Thursday 21 July 1pm AEST

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Abstract: (Optical) conductivity is one of the most important characteristics of materials. Recently, nonlinearconductivities are of increasing experimental and theoretical interest, but the subject is largely open. I will discuss our recent approach to the fundamentals of the nonlinear optical conductivities. A system under the periodic boundary condition in one direction can be regarded as a "ring". A static magnetic flux through the ring induces the quantum mechanical Aharonov-Bohm effect. Furthermore, increasing the flux over time induces a uniform electric field in the system. The uniform electric conductivity can be regarded as the response of the system to the increase of the magnetic flux. This not only allows a unified formulation of the "frequency sum rule" (f-sum rule) and "Kohn formula", which have been important in many applications of linear response theory, but their natural generalization to nonlinear conductivities at all orders.