Universal self-similar evolution of two-dimensional acoustic turbulence in Bose-Einstein condensates

Guillaume Costa; Sergey Nazarenko; Giorgio Krstulovic

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arXiv · 2607.06062

Universal self-similar evolution of two-dimensional acoustic turbulence in Bose-Einstein condensates

Guillaume Costa·Sergey Nazarenko·Giorgio Krstulovic

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Abstract

When driven out of equilibrium, a Bose-Einstein condensate develops nonlinearly interacting density waves that trigger a turbulent cascade, transferring energy toward small scales. In this Letter, we investigate the nonstationary evolution of solutions to the two-dimensional Gross-Pitaevskii equation (GPE). Through numerical simulations of both the GPE and the corresponding Wave Kinetic Equation (WKE), we identify self-similar solutions relevant to turbulence in atomic and polariton Bose-Einstein Condensates. These solutions correspond to a new type of non-thermal fixed point and exhibit characteristics of both first and second kind self-similarity. In particular, we show that the dynamics of the propagating front is universal, governed by a dimensionless universal constant $\beta$, which we determine numerically.

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Guillaume Costa, Sergey Nazarenko, Giorgio Krstulovic. 2026-07-07. Universal self-similar evolution of two-dimensional acoustic turbulence in Bose-Einstein condensates. https://arxiv.org/abs/2607.06062

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