  A droplet bouncing on a liquid bath can self-propel due to its interaction
with the waves it generates. The resulting "walker" is a dynamical association
where, at a macroscopic scale, a particle (the droplet) is driven by a
pilot-wave field. A specificity of this system is that the wave field itself
results from the superposition of the waves generated at the points of space
recently visited by the particle. It thus contains a memory of the past
trajectory of the particle. Here, we investigate the response of this object to
forces orthogonal to its motion. We find that the resulting closed orbits
present a spontaneous quantization. This is observed only when the memory of
the system is long enough for the particle to interact with the wave sources
distributed along the whole orbit. An additional force then limits the possible
orbits to a discrete set. The wave-sustained path memory is thus demonstrated
to generate a quantization of angular momentum. Because a quantum-like
uncertainty was also observed recently in these systems, the nonlocality
generated by path memory opens new perspectives.
