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Bethe Ansatz for the Bloch Particle in Magnetic Field

  • P. B. Wiegmann
  • A. V. Zabrodin
Part of the NATO ASI Series book series (NSSB, volume 328)

Abstract

We present a new approach to the problem of Bloch electrons in magnetic field, by making explicit a natural relation between the group of magnetic translations and the quantum group U q (sl 2). The Hamiltonian is represented as trace of a monodromy matrix of an integrable quantum model. This opens a way for an application of the functional Bethe ansatz technique. The approach allows one to express the “mid” band spectrum of the model and the Bloch wave function by solutions of the Bethe Ansatz equations typical for completely integrable quantum systems. The zero mode wave functions are found explicitly in terms of q-deformed classical orthogonal polynomials. Others quasiperiodic equations related to the Quantum group are discussed.

Keywords

Quantum Group Casimir Operator Monodromy Matrix Landau Gauge Bethe Equation 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • P. B. Wiegmann
    • 1
  • A. V. Zabrodin
    • 2
    • 3
  1. 1.James Franck Institute and Enrico Fermi InstituteUniversity of ChicagoChicagoUSA
  2. 2.Institute of Theoretical PhysicsUppsala UniversityUppsalaSweden
  3. 3.Institute of Chemical PhysicsMoscowRussia

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