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 et al. (2008) , 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. - Highlights: ► The chiral decomposition of Alvarez et al. is extended to a non-commutative particle. ► The chiral decomposition is used to derive the "exotic" Newton–Hooke symmetry. ► The "phase transition" when the effective mass changes sign is studied in detail.