Abstract
A discussion is given of the derivation of the Kubo-Green formulas. A reformulation of the derivation is presented, which leads to an exact result, involving field-dependent transport coefficients. Kubo's result is obtained as the first-order term in a resolvent expansion. For the general Liouville operator case, in accord with van Kampen's objections, it cannot be argued that the other terms are negligible. However, for a large class of systems, this can be justified. This is shown for systems where dissipation is due to weak interactions, amenable to the Van Hove limit, and having sufficiently short relaxation times.
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Van Vliet, C.M. On van Kampen's objections against linear response theory. J Stat Phys 53, 49–60 (1988). https://doi.org/10.1007/BF01011544
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DOI: https://doi.org/10.1007/BF01011544