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

Simulation of time crystal behavior for a few boson chiral soliton model in a ring