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Russian Journal of Mathematical Physics

, Volume 19, Issue 3, pp 299–306 | Cite as

Hall quantum Hamiltonians and electric 2D-curvature

  • M. V. KarasevEmail author
Article

Abstract

For the Dirac 2D-operator in a constant magnetic field with perturbing electric potential, we derive Hamiltonians describing the quantum quasiparticles (Larmor vortices) at Landau levels. The discrete spectrum of this Hall-effect quantum Hamiltonian can be computed to all orders of the semiclassical approximation by a deformed Planck-type quantization condition on the 2D-plane; the standard magnetic (symplectic) form on the plane is corrected by an “electric curvature” determined via derivatives of the electric field. The electric curvature does not depend on the magnitude of the electric field and vanishes for homogeneous fields (i.e., for the canonical Hall effect). This curvature can be treated as an effective magnetic charge of the inhomogeneous Hall 2D-nanosystem.

Keywords

Mathematical Physic Electric Potential Discrete Spectrum Landau Level Magnetic Charge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Moscow Institute for Electronics and Mathematics at National Research University HSEMoscowRussia

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