It has been predicted and numerically shown that the spectrum of the Hamiltonian H(P)= Sigma n in -( infinity infinity )(E(P,n) a nDaggeran+t(an+1 Daggeran+an-1Daggeran)), in which E(P,n)=V cos (P2 pi n) and P is an irrational number, has a fractal distribution of eigenstates. Using a self-referential decomposition of a pertinent class of quadratic irrationals, it is shown here that such a conclusion is viable.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics