# Time crystals: a review.

@article{Sacha2018TimeCA, title={Time crystals: a review.}, author={Krzysztof Sacha and Jakub J. Zakrzewski}, journal={Reports on progress in physics. Physical Society}, year={2018}, volume={81 1}, pages={ 016401 } }

Time crystals are time-periodic self-organized structures postulated by Frank Wilczek in 2012. While the original concept was strongly criticized, it stimulated at the same time an intensive research leading to propositions and experimental verifications of discrete (or Floquet) time crystals-the structures that appear in the time domain due to spontaneous breaking of discrete time translation symmetry. The struggle to observe discrete time crystals is reviewed here together with propositions…

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## 220 Citations

Classical Many-Body Time Crystals.

- Physics, MedicinePhysical review letters
- 2019

This work provides a simple and pedagogical framework by which to obtain many-body time crystals using parametrically coupled resonators and presents a clear distinction between single-mode time-translation symmetry breaking and a situation where an extensive number of degrees of freedom undergo the transition.

Fractional time crystals

- PhysicsPhysical Review A
- 2019

Time crystals are quantum systems that are able to reveal condensed matter behavior in the time domain. It is known that crystallization in time can be observed in a periodically driven many-body…

Topological time crystals

- PhysicsNew Journal of Physics
- 2019

By analogy with the formation of space crystals, crystalline structures can also appear in the time domain. While in the case of space crystals we often ask about periodic arrangements of atoms in…

Controlled preparation of phases in two-dimensional time crystals

- PhysicsPhysical Review Research
- 2021

The study of phases is useful for understanding novel states of matter. One such state of matter are time crystals which constitute periodically driven interacting many-body systems that…

Time Crystal Platform: From Quasicrystal Structures in Time to Systems with Exotic Interactions.

- Physics, MedicinePhysical review letters
- 2018

Here it is shown that condensed matter problems ranging from single particles in potentials of quasicrystal structure to many-body systems with exotic long-range interactions can be realized in the time domain with an appropriate periodic driving.

Time crystals: Analysis of experimental conditions

- PhysicsPhysical Review A
- 2018

Time crystals are quantum many-body systems which are able to self-organize their motion in a periodic way in time. Discrete time crystals have been experimentally demonstrated in spin systems.…

A colloidal time crystal and its tempomechanical properties

- Physics
- 2021

The spontaneous breaking of symmetries is a widespread phenomenon in physics. When time translational symmetry is spontaneously broken, an exotic nonequilibrium state of matter in which the same…

Time crystal minimizes its energy by performing Sisyphus motion

- Physics, MedicineProceedings of the National Academy of Sciences
- 2019

Motion and minimal energy seem to contradict each other but Shapere and Wilczek showed that if the kinetic energy of a particle on a ring is a quartic function of its velocity, it may happen that the minimal energy corresponds to a particle moving along a ring with non-zero velocity.

Boundary Time Crystals.

- Medicine, PhysicsPhysical review letters
- 2018

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

Discrete time crystals in Bose-Einstein condensates and the symmetry-breaking edge in a simple two-mode theory

- PhysicsPhysical Review A
- 2021

Discrete time crystals (DTCs) refer to a novel many-body steady state that spontaneously breaks the discrete time-translational symmetry in a periodically-driven quantum system. Here, we study DTCs…

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