SELF-DUALITY AND LYAPUNOV EXPONENT OF SLOWLY VARYING APERIODIC POTENTIALS

The self-duality property of one-dimensional tight-binding Hamiltonians, usually considered in the literature in the special case of the almost-Mathieu potential, is extended to more complex models, where this property can be achieved in the thermodynamic limit. We examine the consequences as they apply to the Lyapunov exponents, and we confirm our analytic deductions by means of a recently proposed numerical procedure based on the renormalization formalism.