Green-Kubo Formulas with Symmetrized Correlation Functions for Quantum Systems in Steady States: The Shear Viscosity of a Fluid in a Steady Shear Flow |
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Authors: | Hiroshi Matsuoka |
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Institution: | 1.Department of Physics,Illinois State University,Normal,USA |
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Abstract: | 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 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. |
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