Advances and Challenges in Two-Dimensional Quantum Turbulence: Theoretical Insights, Experimental Platforms, and Future Perspectives Dr. Manju Bala1

Abstract

Two-dimensional quantum turbulence (2DQT) has emerged as a significant area of study that bridges the domains of quantum mechanics, fluid dynamics, and statistical physics. Unlike classical turbulence, where flow is characterized by continuous vortices, 2DQT is governed by discrete, quantized vortices confined within a plane. These vortices exhibit unique interaction dynamics such as clustering, annihilation, and energy transfer, leading to phenomena like the inverse energy cascade, where energy flows from smaller to larger scales. Recent advancements in experimental platforms, including Bose-Einstein condensates, superfluid helium films, and hybrid exciton-polariton systems, combined with cutting-edge imaging and manipulation techniques, have enabled unprecedented observation and control of vortex behaviour. Theoretical frameworks, particularly the Gross-Pitaevskii equation and the point-vortex model, have enhanced the understanding of vortex dynamics, sound-vortex coupling, and statistical equilibrium in quantum fluids. Despite notable progress, significant challenges remain, such as developing universal scaling laws, integrating multiscale models, and applying machine learning for turbulence prediction. This study underscores the importance of 2DQT in fundamental physics and highlights its potential applications in quantum computing, nano-engineering, superfluid-based sensing, and astrophysical modelling.

Keywords- Two-Dimensional Quantum Turbulence, Quantized Vortices, Bose-Einstein Condensates, Gross-Pitaevskii Equation, Inverse Energy Cascade