The critical temperature and gap solution in the Bardeen-Cooper-Schrieffer theory of superconductivity

Abstract: "The paper studies the problem of numerical approximations of the critical transition temperature and the energy gap function in the Bardeen-Cooper-Schrieffer equation arising in superconductivity theory. The positive kernel function leads to a phonon dominant state at zero temperature. Much attention is given to the equation defined on a bounded region. Two discretized versions of the equation will be introduced. The first version approximates the desired solution from below, while the second, from above. Numerical examples are presented to illustrate the efficiency of the method. Besides, The [sic] approximations of a full space solution and the associated critical temperature by solution sequences constructed on bounded domains are also investigated."