强作用物质中的非均匀手征凝聚

In a recent decade, the QCD phase structure at finite density and relatively low temperature is studied actively. While the quark Cooper-pair condensates should dominate at an asymptotically high density-limit because of the Cooper instability, the particle-hole condensates become competitive when the interaction is strong enough at moderate density，which are related to the inhomogeneous chiral codensate. It has been realized that by allowing the inhomogeneous chiral condesate vary only in one spatial dimension, the dimensionally reduced effective Hamiltonian becomes formally identical to that the (1＋1)-dimensional Gross-Nevue model, for which self-consistent solutions are already well known. Observing that, One finds the real one-dimensional modulation is the most favored inhomogeneous chiral condensate. However, recent large Nc analysis predicts the Quarkyonic matter, in which the chiral symmetry is broken by the complex chiral spirals. Taking into account that the inhomogeneous condensate breaks the rotational symmetry,there should be many additional channels appearing in the Nambu-Jona-Lasinio model as a consequence of the enlarged Feirz identity.In this respect, we should be able to treat the different inhomogeneous chiral condensates at equal footing and thus find the most favored one by comparing their different free energy. The QCD phase structure in a magnetic field has been extensively studing now, expecially the interplay between chiral symmetry and a magnetic field. Magnetic catalysis is one of the most significant prediction of on the theory side, while the latest lattice-QCD data supports the opposite phenomenon. We will investigate the behavior of inhomogeneous chiral condensate in a magnetic field,expecially in strong magnetic field where fermions undergo dimensional reduction, expecting to provide some explanations for this controdiction. In QCD phase diagram, the inhomogenous chiral condensate emerges in the area which lies just outside the boundary of the ordinary chiral transition and thus extends the chiral symmetry broken phase to a low termperature and high density region.We will reinvestigate predictions of the inhomogeneous chiral condensate to the QCD phase diagram by including the Polyakov loop as well as the presence of a magnetic field.

在中等密度的夸克物质中，除了常规的夸克与反夸克形成的各向同性的手征凝聚和夸克与夸克配对形成的色超导凝聚之外，还可能存在夸克与空穴形成的非均匀的手征凝聚，如手征密度波等。针对目前QCD有效模型对非均匀的手征凝聚的研究的不自洽性，导致其预言的非均匀的手征凝聚的形式与大Nc的分析结果不相同，本项目拟利用QCD的有效模型自洽地比较不同形式的非均匀的手征凝聚，确定中等密度的夸克物质中最稳定的非均匀的凝聚形式，进而研究其对QCD相结构的影响。同时联系当前外磁场中QCD相结构这一热点问题，尤其是格点QCD计算的手征对称性恢复的温度随磁场的变化关系与理论预言的磁场对手征凝聚的催化作用矛盾，研究非均匀的手征凝聚在外磁场中行为及其对外磁场环境中的QCD相结构的影响，并与格点QCD计算的结果比较，探讨解决格点模拟与理论预言产生矛盾的物理根源。

研究强作用物质对电磁探针的响应是理解强相互作用的重要手段。实验上既能产生高温高密的夸克物质也能产生极强的磁场(约为10^18G)的非对心的重粒子碰撞为此类研究提供了极佳的实验平台，同时也要求在理论上更清楚地理解强相互作用的微观机制(QCD)在外磁场中的性质。其中，手征对称性的自发破缺对外磁场的响应和QCD的手征磁效应(CME)是当前的前沿理论问题。上世纪九十年代初，Gusynin, Miransky和Shovkovy发现了QED中的手征磁催化效应，即磁场对手征凝聚有增强作用。该结果被认为具有一般性，即在QCD也是如此。但格点QCD的计算却发现QCD中的手征凝聚随磁场的增加而减小，被称为反磁催化效应。QCD中的反磁催化效应产生的物理根源还不清楚。在本项目的研究中，我们发现磁场除了对手征凝聚有催化效应之外，也会增强量子涨落的效应。尤其在强磁场极限下，量子涨落将导致手征凝聚无法发生，该结果与Coleman-Mermin-Wagner定理一致。因此，我们提出磁场对手征凝聚的效应实际是磁催化与量子涨落相互竞争的结果。如果催化效应强于量子涨落的效应，手征凝聚将随着磁场的增大而增大，表现为磁催化效奕；反之则为反磁催化效应。我们利用与QCD手征凝聚类似的玻色-爱因斯坦凝聚系统作了定量的计算。在非相对论系统中，当费米子之间的耦合较强时，量子涨落的效应将强于磁催化效应， 玻色-爱因斯坦凝聚的临界温度随着磁场的增大而减小，即反磁催化效应。只有当费米子之间的耦合较弱时，量子涨落的效应较小， 玻色-爱因斯坦凝聚的临界温度才随着磁场的增大而增大，即表现为磁催化效应。而在相对论系统中，由于费米子质量对磁场的依赖，即使是在强耦合条件下，也只有在磁场较小时才表现为反磁催化效应。因此我们认为QCD中的反磁催化效应可能不是量子涨落的效应，而是因为QCD本身复杂的动力学性质引起的。另外，本项目还研究了格点QCD中的手征磁效应(CME)。我们发现格点QCD模拟中产生的非零的手征电流可能只是有效格点(finite size)的假象，在连续极限下并不存在。我们初步认为手征磁效应(CME)预言的手征电流可能只在非平衡系统中产生，更肯定的结论还需要进一步的深入研究。