Generalized Kohn formula and f-sum rules on nonlinear conductivities
Masaki Oshikawa, University of Tokyo
There is renewed interest in nonlinear responses, thanks to developments in experimental techniques such as high-power lasers and in theoretical/computational methodologies. However, our understanding of nonlinear responses is far less mature than that of linear responses. As a step towards a systematic understanding, I will present a unified formulation of the higher-order counterparts of two fundamental concepts in the linear conduction: Drude weight and the f-sum rule. They can be understood in terms of two opposite limits of a "flux insertion" process: adiabatic and sudden switching on of the Aharonov-Bohm flux. In some one-dimensional models, the nonlinear Drude weight can be obtained exactly, but it often diverges. Physical meaning of the divergence will be discussed.