超导对称类之间的交叉
Crossovers between superconducting symmetry classes
摘要：
本文研究了在磁场中，与两个具有相位差$π$的超导体耦合的金属小晶粒的平均态密度。用随机矩阵理论描述了晶粒中低能激发的谱，其对称性取决于磁场强度和与超导体的耦合。在极限情况下，实现了纯超导对称类。对于超导体的中间磁场或耦合，系统经历不同对称类之间的交叉。利用超对称σ模型，我们导出了A-C和CI-C对称性交叉区的平均态密度的精确表达式。
英文摘要：
We study the average density of states in a small metallic grain coupled to two superconductors with the phase difference $π$, in a magnetic field. The spectrum of the low-energy excitations in the grain is described by the random matrix theory whose symmetry depends on the magnetic field strength and coupling to the superconductors. In the limiting cases, a pure superconducting symmetry class is realized. For intermediate magnetic fields or couplings to the superconductors, the system experiences a crossover between different symmetry classes. With the help of the supersymmetric sigma-model we derive the exact expressions for the average density of states in the crossovers between the symmetry classes A-C and CI-C.
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