体和纳米相互作用费米体系的量子信息：自旋空间密度矩阵方法
Quantum Information Aspects on Bulk and Nano Interacting Fermi System: Spin-Space Density Matrix Approach
摘要：
本文通过两个电子自旋形成库珀对（Werner态）的量子纠缠、三重态和量子不协，研究了零温下相互作用费米系统的量子关联.通过计算单电子格林函数，得到了X态形式的双电子空间自旋密度矩阵。研究了量子关联与库珀对电子自旋相对距离和能隙的关系。结果之一是，对于d波情形，纠缠度、量子不协调和三分纠缠对能隙的大小变化敏感。另一个结果是同时存在着共存和不和谐振荡。然后，在弱耦合框架下考虑了三维矩形纳米超导晶粒。纳米尺寸效应通过间隙波动进入。确定了量子关联对超导体长度的依赖关系和三重纠缠鲁棒性的下界。此外，我们发现d波纳米尺度超导颗粒的量子关联强烈依赖于颗粒的长度（与s波的情况相反）。一般来说，晶粒长度越小，纳米尺度对量子关联的影响越大。纳米级d波超导体的量子三分性优于体d波超导体。然而，我们发现无论是体材料还是纳米尺度的s波超导体都具有相同的三部分。进一步研究了超导体的纠缠长度和量子关联长度，证明了存在一个不和谐为零的超导体长度。此外，对于一个给定的固定长度的超导体，在不和谐的峰值和一个峰值的并发同时发生。
英文摘要：
In this paper, we investigate quantum correlation of an interacting Fermi system, which is a nodal superconductor (d-wave superconductor) at zero temperature, via quantum entanglement of two electron spins forming Cooper pairs (Werner state), tripartite and quantum discord. After calculating single-electron Green functions, the two-electron space-spin density matrix, which has X-state form, is obtained. The dependence of quantum correlation to the relative distance of electrons spins of Cooper pair and energy gap is investigated. One of the results is, for d-wave case, concurrence (as a measure of entanglement), quantum discord and tripartite are sensitive to the change of magnitude of gap. Another result is both concurrence and discord oscillate. Then, we consider three-dimensional rectangular nano-superconducting grain in the weak coupling frame. The nano-size effect is entered via gap fluctuation. The dependence of quantum correlation to length of superconductor and lower bound of robustness of tripartite entanglement are determined. Moreover, we show that quantum correlation of d-wave nano-size superconducting grain strongly depends on length of grain (in contrast to s-wave case). In general, it is found that the length of grain lower, the effect of nano-size on quantum correlation higher. Quantum tripartite for nano-scale d-wave superconductor is better than for bulk d-wave superconductor. However, we find out both bulk and nano-size s-wave superconductors have the same tripartite. Furthermore, entanglement length and quantum correlation length are investigated and it is shown that there is a length of superconductor in which discord becomes zero. Also, for a given fixed length of superconductor, both a peak in discord and a peak in concurrence occur simultaneously.
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