The semi-circle diagrams in the stochastic limit of the Anderson model

We prove that, in the stochastic limit of the Anderson model only the non-crossing diagrams survive for the transition amplitude from the first excited state of the free Hamiltonian to the first excited state of the interacting Hamiltonian. This confirms a conjecture of Migdal (1958) and Abrikosov, Gorkov, Dzyaloshinski (1975). From this we deduce a closed (nonlinear) Schwinger–Dyson type equation for the limit transition amplitude whose solution can be found and gives the explicit dependence of this amplitude on the momentum of the excited state. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0219025798000259