Completely integrable on $\mathbb{Z}_+^d$ potentials for electromagnetic Schrodinger operator: rays asymptotics and scattering problem

The electromagnetic Schrodinger operator in $l_2(\mathbb{Z}_+^d)$ is considered. The potential satisfies to a discrete integrable system related with multiple orthogonal polynomials with respect to the Angelesco system of measures. The problem on limits of the potential along the rays in $\mathbb{Z}_+^d$ is solved. A statement and solution of the scattering problem is considered as well.