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Advances in Condensed Matter Physics
Volume 2015, Article ID 835897, 9 pages
http://dx.doi.org/10.1155/2015/835897
Research Article

On New Families of Integrals in Analytical Studies of Superconductors within the Conformal Transformation Method

1Faculty of Fundamental Problems of Technology, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
2University of Michigan and Shanghai Jiao Tong University Joint Institute, 800 Dongchuan Road, Shanghai 200240, China
3Faculty of Computer Science and Management, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Received 19 April 2015; Accepted 2 July 2015

Academic Editor: Jaume Gázquez

Copyright © 2015 Ryszard Gonczarek et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We show that, by applying the conformal transformation method, strongly correlated superconducting systems can be discussed in terms of the Fermi liquid with a variable density of states function. Within this approach, it is possible to formulate and carry out purely analytical study based on a set of fundamental equations. After presenting the mathematical structure of the -wave superconducting gap and other quantitative characteristics of superconductors, we evaluate and discuss integrals inherent in fundamental equations describing superconducting systems. The results presented here extend the approach formulated by Abrikosov and Maki, which was restricted to the first-order expansion. A few infinite families of integrals are derived and allow us to express the fundamental equations by means of analytical formulas. They can be then exploited in order to find quantitative characteristics of superconducting systems by the method of successive approximations. We show that the results can be applied in studies of high- superconductors and other superconducting materials of the new generation.