NJL型四费米子模型中的库珀配对和有限尺寸效应
Cooper pairing and finite-size effects in a NJL-type four-fermion model
摘要：
本文从含N个费米子的NJL型模型出发，在非零化学势$μ$和零温度下，研究了具有$S^1\otimes S^1\otimes S^1$和$R^2\otimes S^1$形式的非平凡拓扑空间中的费米子和差费米子凝聚及其相结构.特别注意的是致力于超导相的产生。特别地，对于反周期和周期边界条件的情况下，我们已经发现，手征对称性破缺和超导相之间的相变的临界曲线以及相应的凝聚和粒子密度强烈振荡vs $λ\sim 1/L$，其中$L$是周长$S^1$。此外，它表明，在某些有限的$L$值的超导相变被移动到较小的值的$μ$和粒子密度相比，$L=\infty$的情况。
英文摘要：
Starting from a NJL-type model with N fermion species fermion and difermion condensates and their associated phase structures are considered at nonzero chemical potential $μ$ and zero temperature in spaces with nontrivial topology of the form $S^1\otimes S^1\otimes S^1$ and $R^2\otimes S^1$. Special attention is devoted to the generation of the superconducting phase. In particular, for the cases of antiperiodic and periodic boundary conditions we have found that the critical curve of the phase transitions between the chiral symmetry breaking and superconducting phases as well as the corresponding condensates and particle densities strongly oscillate vs $λ\sim 1/L$, where $L$ is the length of the circumference $S^1$. Moreover, it is shown that at some finite values of $L$ the superconducting phase transition is shifted to smaller values both of $μ$ and particle density in comparison with the case of $L=\infty$.
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