We apply Lieb–Robinson bounds for multi-commutators we recently derived (Bru and de Siqueira Pedra, Lieb–Robinson bounds for multi-commutators and applications to response theory, 2015) to study the (possibly non-linear) ...

We consider free lattice fermions subjected to a static bounded potential and a timeand space-dependent electric field. For any bounded convex region R ⊂ ℠(d (d ≥ 1) of space, electric fields ε within R drive currents. ...

We study the dynamics of interacting lattice fermions with random hopping amplitudes and random static potentials, in presence of time-dependent electromagnetic fields. The interparticle interaction is short-range and ...

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 ...

Electric resistance in conducting media is related to heat (or entropy) production in the presence of electric fields. In this paper, by using Araki's relative entropy for states, we mathematically define and analyze the ...

We define a Banach space $\mathcal{M}_{1}$ of models for fermions or quantum spins in the lattice with long range interactions and explicit the structure of (generalized) equilibrium states for any $\mathfrak{m}\in ...