  We study the spectral properties of two classes of random matrix models:
non-Gaussian RMT with quartic and sextic potentials, and RMT with Gaussian
noise. We compute and analyze the quantum Krylov complexity and the spectral
form factor for both of these models. We find that both models show suppression
of the spectral form factor at short times due to decoherence effects, but they
differ in their long-time behavior. In particular, we show that the Krylov
complexity for the non-Gaussian RMT and RMT with noise deviates from that of a
Gaussian RMT. We discuss the implications and limitations of our results for
quantum chaos and quantum information in open quantum systems. Our study
reveals the distinct sensitivities of the spectral form factor and complexity
to non-Gaussianity and noise, which contribute to the observed differences in
the different time domains.
