Linear response theory revisited. I. The many-body van Hove limit

A critical discussion of linear response theory is given. It is argued that in the formalism as it stands no dissipation is manifest. A physical reinterpretation for the case of a system in weak interaction with a reservoir is given. Mathematically this means that the van Hove limit, as well as the large system limit, is applied to the time-dependent Heisenberg operators of the Kubo formalism. The reduced operators can be put in a very compact form, viz.,BRα(t) =[exp(−Λdt)]Bα, where Bα is a Schrödinger operator and Λd is the Liouville space superoperator corresponding to the transition operator of the master equation. In this form the relaxation character of the transport expressions, and the approach to equilibrium is at once evident. New expressions for the generalized susceptibility and conductivity in this limit are presented. Also, the Onsager relations and other symmetry properties are confirmed.