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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 within external potentials. More precisely, we investigate the heat production of the non-autonomous C*-dynamical system obtained from the fermionic second quantization of a discrete Schrodinger operator with bounded static potential in presence of an electric field that is time- and space-dependent. It is a first preliminary step towards a mathematical description of transport properties of fermions from thermal considerations. This program will be carried out in several papers. The regime of small and slowly varying in space electric fields is important in this context, and is studied the present paper. We use tree-decay bounds of the $n$-point, $nin 2mathbb{N}$, correlations of the many-fermion system to analyze this regime. We verify below the 1st law of thermodynamics for the system under consideration. The latter implies, for systems doing no work, that the heat produced by the electromagnetic field is exactly the increase of the internal energy resulting from the modification of the (infinite volume) state of the fermion system. The identification of heat production with an energy increment is, among other things, technically convenient. We initially focus our study on non-interacting (or free) fermions, but our approach will be later applied to weakly interacting fermions.
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 th
We make use of the Quantum Hamilton-Jacobi (QHJ) theory to investigate conditional quasi-solvability of the quantum symmetric top subject to combined electric fields (symmetric top pendulum). We derive the conditions of quasi-solvability of the time-
It was recently shown [2] that the resolvent algebra of a non-relativistic Bose field determines a gauge invariant (particle number preserving) kinematical algebra of observables which is stable under the automorphic action of a large family of inter
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
We propose a single-step non-generational conjecture of all first class constraints,(involving only variables compatible with canonical Poisson brackets), for a realistic gauge singular field theory. We verify our proposal for the free electromagneti