free energy at positive temperature, the effect of interparticle interaction on the critical temperature for Bose-Einstein condensation, as well as the occurrence of superfluidity and quantized vortices in rapidly rotating gases.
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。
