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

TL;DR

This paper analyzes the wavefunction structure of dense interacting boson systems with random k-body interactions, deriving analytical expressions for strength function variance, thermalization, and chaos indicators across different interaction regimes.

Contribution

It provides the first complete analytical description of strength function variance and introduces a unified approach to describe chaos and fidelity decay in many-boson systems with k-body interactions.

Findings

Derived variance of strength function as a function of interaction strength and body rank

Identified the thermalization threshold $\\lambda_t$ for the system

Described the Gaussian to semi-circle transition in strength functions with increasing k

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.