Can a bright soliton model reveal a genuine time crystal for a finite number of bosons?

TL;DR

This paper investigates whether a finite number of bosons forming a bright soliton on a ring can exhibit genuine time crystal behavior, finding that such behavior is not observable due to soliton decay.

Contribution

It demonstrates that finite boson systems can form moving solitons, but these decay too quickly to produce true time crystal dynamics, contrasting with the infinite particle limit.

Findings

Moving solitons form for finite N but decay rapidly.

Time crystal behavior is absent in finite systems due to soliton decay.

No genuine time crystal observed in the ground state for finite bosons.

Abstract

We analyze time crystal effects in a finite system of bosons which form a bright soliton clump on the Aharonov-Bohm ring. In the large particle number limit, $N\rightarrow\infty$, this setup corresponds to the Wilczek model, where it is known that the time crystal behavior cannot be observed in the ground state of the system because a spontaneously formed soliton does not move. Here, we show that while the spontaneous formation of a moving soliton in the ground state can occur for $N<\infty$, the soliton decays before it makes a single revolution along the ring and the time crystal dynamics is impossible.