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

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

2007-08-29

arxiv.org/abs/0708.3931v2

ANNALES HENRI POINCARE Volume: 10 Issue: 1 Pages: 61-93 Published: MAR 2009

Physics

Mathematical Physics

30 pages, submitted

Scientific paper

10.1007/s00023-009-0400-5

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-Buttiker formulas.

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