  We study the long time behavior of small (in $l^2$) solutions of discrete
nonlinear Schr\"odinger equations with potential. In particular, we are
interested in the case that the corresponding discrete Schr\"odinger operator
has exactly two eigenvalues. We show that under the nondegeneracy condition of
Fermi Golden Rule, all small solutions decompose into a nonlinear bound state
and dispersive wave. We further show the instability of excited states and
generalized equipartition property.
