Semiclassical response theory

The study of the response properties of electron systems, such as the magnetic susceptibility in equilibrium and various transport coefficients out of equilibrium, was one of the primal forces driving the early development of solid state physics. After the classical particle view of electrons was modified by quantum mechanics and the many-body effect and evolved into the modern semiclassical particle view, the semiclassical response theory was established with the further help of the deep insight into Hilbert-space geometry and topology, offering a complete, accurate and, most importantly, intuitive framework for discussing various response properties. In this article we introduce the semiclassical response theory using classical examples from four important aspects, namely, thermoelectric response, spin transport, nonlinear response, and extrinsic mechanisms. Its value in solid state physics will also be demonstrated.