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

Abstract

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.

27 pages, 8 figures

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Cited by in corpus (6)

• Average-fluctuation separation in energy levels in many-particle quantum systems with $k$-body interactions using $q$-Hermite polynomials
• Wavefunction structure in quantum many-fermion systems with $k$-body interactions: conditional $q$-normal form of strength functions
• Statistical Nuclear Spectroscopy with $q$-normal and bivariate $q$-normal distributions and $q$-Hermite polynomials
• Two species $k$-body embedded Gaussian unitary ensembles: $q$-normal form of the eigenvalue density
• Thermalization in many-fermion quantum systems with one- plus random $k$-body interactions
• Distribution of lowest eigenvalue in $k$-body bosonic random matrix ensembles