Chiral decomposition in the non-commutative Landau problem
  The decomposition of the non-commutative Landau (NCL) system into two uncoupled one-dimensional chiral components, advocated by Alvarez, Gomis, Kamimura and Plyushchay [1], is generalized to nonvanishing electric fields. This allows us to discuss the main properties of the NCL problem including its exotic Newton-Hooke symmetry and its relation to the Hall effect. The "phase transition" when the magnetic field crosses a critical value determined by the non-commutative parameter is studied in detail. 
P-M. Zhang and P. A. Horvathy
hep-th cond-mat.str-el math-ph math.MP