朗道费米液体理论已有60年的历史，成功地描述了金属导体、近滕杂质、重费米子等相互作用费米系统的普适量子流体行为。另一方面，拉亭戈液体理论描述了一维多体系统的普适低能物理特性。从微观上他们有着完全不同的色散关系、量子统计及态密度，但是一维和高维量子液体的许多宏观物理特性是相同的。为什么量子液体的普适特性不依赖于系统的微观机制？为什么经典和量子多体系统在连续相变附近的非平衡动力学都服从Kibble-Zurek机制？理解不同量子多体系统的普适现象及之间内在联系一直是前沿物理中极具挑战性的难题。本项目通过研究超冷原子精确解模型的量子涨落、多体关联、临界动力学揭示费米和拉亭戈液体的共同本质；通过研究低维非平衡冷原子系统的量子热化和动力学过程建立量子相变临界动力学的严格标度理论。预期结果将拓展对量子多体现象的理解，并为基于冷原子及离子阱实验的精密测量提供理论参考。

It is already more than 60 years that the Landau Fermi liquid is successfully used for describing universal quantum fluid behaviour in electronic metals, Kondo impurity, heavy fermions, etc. On the other hand, the Luttinger liquid theory describes universal low energy physics of many-body interacting systems in one dimension. Although Fermi and Luttinger liquids have different dispersions, quantum statistics and densities of states at microscopic level, the macroscopic properties of these quantum liquids are common. It is natural to ask why the macroscopic behaviour of such universal quantum liquids does not depend on the microscopic details? Why the dynamics of non-equilibrium classical and quantum many-body systems near continuous phase transitions satisfies a very general Kibble-Zurek mechanism? However, understanding universal nature of quantum liquids of various types and their intrinsic connection is a long-standing challenging problem in the frontiers of theoretical physics. The aim of this project is to discover the essence of the Fermi and Luttinger liquid as well as universal laws of quantum fluids with high symmetries through the study of quantum fluctuations, many-body correlations, critical dynamics of exactly solvable models of ultracold atoms. Moreover, we will build up an exact scaling theory of quantum critical dynamics through the study of thermalization and quantum dynamics in exactly solvable models of cold atoms. The expected results will extend our understanding of quantum many-body phenomena and pave a way for high precision measurement experiment with ultracold atoms, ions, etc.