Abstract Based on BCS model with the external pair potential formulated in a work Grigorishin (2017) [1] , analogous model with electron-phonon coupling and Coulomb coupling is proposed. The generalized Eliashberg equations in the regime of renormalization of the order parameter are obtained. High temperature asymptotics and effect of Coulomb pseudopotential on them are investigated: as in the BCS model the order parameter asymptotically tends to zero as temperature rises, but the accounting of the Coulomb pseudopotential leads to existence of critical temperature. The effective Ginzburg-Landau theory is formulated for such model.

中文翻译：

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Eliashberg 理论与外部对势

摘要 基于Grigorishin (2017) [1] 中建立的具有外部对势的BCS模型，提出了具有电子-声子耦合和库仑耦合的类比模型。得到了阶参数重整化范围内的广义 Eliashberg 方程。研究了高温渐近性和库仑赝势对它们的影响：如在 BCS 模型中，随着温度的升高，阶次参数渐近趋于零，但库仑赝势的计算导致临界温度的存在。有效的 Ginzburg-Landau 理论是为这种模型制定的。