Time crystals: a review

@article{Sacha2017TimeCA,
  title={Time crystals: a review},
  author={Krzysztof Sacha and Jakub J. Zakrzewski},
  journal={Reports on Progress in Physics},
  year={2017},
  volume={81}
}
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… 

Fractional time crystals

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

Classical Many-Body Time Crystals.

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.

Topological time crystals

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

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 crystals: Analysis of experimental conditions

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.

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

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.

A colloidal time crystal and its tempomechanical properties

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

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.

Condensed matter physics in big discrete time crystals

We review the application of discrete time crystals created in a Bose-Einstein condensate (BEC) of ultracold atoms bouncing resonantly on an oscillating atom mirror to the investigation of condensed

Boundary Time Crystals.

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