Self-referential decomposition of a class of quadratic irrationals

D. J. Raup; A. Lakhtakia

doi:10.1088/0305-4470/21/1/032

Self-referential decomposition of a class of quadratic irrationals

D. J. Raup
, A. Lakhtakia

Engineering Science and Mechanics

Research output: Contribution to journal › Article › peer-review

Abstract

It has been predicted and numerically shown that the spectrum of the Hamiltonian H(P)= Sigma _{n in -( infinity infinity )}(E(P,n) a _n^Daggera_n+t(a_n+1 ^Daggera_n+a_n-1^Daggera_n)), 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 language	English (US)
Article number	032
Pages (from-to)	285-287
Number of pages	3
Journal	Journal of Physics A: Mathematical and General
Volume	21
Issue number	1
DOIs	https://doi.org/10.1088/0305-4470/21/1/032
State	Published - 1988

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
General Physics and Astronomy
Mathematical Physics

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Cite this

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title = "Self-referential decomposition of a class of quadratic irrationals",

abstract = "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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AU - Lakhtakia, A.

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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

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JF - Journal of Physics A: Mathematical and General

IS - 1

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Self-referential decomposition of a class of quadratic irrationals

Abstract

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