Limits of the dynamical approach to the nonlinear response of mesoscopic systems

Abstract

We have considered the nonlinear response of mesoscopic systems of noninteracting electrons to the time-dependent external field. In this consideration the inelastic processes have been neglected and the electron thermalization occurs due to the electron exchange with the reservoirs. We have demonstrated that the diagrammatic technique based on the method of analytical continuation or on the Keldysh formalism is capable of describing the heating automatically. The corresponding diagrams contain loose diffusons. We have shown the equivalence of such a diagrammatic technique to the solution to the kinetic equation for the electron-energy distribution function. We have identified two classes of problems with different behavior under ac pumping. In one class of problems (persistent current fluctuations, Kubo conductance) the observable depends on the electron-energy distribution renormalized by heating. In another class of problems (Landauer conductance) the observable is insensitive to heating and depends on the temperature of electron reservoirs. As examples of such problems we have considered in detail the persistent current fluctuations under ac pumping and two types of conductance measurements (Landauer conductance and Kubo conductance) that behave differently under ac pumping. We also foumulate two types of time-dependent random-matrix theories that apply in the ergodic regime for the adiabatic and high-frequency pumping, respectively.