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Understanding transport in diffusive systems far away from equilibrium has been a guiding research question for many years. For classical systems we meanwhile posses a unifying framework, the so-called Macroscopic Fluctuation Theory, that describes the large deviation statistics of density and current profiles in a universal way, relying only on two model-dependent transport coefficients. A natural question is if this theory can be extend to incorporate coherent quantum effects? With this aim in mind, the so-called Quantum Simple Symmetric Exclusion Process (QSSEP), a 1d model of noisy fermions, can serve as a microscopic toy model to study fluctuating coherent and diffusive transport. Besides the physical motivation, QSSEP is also interesting for mathematicians, since it is exactly solvable due to a connection with free probability. In this talk I will focus on our recent effort to connect QSSEP to the literature on mesoscopic disordered conductors. In particular, we have studied numerically fluctuations of the spatial distribution of quantum coherence in the 3d Anderson model, a quantity that is more of theoretical interest, since, to our knowledge, it is not (yet) experimentally accessible in diffusive conductors and for this reason has probably not received much attention. But quite surprisingly, the analytic formulae for quantum coherence in QSSEP seem match the numerical results for the Anderson model to a good degree. This opens the possibility that free probability might also be a useful tool in the description of mesoscopic conductors — given, of course, that we are able to find an analytical justification for this correspondence. I will end by proposing a few ideas in that direction.

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Ludwig Hruza, ENS
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Contact: Silvia Pappalardi