Space Time Crystals

Time to time, i like to think outside the work and enjoy totally random stuff so I decided to learn more on Space-Time Crystal and collected the following:

What is a crystal?

crystal or crystalline solid is a solid material whose constituent atomsmolecules, or ions are arranged in an ordered pattern extending in all three spatial dimensions. (more from wiki)

What is time crystal? (also called as space-time crystal or four dimensional crystal)

space-time crystal or four dimensional crystal is a theoretical structure periodic in time and space. It extends the idea of a crystal to four dimensions (more from wiki)

Classical time crystals:

 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 density waves.

Read Full Paper here

Quantum time crystals:

Difficulties around the idea of spontaneous breaking of time translation symmetry in a closed quantum mechanical system are identified, and then overcome in a simple model. The possibility of ordering in imaginary time is also discussed.

Read Full Paper here.

 

A few notable articles:

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