凝聚态场论常用公式（6）：超导唯象London方程

2023-03-23 15:23 作者:打电动的阿伟嘻嘻嘻 0人读过 | 我要投稿

超导现象是宏观量子现象，相位是关键，对应的宏观电子态为

$%5Cpsi(%5Cboldsymbol%7Br%7D)%3D%5Cpsi_0(%5Cboldsymbol%7Br%7D)e%5E%7Bi%5Ctheta(%5Cboldsymbol%7Br%7D)%7D%2C%5C%20%5Cpsi_0(%5Cboldsymbol%7Br%7D)%E6%98%AF%E6%A8%A1%2C%5C%20%5Ctheta(%5Cboldsymbol%7Br%7D)%E6%98%AF%E7%9B%B8%E4%BD%8D%2C$

$%E8%B6%85%E5%AF%BC%E7%94%B5%E5%AD%90%E5%9C%A8%E5%8D%95%E4%BD%8D%E4%BD%93%E7%A7%AF%E5%86%85%E7%9A%84%E5%B9%B3%E5%9D%87%E5%AF%86%E5%BA%A6%E4%B8%BA%5C%20n_s%3D%5Cpsi%5E%7B%5Cast%7D(%5Cboldsymbol%7Br%7D)%5Cpsi(%5Cboldsymbol%7Br%7D)%3D%5Cpsi_0%5E2(%5Cboldsymbol%7Br%7D).$

考虑匀质系统 $%5Cpsi_0(%5Cboldsymbol%7Br%7D)%3D%5Cpsi_0%2C%5C%20%5Chat%7B%5Cboldsymbol%7Bp%7D%7D%5Cpsi(%5Cboldsymbol%7Br%7D)%3D%5Cfrac%7B%5Chbar%7D%7Bi%7D%5Cnabla%5Cpsi(%5Cboldsymbol%7Br%7D)%5CRightarrow%20%5Cboldsymbol%7Bp%7D%3D%5Chbar%5Cnabla%5Ctheta.$