Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets

Abstract

We show that the integer quantum Hall effect systems in plane, sphere or disc, can be formulated in terms of an algebraic unified scheme. This can be achieved by making use of a generalized Weyl--Heisenberg algebra and investigating its basic features. We study the electromagnetic excitation and derive the Hamiltonian for droplets of fermions on a two-dimensional Bargmann space (phase space). This excitation is introduced through a deformation (perturbation) of the symplectic structure of the phase space. We show the major role of Moser's lemma in dressing procedure, which allows us to eliminate the fluctuations of the symplectic structure. We discuss the emergence of the Seiberg--Witten map and generation of an abelian noncommutative gauge field in the theory. As illustration of our model, we give the action describing the electromagnetic excitation of a quantum Hall droplet in two-dimensional manifold.

23 pages

References in corpus (14)

• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• Nonrelativistic anyons in external electromagnetic field
• Magnetic fields in noncommutative quantum mechanics
• Chiral actions from phase space (quantum Hall) droplets
• Kac-Moody theories for colored phase space (quantum Hall) droplets
• Electromagnetic interactions of higher dimensional quantum Hall droplets
• Anomalous Hall Effect in non-commutative mechanics
• Fractional supersymmetry and hierarchy of shape invariant potentials
• Bosonization of the lowest Landau level in arbitrary dimensions: edge and bulk dynamics
• Effective Wess-Zumino-Witten Action for Edge States of Quantum Hall Systems on Bergman Ball
• The Quantum Hall Effect on R^4
• Quantum Hall Effect on the Flag Manifold F_2
• Quantum Hall Droplets on Disc and Effective Wess-Zumino-Witten Action for Edge States
• Representations and Properties of Generalized $A_r$ Statistics, Coherent States and Robertson Uncertainty Relations

Cited by in corpus (1)

• Transition probabilities and dynamic structure factor in the ASEP conditioned on strong flux