Quantum Quench and f-Sum Rules on Linear and Non-linear Conductivities

Electric conductivity is one of the most important response properties of materials. The "frequency sum rule" is a non-perturbative constraint on the conductivity integrated over all frequency. In this talk, we give a new derivation to the f-sum rule for general quantum many-particle systems by considering a quench process. We then extend the discussion to higher order responses and derive various types of new sum rules on nonlinear conductivities.