Elementary excitations and avalanches in the Coulomb ... - PhysioNet

Self-consistent equation (SCE):(Efros 1976)g(ε) =g 0 (ε) exp[− 2π 3∫ ∞0g(ε ′ )dε ′ ](ε ′ + |ε|) 33DAsymptotic solution forε → 0: g(ε) = 3 π ε2Improved asymptotics: oscillations around g(ε) = 3 π ε2(see Martin Goethe’s poster)Modified SCE:Efros, Skinner, Shklovskii,arXiv:1105.1712v1[g(ε) =g 0 (ε)P (ε) exp − 2π 3[ ( ) ( ∆ ∆P (ε) exp −γ ln −7/4ɛ ɛ∫ ∞g(ε ′ )dε ′ ](ε ′ + |ε|) 3) ( )] ∆fɛ0interpolating functionf(x) = (1 − x) η θ(1 − x)Asymptotic solutiong(ε) ∼ g 0 (ε)P (ε)ε ≪ ∆Approximatelyg(ε) = 3 π ε2forε ∼ ∆