Self-referential decomposition of a class of quadratic irrationals

D. J. Raup, A. Lakhtakia

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number032
Pages (from-to)285-287
Number of pages3
JournalJournal of Physics A: General Physics
Issue number1
StatePublished - 1988

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • General Physics and Astronomy
  • Mathematical Physics


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