Ermakov has shown that harmonic oscillator with time dependent frequency can be rescaled to a time independent one along with a nonlinear equation. This analysis can be extended to QHE with time dependent magnetic fields. This allows to bring in Generalized Laughlin wavefunctions. This helps to study dynamics of density fluctuations (GMP) and edgemodes in integer QHE. We will discuss briefly the case of inhomogeneous magnetic fields also and point out interesting connections to Kosambi, Cartan, Chern (KCC) theory.
In this talk, we will first briefly introduce C*-dynamical systems and crossed product C*-algebras. We will then introduce the notion of Rokhlin dimension for group actions and discuss its role in studying the structure of crossed products. Finally, we will present some permanence results showing how suitable regularity properties of the underlying C*-algebra can be inherited by the crossed product under appropriate assumptions on the action.