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

Dipole excitations:ω ij = ɛ j − ɛ i − 1/r ijɛ0.2µ∆g 0 ∝ 1 WWg(ɛ)Compact: typical sizeklr, typical separationr 0 ∼ ∆ −1Baranovskii, Shklovskii, Efros (1980): ∆E i→j,k→l = ω ij + ω kl − 1 r 3 > 0α =1/2jr 0ig L (!) and f L (!, R max =1)0.150.10.052-DOS∼ ω −1/3r3./pi ! 200 0.1 0.2 0.3 0.4 0.5 0.6!1-DOSSingle-particle DOSPair DOS, R max =12-DOS:f(ω,R)= 1 V∑(ij),r ij ≤R[ 〈δ(ω − ω ij )) 〉] av ∝-> Contribute to ac (but not dc) conductivity-> dominate thermodynamics at low Tg 0ln(∆/ω) α