Title: Structure of wavefunction for interacting bosons in mean-field with random $k$-body interactions

Abstract: Wavefunction structure is analyzed for interacting many-boson systems using Hamiltonian $H$, which is a sum of one-body $h(1)$ and an embedded GOE of $k$-body interaction $V(k)$ with strength $\lambda$. For sufficiently large $\lambda$, the conditional $q$-normal density describes Gaussian to semi-circle transition in strength functions as body rank $k$ of the interaction increases. This interpolating form describes the fidelity decay after $k$-body interaction quench very well. Also, obtained is the smooth form for the number of principal components, which is a measure of chaos in finite interacting many-particle systems and it describes embedded ensemble results well in chaotic domain for all $k$ values.