We present an overview of mathematical results on the low temperature properties of dilute quantum gases, which have been obtained in the past few years. The presentation includes a discussion of Bose–Einstein condensation, the excitation spectrum for trapped gases and its relation to superfluidity, as well as the appearance of quantized vortices in rotating systems. All these properties are intensely being studied in current experiments on cold atomic gases. We will give a description of the mathematics involved in understanding these phenomena, starting from the underlying many-body Schrödinger equation.

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冷气中的热门话题

我们概述了在过去几年中获得的关于稀量子气体的低温特性的数学结果。演讲内容包括Bose-Einstein凝聚，捕集气体的激发光谱及其与超流动性的关系，以及旋转系统中量化涡旋的出现。当前的冷原子气体实验正在对所有这些特性进行深入研究。我们将从基本的多体薛定ding方程开始，对理解这些现象所涉及的数学进行描述。