 0642 M. Merkli, M. Mueck, I.M. Sigal
 Theory of NonEquilibrium Stationary States as a Theory of Resonances. Existence and Properties of NESS
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Mar 1, 06

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Abstract. We study a small quantum system (e.g. a simplified model for an
atom or molecule) interacting with two bosonic or fermionic reservoirs
(say, photon or phonon fields) at different temperatures $T_1$ and $T_2$. We
show that if $T_1$ is not equal to $T_2$ then the combined system has a
stationary, nonequilibrium state (NESS). We show that this state has
nonvanishing heat fluxes and positive entropy production and that it is dynamically
asymptotically stable. The latter means that the evolution with an initial
condition, normal with respect to any state where the reservoirs are in
equilibria at temperatures $T_1$ and $T_2$, converges to this NESS. Our results
are valid for the temperatures satisfying the bound $\min(T_1, T_2) >
g^{2+\alpha}$, where $g$ is the coupling constant and $0< \alpha<1$ is a power
related to the infrared behaviour of the coupling functions. This
restriction is introduced in order to present the setup and techniques
without extra hard and lengthy technical estimates. In a subsequent work
we combine the present setup and techniques with the spectral renormalization
group method to obtain the results as above for all temperatures.
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