Non-Equilibrium Steady States of Finite¶Quantum Systems Coupled to Thermal Reservoirs |
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Authors: | V Jak?i? C-A Pillet |
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Institution: | Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal,?QC, H3A 2K6, Canada, CA Université de Toulon, B.P. 132, 83957 La Garde Cedex, France, FR
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Abstract: | We study the non-equilibrium statistical mechanics of a 2-level quantum system, ?, coupled to two independent free Fermi
reservoirs ?1, ?2, which are in thermal equilibrium at inverse temperatures β1≠β2. We prove that, at small coupling, the combined quantum system ?+?1+?2 has a unique non-equilibrium steady state (NESS) and that the approach to this NESS is exponentially fast. We show that the
entropy production of the coupled system is strictly positive and relate this entropy production to the heat fluxes through
the system.
A part of our argument is general and deals with spectral theory of NESS. In the abstract setting of algebraic quantum statistical
mechanics we introduce the new concept of the C-Liouvillean, L, and relate the NESS to zero resonance eigenfunctions of L
*. In the specific model ?+?1+?2 we study the resonances of L
* using the complex deformation technique developed previously by the authors in JP1].
Dedicated to Jean Michel Combes on the occasion of his sixtieth birthday
Received: 12 July 2001 / Accepted: 11 October 2001 |
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