Green-Kubo formulas with symmetrized correlation functions for quantum systems in steady states: the shear viscosity of a fluid in a steady shear flow

Details Green-Kubo formulas with symmetrized correlation functions for quantum systems in steady states: the shear viscosity of a fluid in a steady shear flow Green-Kubo formulas with symmetrized correlation functions for quantum systems in steady states: the shear viscosity of a fluid in a steady shear flow

2012-04-25

arxiv.org/abs/1204.5533v1

Physics

Condensed Matter

Statistical Mechanics

30 pages. arXiv admin note: text overlap with arXiv:1104.5190

Scientific paper

For a quantum system in a steady state with a constant current of heat or particles driven by a temperature or chemical potential difference between two heat or particle reservoirs attached to the system, the fluctuation theorem for the current was previously shown to lead to the Green-Kubo formula for the linear response coefficient for the current expressed in terms of the symmetrized correlation function of the current density operator. In this article, we show that for a quantum system in a steady state with a constant rate of work done on the system, the fluctuation theorem for a quantity induced in the system also leads to the Green-Kubo formula expressed in terms of the symmetrized correlation function of the induced quantity. As an example, we consider a fluid in a steady shear flow driven by a constant velocity of a solid plate moving above the fluid. We derive the fluctuation theorem for the shear stress on the fluid and obtain the Green-Kubo formula for its shear viscosity expressed in terms of the symmetrized correlation function of its shear stress operator. As steady states in quantum systems are accompanied by either constant currents of heat and/or particles through the systems or constant rates of work done on the systems, the fluctuation theorem for a quantity induced in such a system therefore always leads to the Green-Kubo formula expressed in terms of the symmetrized correlation function of the induced quantity.

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