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arXiv:2504.21641

Universal scaling law for quantum droplet formation

Ian G. Moss

Published Apr 30, 2025• 0 citations
arXivHTMLPDF

Abstract

Given the right set of circumstances, ultracold quantum gases are able to change character and condense into a liquid state of quantum droplets. The size distribution of the droplets is determined dynamically in the condensation process. A semi-quantitative argument is presented which suggests that, at zero temperature, a multiple droplet system has is a preferred scale $\propto v^{-1/3}$, where $v$ is the rate of change of parameters at the time of droplet formation. Numerical simulations of two dimensional systems strongly support a power law $v^{-d}$, with an exponent $d\in(0.327,0.375)$.

DOI
10.48550/arxiv.2504.21641

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Given the right set of circumstances, ultracold quantum gases are able to change character and condense into a liquid state of quantum droplets. The size distribution of the droplets is determined dynamically in the condensation process. A semi-quantitative argument is presented which suggests that, at zero temperature, a multiple droplet system has is a preferred scale ∝v−1/3\propto v^{-1/3}∝v−1/3, where vvv is the rate of change of parameters at the time of droplet formation. Numerical simulations of two dimensional systems strongly support a power law v−dv^{-d}v−d, with an exponent d∈(0.327,0.375)d\in(0.327,0.375)d∈(0.327,0.375).
Droplet impact on a surface is practically relevant to a variety of fields in nature and industry, while a complete control of its outcomes remains challenging due to various unmanageable factors. In this work, we propose the quantum simulation of droplet impact outcomes in the platform of ultracold atoms. Specifically, we study the quantum-fluctuation-driven dynamics (QFDD) of two-dimensional Bose-Bose mixtures from an initial Townes soliton towards the formation of a quantum droplet. By tuning the fluctuation energy of the initial Townes state through its size and number, the subsequent QFDD can produce various outcomes including splashing, recoiling, and deposition, similar to those in droplet impact dynamics. We have utilized the Weber number to identify the thresholds of splashing and recoiling, and further established a universal scaling law between the maximum spreading factor and the Weber number in the recoiling regime. In addition, we show that the residual QFDD in the deposition regime can be used to probe the collective breathing modes of a quantum droplet. Our results reveal a mechanism for the droplet impact outcomes, which can be directly tested in cold-atom experiments and can pave the way for exploring intriguing droplet dynamics in a clean and fully controlled quantum setting.
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Using a schematic interaction we derive and solve temperature-dependent Thomas-Fermi equations for a quantum liquid droplet (nucleus, 3He^{3}\mathrm{He}3He, or similar) in its vapor atmosphere. The results depend on the initial size of the droplet in the iterative numerical procedure, thereby simulating on the computer condensation and evaporation of the unstable droplets. The stationary but unstable droplet configuration is evidenced by a slowing down of the iterative change of the density. We also take into consideration bubble formation and instability for a chemical potential below the Maxwell liquid-vapor equilibrium value.
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