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Phase Diagram of Electron Systems near the Superconductor ...

Phase Diagram of Electron Systems near the Superconductor ...

Idea for GNM:CP pairs

Idea for GNM:CP pairs fill localized states of the random potentialforming Bose-insulator. High magnetic field causes depairing.The appearing fermions are weakly localized.But how to treat random potential ?Replica trickHere:translationally invariant systemmethod of optimal fluctuation

Density of states, search for the optimal fluctuation of random potentialν(E) =DU Tr δ(E − Ĥ)e− d 3 rU 2 /2κ 2DU∼ exp−d 3 rU 2 /2κ 2 + λ(E − min Ψ Ψ|H|Ψ)→ U(r) =−λκ 2 |Ψ| 2→ ĤΨ =EΨ → Ψnon-linear Schroedinger equation

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