Generalized Bethe Ansatz Equations for Hofstadter Problem

Details Generalized Bethe Ansatz Equations for Hofstadter Problem Generalized Bethe Ansatz Equations for Hofstadter Problem

1993-12-15

arxiv.org/abs/hep-th/9312133v1

Commun.Math.Phys. 169 (1995) 181-192

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, plain TeX, report HU-TFT-93-63

Scientific paper

The problem of diagonalization of the quantum mechanical Hamiltonian, governing dynamics of an electron on a two-dimensional triangular or square lattice in external uniform magnetic field, applied perpendicularly to the lattice plane, the flux through lattice cell, divided by the elementary quantum flux, being rational number, is reduced to generalized Bethe ansatz like equations on high genus algebraic curve. Our formulae for the trigonometric case, where genus of the curve vanishes, contain as a particular case recent result of Wiegmann and Zabrodin.

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