Exotic Carroll particles with two-parameter central extension move by an anomalous Hall law, and their critical reduction reproduces the Dunne-Jackiw-Trugenberger model underlying the Peierls substitution.
Chiral decomposition in the non-commutative Landau problem
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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.
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Peierls substitution and Hall motion in exotic Carroll dynamics
Exotic Carroll particles with two-parameter central extension move by an anomalous Hall law, and their critical reduction reproduces the Dunne-Jackiw-Trugenberger model underlying the Peierls substitution.