# what is about the corresponding power series?

According to the papers The absolutely continuous spectrum of Jacobi matrices and these lecture notes:

• 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?

• @ChristianRemling Surely I want more material. But one question is about your article and Simon's article. One conclusion is related to power series: if the coefficients $a_i$are finite($a_i \in A, A is finite$), the sequence of the coefficients $[a_0,a_1,a_2.....]$ will be eventually periodic or random. I think possibly what randomness means in your article, is it consistent with Kolmogorov's definition or Chaitin's definition? Maybe it includes more than strict random sequence in the Kolmogorov's randomness sense. About the randomness, see Kolmogorov, Chaitin, or [to be continued] – XL _At_Here_There Jul 7 '17 at 1:07