Current fluctuations in general open quantum systems and crossover to the isolated thermodynamic limit.
We consider the open quantum set-up of a system connected to two baths with slightly different temperatures and chemical potentials. First, we obtain the open-system current fluctuation-dissipation relations (OCFDR) for this set-up. In doing so, we also obtain a general expression for the non-equilibrium steady state density matrix in the linear response regime. The only assumptions are time reversal and time translation symmetries of the set-up and open-system thermalization. The Onsager relation for thermoelectric transport coefficients is recovered if the system Hamiltonian does not have long range terms. Then, we argue and demonstrate that, the OCFDR and the standard dc Green-Kubo formula which involve the isolated system in the thermodynamic limit have the following relation. They are two different limits of the integrated total current autocorrelation of the open-system in equilibrium. This quantity, which is related to the equilibrium current noise in the open system, can show a crossover between the open-system behavior and the isolated thermodynamic limit behavior as a function of system-size and observation time, even with strong system-bath coupling. This new kind of out-of-equilibrium crossover provides a way to quantify the reaching of isolated thermodynamic limit in real set-ups via current fluctuations.
Publisher URL: http://arxiv.org/abs/1712.01068
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