Results 1 to 10 of about 147 (25)

On Rotated CMV Operators and Orthogonal Polynomials on the Unit Circle [PDF]

, 2023
Split-step quantum walk operators can be expressed as a generalised version of CMV operators with complex transmission coefficients, which we call rotated CMV operators. Following the idea of Cantero, Moral and Velazquez's original construction of the original CMV operators from the theory of orthogonal polynomials on the unit circle (OPUC), we show ...
arxiv   +1 more source

Exact mobility edges for almost-periodic CMV matrices via gauge symmetries [PDF]

Int. Math. Res. Notices, Volume 2024, Issue 8, 6906--6941 (2024), 2023
We investigate the symmetries of so-called generalized extended CMV matrices. It is well-documented that problems involving reflection symmetries of standard extended CMV matrices can be subtle. We show how to deal with this in an elegant fashion by passing to the class of generalized extended CMV matrices via explicit diagonal unitaries in the spirit ...
arxiv   +1 more source

Localization for random CMV matrices [PDF]

arXiv, 2021
We prove Anderson localization (AL) and dynamical localization in expectation (EDL, also known as strong dynamical localization) for random CMV matrices for arbitrary distribution of i.i.d. Verblunsky coefficients.
arxiv  

An inverse spectral theory for finite CMV matrices [PDF]

arXiv, 2007
For finite dimensional CMV matrices the classical inverse spectral problems are considered. We solve the inverse problem of reconstructing a CMV matrix by its Weyl's function, the problem of reconstructing the matrix by two spectra of CMV matrices with different "boundary conditions", and the problem of reconstructing the CMV matrix by its spectrum and
arxiv  

Purely singular continuous spectrum for CMV operators generated by subshifts [PDF]

, 2013
We prove uniform absence of point spectrum for CMV operators corresponding to the period doubling subshift. We also prove almost sure absence of point spectrum for CMV operators corresponding to a class of Sturmian subshifts. Lastly, we prove almost sure absence of point spectrum for CMV operators corresponding to some subshifts generated by a coding ...
arxiv   +1 more source

Trace Formulas and a Borg-type Theorem for CMV Operators with Matrix-valued Coefficients [PDF]

arXiv, 2008
We prove a general Borg-type inverse spectral result for a reflectionless unitary CMV operator (CMV for Cantero, Moral, and Vel\'azquez) associated with matrix-valued Verblunsky coefficients. More precisely, we find an explicit formula for the Verblunsky coefficients of a reflectionless CMV matrix whose spectrum consists of a connected arc on the unit ...
arxiv  

Reflectionless CMV matrices and scattering theory [PDF]

, 2014
Reflectionless CMV matrices are studied using scattering theory. By changing a single Verblunsky coefficient a full-line CMV matrix can be decoupled and written as the sum of two half-line operators. Explicit formulas for the scattering matrix associated to the coupled and decoupled operators are derived. In particular, it is shown that a CMV matrix is
arxiv   +1 more source

CMV matrices: Five years after [PDF]

arXiv, 2006
CMV matrices are the unitary analog of Jacobi matrices; we review their general theory.
arxiv  

Spectral Approximation for Ergodic CMV Operators with an Application to Quantum Walks [PDF]

arXiv, 2017
We establish concrete criteria for fully supported absolutely continuous spectrum for ergodic CMV matrices and purely absolutely continuous spectrum for limit-periodic CMV matrices. We proceed by proving several variational estimates on the measure of the spectrum and the vanishing set of the Lyapunov exponent for CMV matrices, which represent CMV ...
arxiv  

Minimal Rank Decoupling of Full-Lattice CMV Operators with Scalar- and Matrix-Valued Verblunsky Coefficients [PDF]

arXiv, 2010
Relations between half- and full-lattice CMV operators with scalar- and matrix-valued Verblunsky coefficients are investigated. In particular, the decoupling of full-lattice CMV operators into a direct sum of two half-lattice CMV operators by a perturbation of minimal rank is studied. Contrary to the Jacobi case, decoupling a full-lattice CMV matrix by
arxiv