Thermal measurement induced disturbance in the Bose-Hubbard Hamiltonian

We study measurement induced disturbance (MID) in a qutrit –qutrit system with considering the effect of the external magnetic field, nonlinear and linear coupling constants and temperature. We show that all of these parameters have effective roles in MID. We also investigate the effect of finite external magnetic fields direction as parallel and anti-parallel on MID, and find some interesting results.