Abstract
In a recent publication [Phys. Rev. Lett. {\bf 124}, 178902] \"Ohberg and Wright claim that in a chiral soliton model it is possible to realize a genuine time crystal which corresponds to a periodic evolution of an inhomogeneous probability density in the lowest energy state. We show that this result is incorrect and present a solution which possesses lower energy with the corresponding probability density that does not reveal any motion. It implies that the authors' conclusion that a genuine time crystal can exist in the system they consider is not true.
Highlights
The idea of a quantum time crystal was proposed by Wilczek in 2012 [1]
We show that this result is incorrect and present a solution which possesses lower energy with the corresponding probability density that does not reveal any motion
It turned out that the system proposed by Wilczek was not a genuine time crystal, because in the limit of a large number of bosons, the particle density corresponding to the ground state did not reveal any motion [3,4,5]
Summary
The idea of a quantum time crystal was proposed by Wilczek in 2012 [1] He considered attractively interacting bosons on a ring which formed a localized wave packet (more precisely, a bright soliton) and, in the presence of a magneticlike flux, were supposed to move periodically along a ring even if the energy of the system was the lowest possible. Öhberg and Wright have analyzed a mean-field description of a Bose system with a density-dependent gauge potential supporting chiral soliton solutions [69] They asserted that such a system could circumvent the no-go theorems [6,7,8] and reveal a genuine time crystal behavior.
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