- 13-88 J.-B. Bru, W. de Siqueira Pedra, C. Kurig
- AC Conductivity Measure from Heat Production of Free Fermions in Disordered Media
Nov 4, 13
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Abstract. We extend [BPK2] in order to study the linear response of free fermions
on the lattice within a (independently and identically distributed) random
potential to a macroscopic electric field that is time and space dependent. We obtain the notion of a macroscopic AC conductivity measure which only results from the second principle of thermodynamics. The latter corresponds here to the positivity of the heat production for cyclic processes on equilibrium states. Its Fourier transform is a continuous bounded function which is naturally called (macroscopic) conductivity. We additionally derive Green Kubo relations involving time correlations of bosonic fields coming from current fluctuations in the system. This is reminiscent of non commutative central limit theorems.