超导理论中Bogoliubov-Tolmachev-Shirkov模型的数值解和临界温度研究
发布时间：2019-03-17 13:21
【摘要】：本文主要研究的是超导理论中的BTS模型:它是BCS模型核函数变号的情况.据我们所知,BCS模型核函数恒正的情形已做出数值结果,而对于核函数变号的BTS模型还没有相应的数值解.本文针对BTS模型提出了最小-混合近似算法和最大-混合近似算法,并证明了其收敛性.针对两种数值算法,文中分别采用半隐半隐和半显半隐两种迭代格式进行计算,近似求解了该模型的数值解和临界温度.我们提出的算法不仅有效,而且可以解释很多重要的物理现象.数值例子验证了文中给出的理论结果。
[Abstract]:In this paper, we mainly study the BTS model in the theory of superconductivity: it is the case of the change of the sign of the kernel function of the BCS model. As far as we know, numerical results have been obtained in the case of the kernel function being positive in the BCS model, but there is no corresponding numerical solution for the BTS model with the kernel function sign changing. In this paper, the minimum-mixed approximation algorithm and the maximum-mixed approximation algorithm are proposed for the BTS model, and their convergence is proved. For two kinds of numerical algorithms, two iterative schemes, semi-implicit scheme and semi-explicit-semi-implicit scheme, are used to calculate the numerical solution and critical temperature of the model. Our algorithm is not only effective, but also can explain many important physical phenomena. Numerical examples verify the theoretical results given in the paper.
【学位授予单位】：河南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O241.8
本文编号：2442341
[Abstract]:In this paper, we mainly study the BTS model in the theory of superconductivity: it is the case of the change of the sign of the kernel function of the BCS model. As far as we know, numerical results have been obtained in the case of the kernel function being positive in the BCS model, but there is no corresponding numerical solution for the BTS model with the kernel function sign changing. In this paper, the minimum-mixed approximation algorithm and the maximum-mixed approximation algorithm are proposed for the BTS model, and their convergence is proved. For two kinds of numerical algorithms, two iterative schemes, semi-implicit scheme and semi-explicit-semi-implicit scheme, are used to calculate the numerical solution and critical temperature of the model. Our algorithm is not only effective, but also can explain many important physical phenomena. Numerical examples verify the theoretical results given in the paper.
【学位授予单位】：河南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O241.8
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