The variational approximation for two-dimensional quantum droplets

TL;DR

This paper uses a variational approach to analyze the properties and dynamics of quantum droplets in a two-dimensional Bose-Einstein condensate, revealing how quantum fluctuations influence their behavior.

Contribution

It introduces a variational method with super-Gaussian functions to accurately approximate and analyze 2D quantum droplets, including their stationary states and dynamic responses.

Findings

Super-Gaussian functions effectively model QD profiles

Quantum fluctuation modulation induces resonance and splitting

Derived dynamical equations for QD parameters

Abstract

The dynamics of a two-dimensional Bose-Einstein condensate in a presence of quantum fluctuations is studied. The properties of localized density distributions, quantum droplets (QDs), are analyzed by means of the variational approach. It is demonstrated that the super-Gaussian function gives a good approximation for profiles of fundamental QDs and droplets with non-zero vorticity. The dynamical equations for parameters of QDs are obtained. Fixed points of these equations determine the parameters of stationary QDs. The period of small oscillations of QDs near the stationary state is estimated. It is obtained that periodic modulations of the strength of quantum fluctuations can actuate different processes, including resonance oscillations of the QD parameters, an emission of waves and a splitting of QDs into smaller droplets.