  We analyze the energy transfer for solutions to the defocusing cubic
nonlinear Schr\"odinger (NLS) initial value problem on 2D irrational tori.
Moreover we complement the analytic study with numerical experimentation. As a
biproduct of our investigation we also prove that the quasi-resonant part of
the NLS initial value problem we consider, in both the focusing and defocusing
case, is globally well-posed for initial data of finite mass.
