Linear Response Theory

Abstract

A general relationship can be established between fluctuations in a many body system in thermodynamic equilibrium and the response of such a system to external agencies such as electric and magnetic fields. These agencies perturb the equilibrium only slightly, if they are sufficiently weak. The system is considered tc be a member of an ensemble and to be described by the Liouville equation (1.4.8). The weakness of the external agencies allows for a linearization around thermodynamic equilibrium. This is the only basic assumption of the theory. Thes concepts may be extended to the case of internal agencies, such as gradients of temperature and flow velocity. This extension is, however, not straightforward, since the lowest order solution to the Liouville equation can no longer be taken to be thermal equilibrium, which is characterized by a uniform temperature and the absence of flow.