论文标题
超导性准经典理论的稀疏建模方法
Sparse modeling approach for quasiclassical theory of superconductivity
论文作者
论文摘要
我们提出了用于超导性准经典理论的稀疏建模方法，从而降低了求解差距方程的计算成本。最近提出的稀疏建模方法基于以下事实：绿色的功能的信息少于其光谱函数，因此可以压缩而不会丢失相关信息。通过在稀疏建模方法中使用绿色功能的所谓中间表示，只能以10-100个采样的Matsubara Green的功能来求解差距方程，而常规的准经典理论则需要100-1000个。我们通过求解eilenberger方程和差距方程来展示我们方法在批量和涡旋状态下的效率。我们声称，在超导性的准经典理论中，基于Matsubara形式的所有理论方法中，稀疏建模方法都是适当的。
We propose the sparse modeling approach for quasiclassical theory of superconductivity, which reduces the computational cost of solving the gap equations. The recently proposed sparse modeling approach is based on the fact that the Green's function has less information than its spectral function and hence is compressible without loss of relevant information. With the use of the so-called intermediate representation of the Green's function in the sparse modeling approach, one can solve the gap equation with only 10-100 sampled Matsubara Green's functions, while the conventional quasiclassical theory needs 100-1000 ones. We show the efficiency of our method in bulk and vortex states, by self-consistently solving the Eilenberger equations and gap equations. We claim that the sparse modeling approach is appropriate in all theoretical methods based on the Matsubara formalism in the quasiclassical theory of superconductivity.
