  In this article we investigate no-resonance conditions for quantum chaotic
and random matrix models. No-resonance conditions are properties on the
spectrum of a model, usually employed as a theoretical tool in the analysis of
late time dynamics. The first order no-resonance condition holds when a
spectrum is non-degenerate, while higher order no-resonance conditions imply
sums of an equal number of energies are non-degenerate outside of permutations
of the indices. The condition is usually assumed to hold for quantum chaotic
models. In this work we use several tests from random matrix theory to
demonstrate that no-resonance conditions are likely to be violated for all
equal sums containing greater than one energy. This is due to the presence of
level-attraction in the spectra after resolving appropriate symmetries. This
result is produced for both a quantum chaotic Hamiltonian and two random matrix
models. We then generalize important bounds in quantum equilibration theory to
a case where the conditions are violated, and to the case of random matrix
models.
