01-252 Vojkan Jaksic, Claude-Alain Pillet

Non-equilibrium steady states of finite quantum systems coupled to thermal reservoirs (329K, postscript) Jul 9, 01

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Abstract. We study the non-equilibrium statistical mechanics of a $2$-level quantum system, ${\cal S}$, coupled to two independent free Fermi reservoirs ${\cal R}_1$, ${\cal R}_2$, which are in thermal equilibrium at inverse temperatures $\beta_1\not=\beta_2$. We prove that, at small coupling, the combined quantum system ${\cal S} + {\cal R}_1 + {\cal R}_2$ 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 $C$-Liouvillean, $L$, and relate the NESS to zero resonance eigenfunctions of $L^\ast$. In the specific model ${\cal S} + {\cal R}_1 + {\cal R}_2$ we study the resonances of $L^\ast$ using the complex deformation technique developed previously by the authors.

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