Driven Imposters: Controlling Expectations in Solid State Systems*

We present a model to control the observables of a general many-body electron system driven by an incident laser field. The main result is a non-linear, field free equation of motion for tracking observables, together with a constraint on the functional form of expectations which may be reproduced via tracking. As a first test, the strategy is used in the Fermi-Hubbard model to make the current expectation conform to an arbitrary function under a range of model parameters. Additionally, using two reference spectra for materials in the conducting and insulating regimes respectively, we demonstrate that using the developed tracking strategy allows one to make the dipole acceleration spectrum of each material mimic the reference spectra of the other, creating a 'driven imposter'.