Communications in Mathematical Physics

, Volume 331, Issue 1, pp 261–295 | Cite as

On the Steady State Correlation Functions of Open Interacting Systems

  • H. D. Cornean
  • V. Moldoveanu
  • C.-A. Pillet


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.


Entropy Production Open Quantum System Quantum Statistical Mechanic Entropy Production Rate Full Counting Statistic 
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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mathematical SciencesAalborg UniversityAalborgDenmark
  2. 2.National Institute of Materials PhysicsBucharest-MagureleRomania
  3. 3.Aix-Marseille Université, CNRS UMR 7332, CPTMarseilleFrance
  4. 4.Université de Toulon, CNRS UMR 7332, CPTLa GardeFrance
  5. 5.FRUMAMMarseilleFrance

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