高密QCD相结构的普遍性研究和在冷原子体系中的模拟

Achievements in past two years: Based on the Polyakov linear sigma model (PLSM) and Nambu-Jona-Lasinio (NJL) model with three light quark flavors, we have extensively investigated the phase diagram at finite temperature and density，thermodynamic properties, the bulk viscosity over entropy density ratio and the interplay between chiral and deconfinement phase transitions. Also we have compared our results with the lattice QCD simulations and other models at zero chemical potential but finite temperature..New proposal: Using a general Ginzburg-Landau-Wilson theory and numerical model calculations, we will study the topological phase structures of dense QCD having both chiral and diquark condensates for two and three flavors. These studies will be investigated both in mean field and beyond mean field approximations deeply and intensively. The dynamical mapping of the topological phase structure to the phenomenological models and lattice QCD simulations will be also addressed with the GLW theory. Dense QCD matter and ultracold atomic systems, although differing by some twenty orders of magnitude in energy scales, share analogous physical aspects. The phase structure for boson-fermion mixtures of cold atoms display features of those in dense QCD with three colors. Based on CJT and functional renormalization group methods, we will extensively study the quantum phase transition, quantum and thermal fluctuations and the transport theory both in dense QCD matter and ultracold atomic systems. Finally, we will try to reveal the properties of dense QCD matter from the atomic physics where boson-fermion mixtures can be realized in the laboratory.

青年科学基金项目进展和主要学术成绩：在三个味夸克的PLSM模型和NJL模型中讨论QCD手征对称性相变和退禁闭相变的相互作用，详细研究体系的热力学性质，并与格点QCD的结果进行比较。.新项目的研究内容：在平均场近似和超出平均场近似下，利用Ginzburg-Landau-Wilson相变理论深入研究高密QCD相图的拓扑结构，并讨论该拓扑结构在唯象模型和格点QCD中的映射和验证，以获得对QCD相变动力学本质有更加深入和全面的理解。与冷原子体系相结合，在平衡态热力学体系中同时研究高密QCD物质和冷原子玻色-费米子耦合体系的量子相变动力学机制，建立彼此的对应关系，之后在非平衡态热力学体系框架下建立相对论量子体系和非相对论体系的微观输运理论。最后与冷原子实验相结合，研究用实验的方法验证高密QCD相图结构的具体方案和途径。

本项目主要研究内容是（1）利用对称性改进的CJT有效势方法，研究了O(4)线性sigma模型在手征极限下的QCD手征相变，证实了在Hatree近似下该方法不但可以得到正确的相变级数，而且保持Goldstone定理不被破坏。利用Kibble-Zurek机制，我们继而讨论了相对论重离子对撞实验LHC中pion弦的产生、演化和衰变，并预言pion弦产生的个数以及可能的观测效应；（2）在平均场近似和考虑费米子真空涨落效应情况下，我们在PQM模型中率先研究了手征孤子解随温度和重子数化学势密度的变化关系，得到了与格点QCD和相对论重离子对撞实验一致的QCD相图结构，最后，我们利用该模型初步讨论了强子-夸克过渡相变的热力学描述。该方法最大的优势是即可以用来研究过渡强子-夸克相变，也可以讨论一级强子-夸克相变，并且能够同时处理手征和退禁闭QCD相变，此外，无论在强子相还是在夸克相研究所依据的唯象模型都是PQM模型，使得我们研究工作方法更加的自洽。

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