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

Wavefunction structure is analyzed for dense 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 $\lambda$. In the first analysis, a complete analytical description of the variance of the strength function as a function of $\lambda$ and $k$ is derived and the marker $\lambda_t$ defining thermalization region is obtained. In the strong coupling limit ($\lambda > \lambda_t$), the conditional $q$-normal density describes Gaussian to semi-circle transition in strength functions as body rank $k$ of the interaction increases. In the second analysis, this interpolating form of the strength function is utilized to describe the fidelity decay after $k$-body interaction quench and also to obtain the smooth form for the number of principal components, a measure of chaos in finite interacting many-particle systems. The smooth form very well describes embedded ensemble results for all $k$ values.