1306.4284 (David Damanik et al.)

Absolutely Continuous Convolutions of Singular Measures and an
Application to the Square Fibonacci Hamiltonian    [PDF]

David Damanik, Anton Gorodetski, Boris Solomyak

We prove for the square Fibonacci Hamiltonian that the density of states measure is absolutely continuous for almost all pairs of small coupling constants. This is obtained from a new result we establish about the absolute continuity of convolutions of measures arising in hyperbolic dynamics with exact-dimensional measures.

View original: http://arxiv.org/abs/1306.4284