  We present numerical simulations for a chiral soliton model with N=2,3 bosons
in a ring, this being a few-particle version of our previous mean-field model
for a quantum time crystal. Following Syrwid, Kosior, and Sacha (SKS), the
notion is that a precise position measurement of one particle can lead to
spontaneous formation of a bright soliton that in a time crystal should rotate
intact for at least a few revolutions around the ring. In their work SKS find
spontaneous formation of a soliton due to the position measurement, but quantum
fluctuations cause the soliton to subsequently decay before it has a chance to
perform even one revolution of the ring. Based on this they conclude that time
crystal dynamics are impossible. In contrast, for our few boson chiral soliton
model, and allowing for imprecise (weak) measurements of the particle position,
we show that time crystal behavior is possible allowing for several revolutions
of the spontaneously formed soliton around the ring. We therefore argue that
our chiral soliton model can realize a quantum time crystal when weak position
measurements are allowed for.
