The coupled linearised Usadel and self-consistency equations are transformed into an explicit matrix eigenvalue problem whose solution gives T_c and the spatial profiles of the order parameter.
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Analytical solution of coupled self--consistency and linearised Usadel equations for the dirty superconductors at $T_c$ and with the proximity effect
The coupled linearised Usadel and self-consistency equations are transformed into an explicit matrix eigenvalue problem whose solution gives T_c and the spatial profiles of the order parameter.