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Mathematical Physics

arXiv:0708.3931 (math-ph)
[Submitted on 29 Aug 2007 (v1), last revised 20 Sep 2007 (this version, v2)]

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

Authors:Horia D. Cornean, Hagen Neidhardt, Valentin A. Zagrebnov
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Abstract: 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.
Comments: 30 pages, submitted
Subjects: Mathematical Physics (math-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
Cite as: arXiv:0708.3931 [math-ph]
  (or arXiv:0708.3931v2 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.0708.3931
Journal reference: ANNALES HENRI POINCARE Volume: 10 Issue: 1 Pages: 61-93 Published: MAR 2009
Related DOI: https://doi.org/10.1007/s00023-009-0400-5

Submission history

From: Horia Cornean [view email]
[v1] Wed, 29 Aug 2007 10:33:11 UTC (23 KB)
[v2] Thu, 20 Sep 2007 09:41:18 UTC (24 KB)
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