Coupled-channel scattering in 1+1 dimensional lattice model

Based on the Lippmann-Schwinger equation approach, a generalized L\"uscher's formula in 1+1 dimensions for two particles scattering in both the elastic and coupled-channel cases in moving frames is derived. A 2D coupled-channel scattering lattice model is presented, the model represents a two-coupled-channel resonant scattering scalars system. The Monte Carlo simulation is performed on finite lattices and in various moving frames. The 2D generalized L\"uscher's formula is used to extract the scattering amplitudes for the coupled-channel system from the discrete finite-volume spectrum.