TY - JOUR

T1 - Self-referential decomposition of a class of quadratic irrationals

AU - Raup, D. J.

AU - Lakhtakia, A.

PY - 1988/12/1

Y1 - 1988/12/1

N2 - 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.

AB - 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.

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U2 - 10.1088/0305-4470/21/1/032

DO - 10.1088/0305-4470/21/1/032

M3 - Article

AN - SCOPUS:36149032019

VL - 21

SP - 285

EP - 287

JO - Journal of Physics A: General Physics

JF - Journal of Physics A: General Physics

SN - 0305-4470

IS - 1

M1 - 032

ER -