Title: Nontrivial saddle points for spectral form factors of flat band superconductors Show Chinese title

Title: 平带超导体谱形式因子的非平凡鞍点

Abstract: We derive the spectral form factor of a flat band superconductor in two different ways. In the first approach, we diagonalize the Hamiltonian of this system exactly and numerically sum over the exact eigenstates to find the spectral form factor. In the second approach, we use mean field theory to evaluate the same spectral form factor. We demonstrate that both methods produce the same answer. Mean field theory for spectral form factors possesses features not previously seen in the theory of superconductivity, in particular complex gap functions and non-Hermitian effective Hamiltonians. We explicitly show that these features are indeed necessary to obtain the correct spectral form factor. Show Chinese abstract

Abstract: 我们用两种不同的方法推导了平带超导体的谱函数。 在第一种方法中，我们精确地对角化该系统的哈密顿量，并通过对精确本征态进行数值求和来找到谱函数。 在第二种方法中，我们使用平均场理论来评估相同的谱函数。 我们证明这两种方法都得到了相同的结果。 对于谱函数的平均场理论具有超导理论中以前未见过的特点，特别是复数能隙函数和非厄米有效哈密顿量。 我们明确表明这些特点确实是得到正确的谱函数所必需的。