2005/08/05 by Rowan Killip, R. Killip, Irina Nenciu +3
Mathematics · Physics and Astronomy · #70H06 #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG) #math-ph #math.MP #math.SG #msc:70H06
paper · pdf · doi:10.48550/arxiv.math/0508113
arxiv created 2005/08/05 · openalex publication_date 2005/08/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss a number of properties of CMV matrices, by which we mean the class of unitary matrices recently introduced by Cantero, Moral, and Velazquez. We argue that they play an equivalent role among unitary matrices to that of Jacobi matrices among all Hermitian matrices. In particular, we describe the analogues of well-known properties of Jacobi matrices: foliation by co-adjoint orbits, a natural symplectic structure, algorithmic reduction to this shape, Lax representation for an integrable lattice system (Ablowitz-Ladik), and the relation to orthogonal polynomials. As offshoots of our analysis, we will construct action/angle variables for the finite Ablowitz-Ladik hierarchy and describe the long-time behaviour of this system.