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dc.contributor.authorBru, J.-B. 
dc.contributor.authorde Siqueira Pedra, W. 
dc.contributor.authorRatsimanetrimanana, A.
dc.description.abstractWe contribute an extension of large-deviation results obtained in [N.J.B. Aza, J.-B. Bru, W. de Siqueira Pedra, A. Ratsimanetrimanana, J. Math. Pures Appl. 125 (2019) 209] on conductivity theory at atomic scale of free lattice fermions in disordered media. Disorder is modeled by (i) a random external potential, like in the celebrated Anderson model, and (ii) a nearest-neighbor hopping term with random complex-valued amplitudes. In accordance with experimental observations, via the large deviation formalism, our previous paper showed in this case that quantum uncertainty of microscopic electric current densities around their (classical) macroscopic value is suppressed, exponentially fast with respect to the volume of the region of the lattice where an external electric field is applied. Here, the quantum fluctuations of linear response currents are shown to exist in the thermodynamic limit and we mathematically prove that they are related to the rate function of the large deviation principle associated with current densities. We also demonstrate that, in general, they do not vanish (in the thermodynamic limit) and the quantum uncertainty around the macroscopic current density disappears exponentially fast with an exponential rate proportional to the squared deviation of the current from its macroscopic value and the inverse current fluctuation, with respect to growing space (volume) scales.en_US
dc.description.sponsorshipFAPESP (2017/22340-9); CNPq (309723/2020-5); by the Basque Government through the grant IT641-13; MTM2017-82160-C2-2-Pen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.subjectQuantum fluctuationsen_US
dc.subjectlarge deviationsen_US
dc.subjectFermionic charge transporten_US
dc.subjectdisordered mediaen_US
dc.titleQuantum Fluctuations and Large Deviation Principle for Microscopic Currents of Free Fermions in Disordered Mediaen_US
dc.identifier.doiDOI: 10.2140/paa.2020.2.943
dc.journal.titlePure and Applied Analysisen_US

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Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España