Annales Henri Poincaré

, Volume 8, Issue 8, pp 1539–1593

Theory of Non-Equilibrium Stationary States as a Theory of Resonances

  • Marco Merkli
  • Matthias Mück
  • Israel Michael Sigal
Open AccessArticle

DOI: 10.1007/s00023-007-0346-4

Cite this article as:
Merkli, M., Mück, M. & Sigal, I.M. Ann. Henri Poincaré (2007) 8: 1539. doi:10.1007/s00023-007-0346-4


We study a small quantum system (e.g., a simplified model for an atom or molecule) interacting with two bosonic or fermionic reservoirs (say, photon or phonon fields). We show that the combined system has a family of stationary states parametrized by two numbers, T1 and T2 (‘reservoir temperatures’). If T1T2, then these states are non-equilibrium stationary states (NESS). In the latter case we show that they have nonvanishing heat fluxes and positive entropy production and are dynamically asymptotically stable. The latter means that the evolution with an initial condition, normal with respect to any state where the reservoirs are in equilibria at temperatures T1 and T2, converges to the corresponding NESS. Our results are valid for the temperatures satisfying the bound min (T1,T2) > g2 + α, where g is the coupling constant and 0 < α < 1 is a power related to the infra-red behaviour of the coupling functions.

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Copyright information

© Birkhaueser 2007

Authors and Affiliations

  • Marco Merkli
    • 1
  • Matthias Mück
    • 2
  • Israel Michael Sigal
    • 3
  1. 1.Department of Mathematics and StatisticsMemorial University of NewfoundlandSt. John’sCanada
  2. 2.Fachbereich MathematikJohannes Gutenberg-UniversitätMainzGermany
  3. 3.Department of MathematicsUniversity of TorontoTorontoCanada