Ermakov has shown how the solution to the classical harmonic oscillator in one spatial dimension with general time-dependent frequency can be reduced to the time-independent case and an associated nonlinear ordinary differential equation, an analysis which has been applied to the Schr\"odinger equation as well. We extend this analysis to the Landau problem of a charged particle in a uniform magnetic field in two dimensions and construct the {\it {generalized}} Laughlin wave functions for the case when the magnetic field is time-dependent. We also work out the dynamics of density fluctuations (the Girvin,MacDonald,Platzman or GMP mode) and argue that it is possible to tune the frequency of the magnetic field to obtain a compressible droplet of fermions. We also analyze the dynamics of the edge modes of the droplet for the integer Hall effect.
Zoom Meeting: https://icts-res-in.zoom.us/j/93951176646?pwd=RZbeIJcDLMifZ8nYYZ3p5MraZq6Qwj.1
Meeting ID: 939 5117 6646
Passcode: 202040