AI 中文总结
本课程分三讲介绍二维量子气体，涵盖玻色-爱因斯坦凝聚、超流性、二维特性如准长程有序和BKT机制，以及快速旋转气体的涡旋晶格熔化。
AI 中文摘要
本课程关于二维量子气体，为圣保罗ICTP-SAIFR第四届光与冷原子学校准备，分为三个讲座。第一讲为导论，涉及理想气体中的玻色-爱因斯坦凝聚、弱相互作用极限下相互作用的影响、Gross-Pitaevskii方程及其流体力学表述，以及超流性。第二讲专门讨论二维量子气体的主要特征：相互作用的重要性、增强的相位涨落和准长程有序的出现、通过Berezinskii-Kosterlitz-Thouless机制的超流性、标度对称性。第三讲以研讨会形式呈现，关于快速旋转的准二维玻色气体和涡旋晶格的热熔化。随附这些笔记的幻灯片可在学校网站上找到：https://www.ictp-saifr.org/slca2025/。
英文摘要
This course on two-dimensional quantum gases, prepared for the S{ã}o Paulo ICTP-SAIFR IVth School on Light and Cold Atoms, is organized into three lectures. The first introductory lecture addresses Bose-Einstein condensation in an ideal gas, the effect of interactions in the weakly interacting limit, Gross-Pitaevskii equation and its hydrodynamic formulation, as well as superfluidity. The second lecture is devoted to the main features of two-dimensional quantum gases: importance of the interactions, enhanced phase fluctuations and the emergence of a quasi long-range order, superfluidity through the Berezinskii-Kosterlitz-Thouless mechanism, scaling symmetry. The third lecture has taken the form of a seminar on fast rotating quasi two-dimensional Bose gases and thermal melting of the vortex lattice. The slides accompanying these notes can be found on the school website: https://www.ictp-saifr.org/slca2025/.
Comments67 pages. Comments welcome
Journal refSao Paulo ICTP-SAIFR IVth School on Light and Cold Atoms, Oct 2025, S{ã}o Paulo, Brazil
