Chiral decomposition in the non-commutative Landau problem

TL;DR

This paper generalizes the chiral decomposition of the non-commutative Landau problem to include electric fields, exploring its symmetries, phase transitions, and relation to the Hall effect.

Contribution

It extends the known decomposition to electric fields and analyzes the resulting symmetry properties and phase transitions in the non-commutative Landau system.

Findings

Chiral decomposition is valid with electric fields.

The system exhibits exotic Newton-Hooke symmetry.

A phase transition occurs at a critical magnetic field.

Abstract

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.