# 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).
81 Citations

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A no-go theorem is proved that rules out the possibility of time crystals defined as such, in the ground state or in the canonical ensemble of a general Hamiltonian, which consists of not-too-long-range interactions.

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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

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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

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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

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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

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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.

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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

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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

## References

SHOWING 1-2 OF 2 REFERENCES

### The European Synchrotron Radiation Facility

• S. Tazzari
• Physics
IEEE Transactions on Nuclear Science
• 1985
A new design study for the European Synchrotron Radiation Facility (ESRF) has been carried out in the past year by the European Synchrotron Radiation Project Group. The aim was to extend the work