2025/11/23 by Aktosun, Tuncay, Choque-Rivero, Abdon E., Papanicolaou, Vassilis G. +2
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Nonlinear Photonic Systems #Quantum Mechanics and Non-Hermitian Physics
paper · doi:10.48550/arxiv.2511.18229
The Jacobi system with matrix-valued coefficients and with the spectral parameter depending on a matrix-valued weight factor is considered on the full-line lattice. The scattering from the full-line lattice is expressed in terms of the scattering from the fragments of the whole lattice by developing a factorization formula for the corresponding transition matrices. In particular, the matrix-valued transmission and reflection coefficients for the full-line lattice are explicitly expressed in terms of the scattering coefficients for the left and right lattice fragments. Since the matrix-valued scattering coefficients are easier to determine for the fragments than for the full-line lattice, the factorization formula presented provides a method to determine the scattering coefficients for full-line lattices. The theory presented is illustrated with various explicit examples, including an example demonstrating that the matrix-valued left transmission coefficient in general is not equal to the matrix-valued right transmission coefficient for a lattice.