Phonons in the quantum Hall effect: A nonlinear-dynamics picture

A model describing a system in which Landau electronic modes are coupled with phonons is proposed and discussed. A simplified version of the model is further analyzed, with special attention to the dynamical symmetries that characterize it. In particular, the corresponding equations of motion are thoroughly examined: they provide a variety of behaviors, ranging from completely integrable (in both the classical and quantum case) to chaotic (in the semiclassical approximation). The chaotic regime is believed to be suitable to eventually represent the stochastic behavior of the longitudinal voltage versus time, recently observed in several quantum Hall effect experiments.