Comment on "Quantum time crystals".

@article{Bruno2012CommentO,
  title={Comment on "Quantum time crystals".},
  author={Patrick Bruno},
  journal={Physical review letters},
  year={2012},
  volume={110 11},
  pages={
          118901
        }
}
  • P. Bruno
  • Published 15 October 2012
  • Physics
  • Physical review letters
A Comment on Frank Wilczek's paper "Quantum Time Crystals" (Phys. Rev. Lett. 109, 160401 (2012); arXiv:1202.2539). 

Comment on "Quantum Time Crystals and Interacting Gauge Theories in Atomic Bose-Einstein Condensates".

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Classes of metastable thermodynamic quantum time crystals

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Absence of Quantum Time Crystals.

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Lack of a genuine time crystal in a chiral soliton model

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

Boundary Time Crystals.

This work introduces boundary time crystals and analyzes in detail a solvable model where an accurate scaling analysis can be performed.

Isolated Heisenberg magnet as a quantum time crystal

Local observables of closed many-body quantum systems are generally believed to quickly equilibrate after a quench, according to the eigenstate thermalization hypothesis. Here, the authors show that

Quantum Time Crystals and Interacting Gauge Theories in Atomic Bose-Einstein Condensates.

This work studies the dynamics of a Bose-Einstein condensate trapped circumferentially on a ring, and shows that the associated density-dependent gauge potential and concomitant current nonlinearity permits a ground state in the form of a rotating chiral bright soliton.

Dynamical nonlocality in quantum time via modular operators

We formalize the concept of the modular energy operator within the Page and Wootters timeless framework. As a result, this operator is elevated to the same status as the more studied modular

Observation of a Space-Time Crystal in a Superfluid Quantum Gas.

The observation of a space-time crystal using ultracold atoms, where the periodic structure in both space and time is directly visible in the experimental images, paving the way for the usage of space- time crystals for the discovery of novel nonequilibrium phases of matter.

A dissipative time crystal with or without Z2 symmetry breaking

We study an emergent semiclassical time crystal composed of two interacting driven-dissipative bosonic modes. The system has a discrete Z2 spatial symmetry which, depending on the strength of the
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