Density of states extracted from modified recursion relations

H. Bahlouli; A. D. Alhaidari; M. S. Abdelmonem

doi:10.1016/j.physleta.2007.02.094

Density of states extracted from modified recursion relations

H. Bahlouli^*, A. D. Alhaidari, M. S. Abdelmonem

^*Corresponding author for this work

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

5 Scopus citations

Abstract

We evaluate the density of states (DOS) associated with tridiagonal symmetric Hamiltonian matrices and study the effect of perturbation on one of its entries. Analysis is carried out by studying the resulting three-term recursion relation and the corresponding orthogonal polynomials of the first and second kind. We found closed form expressions for the new DOS in terms of the original one when perturbation affects a single diagonal or off-diagonal site or a combination of both. The projected DOS is also calculated numerically and its relation to the average DOS is explored both analytically and numerically.

Original language	English
Pages (from-to)	162-172
Number of pages	11
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	367
Issue number	1-2
DOIs	https://doi.org/10.1016/j.physleta.2007.02.094
State	Published - 16 Jul 2007

Bibliographical note

Funding Information:
The authors acknowledge the support of King Fahd University of Petroleum and Minerals under project FT-2005/11.

Keywords

Continued fractions
Density of states
Orthogonal polynomials
Recursion relations
Resolvent operators
Tridiagonal matrices

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/j.physleta.2007.02.094

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title = "Density of states extracted from modified recursion relations",

abstract = "We evaluate the density of states (DOS) associated with tridiagonal symmetric Hamiltonian matrices and study the effect of perturbation on one of its entries. Analysis is carried out by studying the resulting three-term recursion relation and the corresponding orthogonal polynomials of the first and second kind. We found closed form expressions for the new DOS in terms of the original one when perturbation affects a single diagonal or off-diagonal site or a combination of both. The projected DOS is also calculated numerically and its relation to the average DOS is explored both analytically and numerically.",

keywords = "Continued fractions, Density of states, Orthogonal polynomials, Recursion relations, Resolvent operators, Tridiagonal matrices",

author = "H. Bahlouli and Alhaidari, \{A. D.\} and Abdelmonem, \{M. S.\}",

note = "Funding Information: The authors acknowledge the support of King Fahd University of Petroleum and Minerals under project FT-2005/11. ",

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doi = "10.1016/j.physleta.2007.02.094",

language = "English",

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pages = "162--172",

journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",

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TY - JOUR

T1 - Density of states extracted from modified recursion relations

AU - Bahlouli, H.

AU - Alhaidari, A. D.

AU - Abdelmonem, M. S.

N1 - Funding Information: The authors acknowledge the support of King Fahd University of Petroleum and Minerals under project FT-2005/11.

PY - 2007/7/16

Y1 - 2007/7/16

N2 - We evaluate the density of states (DOS) associated with tridiagonal symmetric Hamiltonian matrices and study the effect of perturbation on one of its entries. Analysis is carried out by studying the resulting three-term recursion relation and the corresponding orthogonal polynomials of the first and second kind. We found closed form expressions for the new DOS in terms of the original one when perturbation affects a single diagonal or off-diagonal site or a combination of both. The projected DOS is also calculated numerically and its relation to the average DOS is explored both analytically and numerically.

AB - We evaluate the density of states (DOS) associated with tridiagonal symmetric Hamiltonian matrices and study the effect of perturbation on one of its entries. Analysis is carried out by studying the resulting three-term recursion relation and the corresponding orthogonal polynomials of the first and second kind. We found closed form expressions for the new DOS in terms of the original one when perturbation affects a single diagonal or off-diagonal site or a combination of both. The projected DOS is also calculated numerically and its relation to the average DOS is explored both analytically and numerically.

KW - Continued fractions

KW - Density of states

KW - Orthogonal polynomials

KW - Recursion relations

KW - Resolvent operators

KW - Tridiagonal matrices

UR - https://www.scopus.com/pages/publications/34347341494

U2 - 10.1016/j.physleta.2007.02.094

DO - 10.1016/j.physleta.2007.02.094

M3 - Article

AN - SCOPUS:34347341494

SN - 0375-9601

VL - 367

SP - 162

EP - 172

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 1-2

ER -

Density of states extracted from modified recursion relations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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