Abstract
The linear response means a change in the system proportional to the magnitude of the external force. If the external force is infinitesimally small, the higher order effects can safely be neglected. Actually the dominance of linear response often extends to the practical range of the external force. Thus physical properties such as electrical conduction and magnetic susceptibility are conveniently described by the linear response theory. Furthermore, the linear response theory leads to a simple relation between dissipation of energy, such as the Joule heat, and fluctuation without external force. In this Chapter, we explain the linear response theory starting with basics of statistical physics, proceeding to practical applications such as deriving resistivity and magnetic relaxation. Various kinds of Green functions appear in the linear response theory. In addition to those related to response functions, we also discuss single-particle Green functions which describe propagation and damping of bosons and fermions.
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