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

No-resonance conditions, random matrices, and quantum chaotic models