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We extend [Bru-de Siqueira Pedra-Hertling, J. Math. Phys. 56 (2015) 051901] 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.
We conclude our analysis of the linear response of charge transport in lattice systems of free fermions subjected to a random potential by deriving general mathematical properties of its conductivity at the macroscopic scale. The present paper belong
Electric resistance in conducting media is related to heat (or entropy) production in presence of electric fields. In this paper, by using Arakis relative entropy for states, we mathematically define and analyze the heat production of free fermions w
Free fermions on Johnson graphs $J(n,k)$ are considered and the entanglement entropy of sets of neighborhoods is computed. For a subsystem composed of a single neighborhood, an analytical expression is provided by the decomposition in irreducible sub
Electromagnetic Casimir stresses are of relevance to many technologies based on mesoscopic devices such as MEMS embedded in dielectric media, Casimir induced friction in nano-machinery, micro-fluidics and molecular electronics. Computation of such st
We propose and analyse a mathematical measure for the amount of squeezing contained in a continuous variable quantum state. We show that the proposed measure operationally quantifies the minimal amount of squeezing needed to prepare a given quantum s