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On Thouless bandwidth formula in the Hofstadter model

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 Added by Stephane Ouvry
 Publication date 2017
  fields Physics
and research's language is English




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We generalize Thouless bandwidth formula to its n-th moment. We obtain a closed expression in terms of polygamma, zeta and Euler numbers.



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We consider the generating function of the algebraic area of lattice walks, evaluated at a root of unity, and its relation to the Hofstadter model. In particular, we obtain an expression for the generating function of the n-th moments of the Hofstadter Hamiltonian in terms of a complete elliptic integral, evaluated at a rational function. This in turn gives us both exact and asymptotic formulas for these moments.
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