超越现有的理论模式和框架，我们的研究工作将利用Polyakov-Quark-Meson和Polyakov- Nambu-Jona-Lasinio手征孤子模型深入、系统地研究从强子相到夸克相热力学状态方程的一致性自洽描述。我们研究方法最大的优势是：一方面在强子相，理论方法能够很好地描述核子及强子在核物质和有限核中结构的改变，并考虑强子之间的叠加问题；另一方面在高温、高密情况下，无论对于连续过渡相变还是一级相变，理论方法自然地实现对夸克物质热力学性质及其相图结构的成功描述，且可以与格点QCD和相对论重离子对撞实验的结果进行直接比较。此外，实用性和有效性是我们发展该新研究途径的最大要求，所以我们还将引入强磁场的影响，以及包括库仑相互作用和表面能等有限尺度效应，探讨强子-夸克相变过程中可能存在的各向异性几何结构“Pasta”相，并且将所得结果检验应用到超新星爆发和致密星体的结构等问题中。

Based on the Polyakov-Quark-Meson model (PQM) and the Polyakov- Nambu-Jona-Lasinio model (PNJL), we will extensively study the hadron-quark phase transition, especially focus on the thermodynamical aspects of the hadron-quark phase transition. PQM and PNJL models have so far facilitated the investigation of the full QCD thermodynamics and phase structure at zero and finite quark chemical potential, while it has been shown that the bulk thermodynamic predictions of the model agree well with the lattice QCD data and the experiment. Moreover, the nontopological soliton of the PQM model or the PNJL model has been proven to be a successful approach for the description of the nucleon and hadron structure changes in the nuclear medium. Combining these two features together, while also requiring a soliton embedded in a thermal medium, the model provides a suitable working scheme to simultaneously study both the restoration of chiral symmetry and the possible dissolution of the soliton, which simulates the deconfinement transition of nuclear matter to quark matter. In order to obtain a more precise picture of the hadron-quark phase transition, we also include the effect of the strong magnetic field on the studies. Moreover, another interesting topic about the appearance of the inhomogeneous structures called “pasta”, which are brought about by the surface and the Coulomb interaction effects, will also be considered in the project. Finally, we will discuss some implications on supernova explosion and cooling of compact stars.