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On the Steady State Correlation Functions of Open Interacting Systems

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Abstract

We address the existence of steady state Green-Keldysh correlation functions of interacting fermions in mesoscopic systems for both the partitioning and partition-free scenarios. Under some spectral assumptions on the non-interacting model and for sufficiently small interaction strength, we show that the system evolves to a NESS which does not depend on the profile of the time-dependent coupling strength/bias. For the partitioned setting we also show that the steady state is independent of the initial state of the inner sample. Closed formulae for the NESS two-point correlation functions (Green-Keldysh functions), in the form of a convergent expansion, are derived. In the partitioning approach, we show that the 0th order term in the interaction strength of the charge current leads to the Landauer-Büttiker formula, while the 1st order correction contains the mean-field (Hartree–Fock) results.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220, Aalborg, Denmark

    H. D. Cornean

  2. National Institute of Materials Physics, P.O. Box MG-7, Bucharest-Magurele, Romania

    V. Moldoveanu

  3. Aix-Marseille Université, CNRS UMR 7332, CPT, 13288, Marseille, France

    C.-A. Pillet

  4. Université de Toulon, CNRS UMR 7332, CPT, 83957, La Garde, France

    C.-A. Pillet

  5. FRUMAM, Marseille, France

    C.-A. Pillet

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  1. H. D. Cornean
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  2. V. Moldoveanu
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Communicated by H. Spohn

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Cornean, H.D., Moldoveanu, V. & Pillet, CA. On the Steady State Correlation Functions of Open Interacting Systems. Commun. Math. Phys. 331, 261–295 (2014). https://doi.org/10.1007/s00220-014-1925-0

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