generates are phase locked. Correla

generates are phase locked. Correlatively, the drop starts
moving at a velocity V of the order of 9 mm=s. We call a
walker the resulting wave-particle association. Of particular
relevance is the structure of the wave field that drives the
drop motion. At each impact, the drop excites a Bessel-like
Faraday wave of period TF ¼ 2=f0 and wavelength
λF ¼ 4.75 mm, centered at the impact point. Since
γ0 < γF, the waves are damped with a typical nondimensional
time: Me ¼ τ=TF. The global wave field that pilots
the drop is the linear superposition of all the waves
generated by the successive impacts located along a
memory length SMe ¼ Vτ=λF of the past trajectory. It thus
contains in its interference pattern a path memory of the
particle motion [6,15]. Since Me ≈ γF=ðγF − γ0Þ [15], its
value can be chosen by tuning γ0 in the vicinity of γF.
Previous works have shown that the memory has major
effects on the drop motion whenever the walker is confined:
in cavities [16], due to a Coriolis force [17,18], or in a
potential well [11].
Here, we investigate the latter situation obtained by
applying a central force to the drop. The setup, schematized
in Fig. 1(a), is described in detail in Ref. [11]. The bouncing
drop is loaded with a ferrofluid and polarized by a
homogeneous magnetic field B0. It thus forms a magnetic
dipole perpendicular to the bath surface. A magnet, placed
on the cell’s axis provides a second spatially varying
magnetic field BdðrÞ, where r is the distance to the axis.
The drop is thus trapped by a magnetic force:
FðdÞ ¼ −κðdÞr. The spring constant κ can be tuned by
changing the distance d of the magnet to the liquid surface.
The walker confinement is controlled by the nondimensional
half-width of the potential well Λ ¼ V ffiffiffiffiffiffiffiffiffiffiffiffi mW=κ
p =λF,
where mW is the drop effective mass. The nature of the