Some remarks on the quantum hall effect

Abstract

This review is destinated to an integrable systems community and attempts to motivate the Quantum Hall Effect as a possible field of application. We review some of its aspects using a microscopic (wave function) point of view, and we describe it as an incompressible quantum fluid droplet deforming under external perturbations. In particular, we discuss some well known open and closed geometries. We attempt to relate the Q.H.E. hydrodynamics to the Calogero-Sutherland model and Benjamin Ono equation from the bulk and boundary point of view. Finally, as an illustration, we discuss the so called non dissipative viscosity. © Springer-Verlag London 2013.