Generalized Gross-Pitaevskii Equation for 2D Bosons with Attractive Interactions

TL;DR

This paper introduces a generalized 2D Gross-Pitaevskii equation with a logarithmic density dependence, enabling analysis of quantum droplets, breathing modes, and vortex states in attractive Bose systems.

Contribution

It presents a novel nonlinear framework that incorporates quantum anomalies and predicts universal excited states, including vortices, for 2D attractive Bose gases.

Findings

Derived a nonlinear equation with logarithmic density dependence.

Analyzed quantum droplets, breathing modes, and quench dynamics.

Predicted universal excited states, including vortex configurations.

Abstract

We introduce a generalized Gross-Pitaevskii equation that provides a nonlinear framework for studying two-dimensional (2D) attractive Bose systems. Its defining feature is the logarithmic density dependence of the coupling constant, which breaks the scale invariance inherent in the standard mean-field equations. This framework allows straightforward calculations of the system properties arising from the quantum anomaly. As a first illustration, we study universal bound states in free space, commonly referred to as quantum droplets. Then, we analyze breathing modes and quench dynamics in trapped systems, paving the way for a systematic exploration of non-equilibrium phenomena in 2D attractive Bose systems. Finally, we predict the existence of universal excited states, including vortex configurations, which may be more accessible to experimental investigation than the ground state. Our results provide a robust theoretical foundation for studying both static and dynamical properties of finite systems, and offer guidance for the design of future experiments.