Beyond-mean-field analysis of the Townes soliton and its breathing mode

TL;DR

This paper uses Bogoliubov perturbation theory to analyze the ground and excited states of two-dimensional bosons with attractive interactions, revealing quantum effects on breathing modes and improving large-N asymptotic results.

Contribution

It introduces a beyond-mean-field analysis of the Townes soliton, providing improved energy and size estimates and elucidating the quantum origin of breathing oscillations.

Findings

Improved large-N asymptotes for ground state energy and size.

Identification of quantum-mechanical breaking of scale symmetry causing breathing modes.

Scaling law for breathing-mode frequency at large N.

Abstract

By using the Bogoliubov perturbation theory we describe the self-bound ground state and excited breathing states of $N$ two-dimensional bosons with zero-range attractive interactions. Our results for the ground state energy $B_N$ and size $R_N$ improve previously known large-$N$ asymptotes and we better understand the crossover to the few-body regime. The breathing oscillations, absent at the mean-field level, result from the quantum-mechanical breaking of the mean-field scale symmetry. The breathing-mode frequency scales as $\Omega\propto |B_N|/\sqrt{N}$ at large $N$.