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 λ. In the first analysis, a complete analytical description of the variance of the strength function as a function of λ and k is derived and the marker λ_t defining thermalization region is obtained. In the strong coupling limit $λ> λ_t$, 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.