  A characteristic of the defocusing cubic nonlinear Schr\"odinger equation
(NLSE), when defined so that the space variable is the multi-dimensional square
(hence rational) torus, is that there exist solutions that start with
arbitrarily small norms Sobolev norms and evolve to develop arbitrarily large
modes at later times; this phenomenon is recognized as a weak energy transfer
to high modes for the NLSE. In this paper, we show that when the system is
considered on an irrational torus, energy transfer is more difficult to detect.
