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

Michał Suchorowski1,*, Fabian Brauneis2, Hans-Werner Hammer2,3, Michał Tomza1, and Artem G. Volosniev4,†

  • *Contact author: m.suchorowski@uw.edu.pl
  • †Contact author: artem@phys.au.dk
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Phys. Rev. Lett. 136, 243402 – Published 18 June, 2026

DOI: https://doi.org/10.1103/2831-t3jk

Abstract

We introduce a generalized Gross-Pitaevskii equation that provides a nonlinear framework for studying 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 nonequilibrium 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.

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Phys. Rev. Lett. 136, 243402– Published 18 June, 2026
  • Received 20 November 2025
  • Revised 9 March 2026
  • Accepted 14 May 2026
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