Séminaire de Physique Théorique
Biased and unbiased random walks and the Hofstadter modelStéphane Ouvry (LPTMS, Université Paris 11)
Thursday 06 November 2014 14:00 - Tours - Salle 1180 (Bât E2)
Résumé :
When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be exactly obtained. We explicitly map this biased classical random system on a non-Hermitian Hofstadter-like quantum model where a charged particle on a square lattice coupled to a perpendicular magnetic field hopps only to the right. In the commensurate case when the magnetic flux per unit cell is rational, an exact solution of the quantum model is obtained. Periodicity on the lattice allows to relate traces of the Nth power of the Hamiltonian to probability distribution generating functions of biased walks of length. Some considerations are also made on a Sieving interpretation of the integers which appear in this context.
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