Weinberg本征值与低动量势对
Weinberg Eigenvalues and Pairing with Low-Momentum Potentials
摘要：
核子-核子相互作用演化到低动量时的非微扰性质最近在自由空间和有限密度下用Weinberg本征值作诊断进行了研究。这种分析在这里扩展到费米面附近的介质本征值研究配对。对于一个固定的密度和截止λ值，本征值在费米面附近的幅度上任意增加，表明配对不稳定性。当使用正常相位传播子时，具有复能量的Weinberg分析成为稳定性分析的一种形式，并且可以从最大吸引本征值估计配对间隙。用Nambu-Gorkov格林函数，最大的吸引本征值接近费米面，表明存在束缚态（库珀对），相应的本征向量导致自洽能隙函数。
英文摘要：
The nonperturbative nature of nucleon-nucleon interactions evolved to low momentum has recently been investigated in free space and at finite density using Weinberg eigenvalues as a diagnostic. This analysis is extended here to the in-medium eigenvalues near the Fermi surface to study pairing. For a fixed value of density and cutoff Lambda, the eigenvalues increase arbitrarily in magnitude close to the Fermi surface, signaling the pairing instability. When using normal-phase propagators, the Weinberg analysis with complex energies becomes a form of stability analysis and the pairing gap can be estimated from the largest attractive eigenvalue. With Nambu-Gorkov Green's functions, the largest attractive eigenvalue goes to unity close to the Fermi surface, indicating the presence of bound states (Cooper pairs), and the corresponding eigenvector leads to the self-consistent gap function.
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