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)]. 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 functionsRahil N. Valani, Anja C. Slim, and Tapio P. Simul

Unsteady dynamics of a classical particle-wave entity

Published 8 July 2021A 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.Rahil N. Valani, Anja C. Slim, David M. Paganin, Tapio P. Simula, and Theodore V

Vortex Lattice Structures of a Bose-Einstein Condensate in a Rotating Lattice Potential

We study vortex lattice structures of a trapped Bose-Einstein condensate in a rotating lattice potential by numerically solving the time-dependent Gross-Pitaevskii equation. By rotating the lattice potential, we observe the transition from the Abrikosov vortex lattice to the pinned lattice. We investigate the transition of the vortex lattice structure by changing conditions such as angular velocity, intensity, and lattice constant of the rotating lattice potential.Comment: 6 pages, 8 figures, submitted to Quantum Fluids and Solids Conference (QFS 2006

Stabilization and pumping of giant vortices in dilute Bose-Einstein condensates

Recently, it was shown that giant vortices with arbitrarily large quantum numbers can possibly be created in dilute Bose-Einstein condensates by cyclically pumping vorticity into the condensate. However, multiply quantized vortices are typically dynamically unstable in harmonically trapped nonrotated condensates, which poses a serious challenge to the vortex pump procedure. In this theoretical study, we investigate how the giant vortices can be stabilized by the application of a Gaussian potential peak along the vortex core. We find that achieving dynamical stability is feasible up to high quantum numbers. To demonstrate the efficiency of the stabilization method, we simulate the adiabatic creation of an unsplit 20-quantum vortex with the vortex pump.Comment: 8 pages, 6 figures; to be published in J. Low Temp. Phys., online publication available at http://dx.doi.org/10.1007/s10909-010-0216-

Nonlinear dynamics for vortex lattice formation in a rotating Bose-Einstein condensate

We study the response of a trapped Bose-Einstein condensate to a sudden turn-on of a rotating drive by solving the two-dimensional Gross-Pitaevskii equation. A weakly anisotropic rotating potential excites a quadrupole shape oscillation and its time evolution is analyzed by the quasiparticle projection method. A simple recurrence oscillation of surface mode populations is broken in the quadrupole resonance region that depends on the trap anisotropy, causing stochastization of the dynamics. In the presence of the phenomenological dissipation, an initially irrotational condensate is found to undergo damped elliptic deformation followed by unstable surface ripple excitations, some of which develop into quantized vortices that eventually form a lattice. Recent experimental results on the vortex nucleation should be explained not only by the dynamical instability but also by the Landau instability; the latter is necessary for the vortices to penetrate into the condensate.Comment: RevTex4, This preprint includes no figures. You can download the complete article and figures at http://matter.sci.osaka-cu.ac.jp/bsr/cond-mat.htm

From Coherent Modes to Turbulence and Granulation of Trapped Gases

The process of exciting the gas of trapped bosons from an equilibrium initial state to strongly nonequilibrium states is described as a procedure of symmetry restoration caused by external perturbations. Initially, the trapped gas is cooled down to such low temperatures, when practically all atoms are in Bose-Einstein condensed state, which implies the broken global gauge symmetry. Excitations are realized either by imposing external alternating fields, modulating the trapping potential and shaking the cloud of trapped atoms, or it can be done by varying atomic interactions by means of Feshbach resonance techniques. Gradually increasing the amount of energy pumped into the system, which is realized either by strengthening the modulation amplitude or by increasing the excitation time, produces a series of nonequilibrium states, with the growing fraction of atoms for which the gauge symmetry is restored. In this way, the initial equilibrium system, with the broken gauge symmetry and all atoms condensed, can be excited to the state, where all atoms are in the normal state, with completely restored gauge symmetry. In this process, the system, starting from the regular superfluid state, passes through the states of vortex superfluid, turbulent superfluid, heterophase granular fluid, to the state of normal chaotic fluid in turbulent regime. Both theoretical and experimental studies are presented.Comment: Latex file, 25 pages, 4 figure

Emergence of superwalking droplets

A new class of self-propelled droplets, coined superwalkers, has been shown to emerge when a bath of silicone oil is vibrated simultaneously at a given frequency and its subharmonic tone with a relative phase difference between them (Valani et al., Phys. Rev. Lett., vol. 123, 2019, 024503). To understand the emergence of superwalking droplets, we explore their vertical and horizontal dynamics by extending previously established theoretical models for walkers driven by a single frequency to superwalkers driven by two frequencies. Here, we show that driving the bath at two frequencies with an appropriate phase difference raises every second peak and lowers the intermediate peaks in the vertical periodic motion of the fluid surface. This allows large droplets that could otherwise not walk to leap over the intermediate peaks, resulting in superwalking droplets whose vertical dynamics is qualitatively similar to normal walkers. We find that the droplet’s vertical and horizontal dynamics are strongly influenced by the relative height difference between successive peaks of the bath motion, a parameter that is controlled by the phase difference. Comparison of our simulated superwalkers with the experiments of Valani et al. (2019) shows good agreement for small- to moderate-sized superwalkers.Rahil N. Valani, Jack Dring, Tapio P. Simula and Anja C. Sli