Thresholds properties for matrix-valued Schrödinger operators

We present some results on the perturbation of eigenvalues embedded at a threshold for a two-channel Hamiltonian with three-dimensional Schr\"{o}dinger operators as entries and with a small off-diagonal perturbation. In particular, we show how the threshold eigenvalue gives rise to discrete eigenvalues below the threshold and, moreover, we establish a criterion on existence of half-bound states associated with embedded pseudo eigenvalues.