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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2016

On the algebraic area of lattice walks and the Hofstadter model

Résumé

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.

Dates et versions

hal-01407689 , version 1 (02-12-2016)

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Stephane Ouvry, Stephan Wagner, Shuang Wu. On the algebraic area of lattice walks and the Hofstadter model. Journal of Physics A: Mathematical and Theoretical, 2016, 49, pp.495205. ⟨hal-01407689⟩
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