(De)Localization in the Prime Schrodinger Operator

Abstract

It is reported a combined numerical approach to study the localization properties of the one-dimensional tight-binding model with potential modulated along the prime numbers. A localization-delocalization transition was found as function of the potential intensity; it is also argued that there are delocalized states for any value of the potential intensity.

7 pages, 4 figures; to be published in J. Phys. A: Math. Gen

Cited by in corpus (3)

• Quantum hamiltonians and prime numbers
• Localization in One-Dimensional Tight-Binding Model with Chaotic Binary Sequences
• Delocalization in One-Dimensional Tight-Binding Models with Fractal Disorder II: Existence of Mobility Edge