# 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…

## 219 Citations

### 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…

### Adiabatic and irreversible classical discrete time crystals

- PhysicsSciPost Physics
- 2022

We simulate the dynamics of paramagnetic colloidal particles that are placed above a magnetic hexagonal pattern and exposed to an external field periodically changing its direction along a control…

### Six-dimensional time-space crystalline structures

- Physics
- 2021

Time crystalline structures are characterized by regularity that single-particle or many-body systems manifest in the time domain, closely resembling the spatial regularity of ordinary space…

### Autonomous topological time crystals and knotty molecular motors

- 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-Crystal Particles and Classical Spin 4-vector

- Physics
- 2021

Time crystals are exotic phases of matter characterized by a broken time-translational symmetry, such that the ground state of the system evolves in time in a periodic fashion. Even though the…

### Time-Crystalline Topological Superconductors.

- PhysicsPhysical 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.

### Time crystals in a shaken atom-cavity system

- PhysicsPhysical Review A
- 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…

### Observation of a Dissipative Time Crystal.

- PhysicsPhysical review letters
- 2021

The first experimental realization of a time crystal stabilized by dissipation is presented, demonstrating the robustness of this dynamical phase against system parameter changes and temporal perturbations of the driving.

### 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…

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