NDLI: Spectral Approximation for Quasiperiodic Jacobi Operators

Content Provider	Springer Nature Link
Author	Puelz, Charles Embree, Mark Fillman, Jake
Copyright Year	2015
Abstract	Quasiperiodic Jacobi operators arise as mathematical models of quasicrystals and in more general studies of structures exhibiting aperiodic order. The spectra of these self-adjoint operators can be quite exotic, such as Cantor sets, and their fine properties yield insight into the associated quantum dynamics, that is, the one-parameter unitary group that solves the time-dependent Schrödinger equation. Quasiperiodic operators can be approximated by periodic ones, the spectra of which can be computed via two finite dimensional eigenvalue problems. Since long periods are necessary for detailed approximations, both computational efficiency and numerical accuracy become a concern. We describe a simple method for numerically computing the spectrum of a period-K Jacobi operator in O(K 2) operations, then use the algorithm to investigate the spectra of Schrödinger operators with Fibonacci, period doubling, and Thue–Morse potentials.
Ending Page	554
Page Count	22
Starting Page	533
File Format	PDF
ISSN	0378620X
e-ISSN	14208989
Journal	Integral Equations and Operator Theory
Issue Number	4
Volume Number	82
Language	English
Publisher	Springer Basel
Publisher Date	2015-01-11
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Eigenvalues, singular values, and eigenvectors Selfadjoint operator theory in quantum theory, including spectral analysis Thue–Morse Jacobi operator Eigenvalue problems Analysis Schrödinger operator period doubling Eigenvalues, eigenvectors Jacobi (tridiagonal) operators (matrices) and generalizations Fibonacci quasicrystal
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Analysis

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Spectral Approximation for Quasiperiodic Jacobi Operators

The characteristic function for Jacobi matrices with applications

The characteristic function for complex doubly infinite Jacobi matrices

Eigenvalue bounds in the gaps of Schrodinger operators and Jacobi matrices

The Eigenvalues of Tridiagonal Sign Matrices are Dense in the Spectra of Periodic Tridiagonal Sign Operators

Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States

Inequalities for the Eigenvalues of Non-Selfadjoint Jacobi Operators

Eigenvalue enclosures and convergence for the linearized MHD operator

Decay bounds on eigenfunctions and the singular spectrum of unbounded Jacobi matrices

Spectral Approximation for Quasiperiodic Jacobi Operators

Similar Documents

Spectral Approximation for Quasiperiodic Jacobi Operators

The characteristic function for Jacobi matrices with applications

The characteristic function for complex doubly infinite Jacobi matrices

Eigenvalue bounds in the gaps of Schrodinger operators and Jacobi matrices

The Eigenvalues of Tridiagonal Sign Matrices are Dense in the Spectra of Periodic Tridiagonal Sign Operators

Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States

Inequalities for the Eigenvalues of Non-Selfadjoint Jacobi Operators

Eigenvalue enclosures and convergence for the linearized MHD operator

Decay bounds on eigenfunctions and the singular spectrum of unbounded Jacobi matrices

Spectral Approximation for Quasiperiodic Jacobi Operators