Unsteady dynamics of a classical particle-wave entity.

A droplet bouncing on the surface of a vertically vibrating liquid bath can walk horizontally, guided by the waves it generates on each impact. This results in a self-propelled classical particle-wave entity. By using a one-dimensional theoretical pilot-wave model with a generalized wave form, we investigate the dynamics of this particle-wave entity. We employ different spatial wave forms to understand the role played by both wave oscillations and spatial wave decay in the walking dynamics. We observe steady walking motion as well as unsteady motions such as oscillating walking, self-trapped oscillations, and irregular walking. We explore the dynamical and statistical aspects of irregular walking and show an equivalence between the droplet dynamics and the Lorenz system, as well as making connections with the Langevin equation and deterministic diffusion.

Stop-and-go locomotion of superwalking droplets.

Vertically vibrating a liquid bath at two frequencies, f and f/2, having a constant relative phase difference can give rise to self-propelled superwalking droplets on the liquid surface. We have numerically investigated such superwalking droplets in the regime where the phase difference varies slowly with time. We predict the emergence of stop-and-go motion of droplets, consistent with experimental observations [Valani et al. Phys. Rev. Lett. 123, 024503 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.024503]. Our simulations in the parameter space spanned by the droplet size and the rate of traversal of the phase difference uncover three different types of droplet motion: back-and-forth, forth-and-forth, and irregular stop-and-go motion, which we explore in detail. Our findings lay a foundation for further studies of dynamically driven droplets, whereby the droplet's motion may be guided by engineering arbitrary time-dependent phase difference functions.

Evolution of large-scale flow from turbulence in a two-dimensional superfluid.

Nonequilibrium interacting systems can evolve to exhibit large-scale structure and order. In two-dimensional turbulent flow, the seemingly random swirling motion of a fluid can evolve toward persistent large-scale vortices. To explain such behavior, Lars Onsager proposed a statistical hydrodynamic model based on quantized vortices. Here, we report on the experimental confirmation of Onsager's model. We dragged a grid barrier through an oblate superfluid Bose-Einstein condensate to generate nonequilibrium distributions of vortices. We observed signatures of an inverse energy cascade driven by the evaporative heating of vortices, leading to steady-state configurations characterized by negative absolute temperatures. Our results open a pathway for quantitative studies of emergent structures in interacting quantum systems driven far from equilibrium.

Vortex Thermometry for Turbulent Two-Dimensional Fluids.

We introduce a new method of statistical analysis to characterize the dynamics of turbulent fluids in two dimensions. We establish that, in equilibrium, the vortex distributions can be uniquely connected to the temperature of the vortex gas, and we apply this vortex thermometry to characterize simulations of decaying superfluid turbulence. We confirm the hypothesis of vortex evaporative heating leading to Onsager vortices proposed in Phys. Rev. Lett. 113, 165302 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.165302, and we find previously unidentified vortex power-law distributions that emerge from the dynamics.