Efficient Computational Procedure for the Analytic Continuation of Eliashberg Equations

• Main Authors: Johansson, Joakim, Lauren, Fredrik
• Format: Others
• Language: English
• Published: Uppsala universitet, Institutionen för teknikvetenskaper 2014
• Subjects: superconductivity; analytic continuation; BCS theory
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-226315

The superconducting order parameter and the mass renormalization function can be solved either at discrete frequencies along the imaginary axis, or as a function of continuous real frequencies. The latter is done with a method called analytic continuation. The analytic continuation can conveniently be done by approximating a power series to the functions, the Padè approximation. Studied in this project is the difference between the Padè approximation, and a formally exact analytic continuation of the functions. As it turns out, the Padè approximant is applicable to calculate the superconducting order parameter at temperatures sufficiently below the critical temperature. However close to the critical temperature the approximation fails, while the solution presented in this report remains reliable.