WIAS Preprint No. 1267, (2007)

The effect of time-dependent coupling on non-equilibrium steady states


  • Cornean, Horia D.
  • Neidhardt, Hagen
  • Zagrebnov, Valentin A.

2010 Mathematics Subject Classification

  • 46N55 47N55 47A40 35L90 47E05


  • non-equilibrium steady states, Landauer-Büttiker formula, Landau-Lifschitz formula, quantum Liouville equation, wave and scattering operator


Consider (for simplicity) two one-dimensional semi-infinite leads coupled to a quantum well via time dependent point interactions. In the remote past the system is decoupled, and each of its components is at thermal equilibrium. In the remote future the system is fully coupled. We define and compute the non equilibrium steady state (NESS) generated by this evolution. We show that when restricted to the subspace of absolute continuity of the fully coupled system, the state does not depend at all on the switching. Moreover, we show that the stationary charge current has the same invariant property, and derive the Landau-Lifschitz and Landauer-Büttiker formulas.

Appeared in

  • Ann. Henri Poincare, 10 (2009) pp. 61--93.

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