Time-dependent magnetic fields and the quantum Hall effect
Phys. Rev. B 114, 065434 – Published 30 July, 2026
DOI: https://doi.org/10.1103/drkn-yv3k
Abstract
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 that has been applied to the Schrödinger equation as well. We extend this analysis to the Landau problem of a charged particle in a uniform magnetic field in two dimensions, and we construct the 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 (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.
