Boyle's 1662 observation that the volume of a gas is, at constant temperature, inversely proportional to pressure, offered a prototypical example of how an equation of state (EoS) can succinctly capture key properties of a many-particle system. Such relations are now cornerstones of equilibrium thermodynamics. Extending thermodynamic concepts to far-from-equilibrium systems is of great interest in various contexts including glasses, active matter, and turbulence, but is in general an open problem. Here, using a homogeneous ultracold atomic Bose gas, we experimentally construct an EoS for a turbulent cascade of matter waves. Under continuous forcing at a large length scale and dissipation at a small one, the gas exhibits a non-thermal, but stationary state, which is characterised by a power-law momentum distribution sustained by a scale-invariant momentum-space energy flux. We establish the amplitude of the momentum distribution and the underlying energy flux as equilibrium-like state variables, related by an EoS that does not depend on the details of the energy injection or dissipation, or the history of the system. Moreover, we show that the equations of state for a wide range of interaction strengths and gas densities can be empirically scaled onto each other. This results in a universal dimensionless EoS that sets benchmarks for the theory and should also be relevant for other turbulent systems.
Nonthermal fixed points, vortex statistics, and superfluid turbulence in an ultracold Bose gas
在二维和三维空间中分析了远离热平衡的稀薄简并玻色气体动力学的非热不动点。详细研究了以前在非微扰量子场论方法中发现的、最近被证明与涡旋动力学和超流湍流有关的普适幂律分布[Phys. Rev. B 84，020506（R）（2011）]。结果意味着解释的标度行为的独立涡激发的超流体和拓扑激发的统计可以描述的波动湍流的框架。发现在单粒子动量分布中观察到的特定标度指数与不可逆性以及波相互作用所遵守的守恒定律是一致的。此外，长波长的声学激励的涡旋轴承冷凝物，驱动的涡旋湮灭，发现遵循非热幂律。在统计模式中考虑涡的相关性，长时间偏离非热不动点与涡-反涡配对有关。所研究的非热不动点可在冷气体实验中得到。这些结果揭示了超流湍流的基本方面，并对相关现象具有很强的潜在影响，例如，在早期宇宙膨胀或夸克-胶子等离子体动力学中。
Universal scaling and relaxation in decaying turbulence of Bose gases
Instituto de Física de São Carlos, Universidade de São Paulo（圣卡洛斯物理研究所，圣保罗大学）；Department of Biomedical Engineering, Texas A&M University（德州农工大学生物医学工程系）；Hagler Institute for Advanced Study, Texas A&M University（德州农工大学哈格勒高级研究学院）
Life Cycle of Superfluid Vortices and Quantum Turbulence in the Unitary Fermi Gas
幺正费米气体（UFG）提供了一个独特的机会来研究强相互作用的费米超流体中的量子湍流的实验和理论。它产生于精确和受控的实验，并承认唯一的动力学微观描述通过时间相关的密度泛函理论（DFT）-除了稀释玻色子气体-的交叉和重新连接的超流体涡旋线费曼在1955年提出的是在零温度下的超流体量子湍流的起源。我们演示了如何通过使用完善的实验技术：激光搅拌和相印可以产生各种涡流配置。麻省理工学院研究小组展示的新成像技术[Ku et al. arXiv：1402.7052]应该能够直接可视化这些交叉和重新连接，比迄今为止在液氦中进行的更详细。我们展示了在UFG中的涡旋的形成和动力学中的陷阱的几何形状所起的关键作用，以及如何使用激光搅拌和相位印记来创建具有量子湍流开始的清晰签名的涡旋缠结。
