According to the papers [The absolutely continuous spectrum of Jacobi matrices](https://arxiv.org/abs/0706.1101) and [these lecture notes](https://nms.kcl.ac.uk/alexander.pushnitski/ebd65/simon.pdf):


* periodicity ~ potential well or lattice (order)
* lack of absolutely continued spectrum ~ Anderson localization(disorder)


Given this, what is the corresponding spectrum of a particle in quasi-order materials (like quasicrystals，quasi-order)? or what is about corresponding power series?



what is about the corresponding power series?
Quasiperiodic potentials, such as the [Fibonacci chain](https://en.wikipedia.org/wiki/Fibonacci_quasicrystal), have a spectrum that is called [singular continuous](https://en.wikipedia.org/wiki/Singular_distribution), with a fractal structure, see


* [Fractal energy spectrum of a polariton gas in a Fibonacci quasi-periodic potential](https://arxiv.org/abs/1311.3453) (2013)
* [From the Hofstadter
to the Fibonacci butterfly](https://arxiv.org/abs/cond-mat/0610192) (2006)
* [Schrödinger difference
equation with deterministic ergodic potentials](https://arxiv.org/abs/1203.3646) (2012)
* [Cantor spectrum for the quasi-periodic Schrödinger equation](http://www.sciencedirect.com/science/article/pii/002203969190133T) (1991)
* [Operators with singular continuous spectrum: Almost periodic Schrödinger operators](http://www.math.caltech.edu/papers/bsimon/p236.pdf) (1992)


