From Scale Invariance to Universal Droplets: Generalised GPE for Attractive 2D Bose Gases

Dilute two-dimensional (2D) gases exhibit scale-invariant behaviour that is absent in their three-dimensional counterparts. In attractive systems, this symmetry can be strongly broken — a phenomenon known as the quantum anomaly — by the presence of universal many-body bound states (droplets). To explore this anomaly, especially the corresponding time dynamics, a simple yet powerful theoretical tool is required.

In this work, we introduce a density-dependent coupling into the Gross-Pitaevskii equation (GPE), which not only captures the quantum anomaly but also retains a structure suitable for both intuitive analytical and numerical analysis. In my talk, I will demonstrate how this approach naturally bridges the physics of trapped systems and self-bound droplets, and how it enables the investigation of excited states and complex collective dynamics.