# Classical time crystals.

@article{Shapere2012ClassicalTC, title={Classical time crystals.}, author={Alfred Shapere and Frank Wilczek}, journal={Physical review letters}, year={2012}, volume={109 16}, pages={ 160402 } }

We consider the possibility that classical dynamical systems display motion in their lowest-energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary orbits of an angular variable as lowest-energy trajectories for nonsingular Lagrangian systems. Dynamics within orbits of broken symmetry provide a natural arena for formation of time crystals. We exhibit models of that kind, including a model with traveling…

## Figures and Topics from this paper

## 193 Citations

Discrete Time Crystals in the Absence of Manifest Symmetries or Disorder in Open Quantum Systems.

- Physics, MedicinePhysical review letters
- 2019

A semiclassical approach reveals the emergence of a robust discrete time-crystalline phase in the thermodynamic limit in which metastability, dissipation, and interparticle interactions play a crucial role.

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…

Autonomous topological time crystals and knotty molecular motors.

- Medicine, PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2020

It is demonstrated how the time crystalline qualities of a closed string are greatly enhanced when the string becomes knotted, which means that physical realizations of Hamiltonian time crystals can be constructed in terms of knotted ring molecules.

Time-Crystalline Topological Superconductors.

- Physics, Materials SciencePhysical review letters
- 2020

This work introduces one-dimensional time-crystalline topological superconductors, for which time-translation symmetry breaking and topological physics intertwine-yielding anomalous Floquet Majorana modes that are not possible in free-fermion systems.

Classical discrete time crystals

- Physics
- 2018

The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: the discrete time crystal (DTC). This phase exhibits collective…

Time crystals in primordial perturbations

- Physics
- 2019

Cosmological time crystal (TC) corresponds to a matter state where the periodic motion of field forms a limit cycle in its phase space. We explore what would happen if it existed in inflationary…

Time crystals in a shaken atom-cavity system

- Physics
- 2019

We demonstrate the emergence of a time crystal of atoms in a high-finesse optical cavity driven by a phase-modulated transverse pump field, resulting in a shaken lattice. This shaken system exhibits…

Exact solution of a boundary time-crystal phase transition: time-translation symmetry breaking and non-Markovian dynamics of correlations

- Physics
- 2021

The breaking of the continuous time-translation symmetry manifests, in Markovian open quantum systems, through the emergence of non-stationary dynamical phases. Systems that display nonequilibrium…

Discrete time quasicrystals

- PhysicsPhysical Review B
- 2019

Periodically driven quantum many-body systems can spontaneously reorganize their motion and start moving with a period different than the driving period. These are ``discrete time crystals'' and they…

Quantum Time Crystals from Hamiltonians with Long-Range Interactions.

- Physics, MedicinePhysical review letters
- 2019

This study proposes a form of a Hamiltonian for which the unitary dynamics exhibits the time crystalline behavior and breaks continuous TTS, based on a spin-1/2 many-body Hamiltonian which has long-range multispin interactions in the form of spin strings, thus bypassing previously known no-go theorems.

## References

SHOWING 1-10 OF 18 REFERENCES

Branched quantization.

- Medicine, PhysicsPhysical review letters
- 2012

A method for quantization of Lagrangians for which the Hamiltonian, as a function of momentum, is a branched function, possibly with cusps is proposed, and several possible applications are indicated.

The geometry of biological time

- Biology, Physics
- 1980

The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways is presented.

"J."

- 1890

however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)…

PRL

- PRL
- 2012

Phys. Rev. Lett

- Phys. Rev. Lett
- 2012

preceding Letter

- Phys. Rev. Lett. 109, 160401
- 2012

J. High Energy Phys

- J. High Energy Phys
- 2004

S

- Mukohyama, JHEP 0405 (05): 074
- 2004

Biological Rhythm Research 8

- 1 (1977); A. Winfree, The Geometry of Biological Time, 2nd ed.
- 2001

Phys

- Lett. B 458, 209
- 1999