Quantum versus mean-field collapse in a many-body system

TL;DR

This paper demonstrates that in a quantum many-body system, repulsive interactions can create a metastable state preventing collapse predicted by mean-field theory, with stability increasing as particle number grows.

Contribution

It extends the mean-field analysis to many-body systems, showing metastability and collapse suppression through variational and Monte Carlo calculations.

Findings

Repulsive interactions lead to a metastable gaseous state.

Stability of the state increases with particle number.

Collapse can still occur but is hindered by a potential barrier.

Abstract

The recent analysis, based on the mean-field approximation (MFA), has predicted that the critical quantum collapse of the bosonic wave function, pulled to the center by the inverse-square potential in the three-dimensional space, is suppressed by the repulsive cubic nonlinearity in the bosonic gas, the collapsing ground state being replaced by a regular one. We demonstrate that a similar stabilization acts in a quantum many-body system, beyond the MFA. While the collapse remains possible, repulsive two-particle interactions give rise to a metastable gaseous state, which is separated by a potential barrier from the collapsing regime. The stability of this state improves with the increase of the number of particles. The results are produced by calculations of the variational energy, with the help of the Monte Carlo method.