Spectral analysis of tridiagonal Fibonacci Hamiltonians
نویسندگان
چکیده
منابع مشابه
Inverse Spectral Problems for Tridiagonal N by N Complex Hamiltonians ⋆
In this paper, the concept of generalized spectral function is introduced for finite-order tridiagonal symmetric matrices (Jacobi matrices) with complex entries. The structure of the generalized spectral function is described in terms of spectral data consisting of the eigenvalues and normalizing numbers of the matrix. The inverse problems from generalized spectral function as well as from spec...
متن کاملSpectral Analysis of Percolation Hamiltonians
We study the family of Hamiltonians which corresponds to the adjacency operators on a percolation graph. We characterise the set of energies which are almost surely eigenvalues with finitely supported eigenfunctions. This set of energies is a dense subset of the algebraic integers. The integrated density of states has discontinuities precisely at this set of energies. We show that the convergen...
متن کاملSpectral Duality and Distribution of Exponents for Transfer Matrices of Block Tridiagonal Hamiltonians
Abstract: The block-tridiagonal matrix structure is a common feature in Hamiltonians of models of transport. By allowing for a complex Bloch parameter in the boundary conditions, the Hamiltonian matrix and its transfer matrix are related by a spectral duality. As a consequence, I derive the distribution of the exponents of the transfer matrix in terms of the spectral density of the non-Hermitia...
متن کاملThe Spectral Decomposition of Some Tridiagonal Matrices
Some properties of near-Toeplitz tridiagonal matrices with specific perturbations in the first and last main diagonal entries are considered. Applying the relation between the determinant and Chebyshev polynomial of the second kind, we first give the explicit expressions of determinant and characteristic polynomial, then eigenvalues are shown by finding the roots of the characteristic polynomia...
متن کاملReconstruction of tridiagonal matrices from spectral data
Jacobi matrices are parametrized by their eigenvalues and norming constants (first coordinates of normalized eigenvectors): this coordinate system breaks down at reducible tridiagonal matrices. The set of real symmetric tridiagonal matrices with prescribed simple spectrum is a compact manifold, admitting an open covering by open dense sets Uπ Λ centered at diagonal matrices Λπ , where π spans t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Spectral Theory
سال: 2013
ISSN: 1664-039X
DOI: 10.4171/jst/39