The source of this essay is the following article:

Scientists unveil new form of matter: Time crystals
By Robert Sanders, UC Berkeley Monday, January 30, 2017

Link: https://www.universityofcalifornia.edu/news/scientists-unveil-new-form-m...

The article discusses the work of Norman Yao and others on these crystals; structures that repeat in time similar to the way that ordinary crystals are structures that repeat in space.

In a paper published online earlier this month in the journal Physical Review Letters, the UC Berkeley assistant professor of physics describes exactly how to make and measure the properties of such a crystal, and even predicts what the various phases surrounding the time crystal should be -- akin to the liquid and gas phases of ice.

This is not mere speculation. Two groups followed Yao's blueprint and have already created the first-ever time crystals. The groups at the University of Maryland and Harvard University reported their successes, using two totally different setups, in papers posted online last year, and have submitted the results for publication. Yao is a co-author on both papers.

Time crystals repeat in time because they are kicked periodically, sort of like tapping Jell-O repeatedly to get it to jiggle, Yao said. The big breakthrough, he argues, is less that these particular crystals repeat in time than that they are the first of a large class of new materials that are intrinsically out of equilibrium, unable to settle down to the motionless equilibrium of, for example, a diamond or ruby.

Among other things, these crystals are examples of non-equilibrium matter. It is asserted that time crystals break time symmetry, such that a system driven by a periodic driver with a period equal to "T" will oscillate, or appear to do so, with a period that is greater than "T". (Imagine jiggling some system at a rate of 10 times per second and having it vibrate at 20 cycles per second.)

The article in Physical Review Letters is by subscription only. It is here: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.030401

The abstract of the article is as follows:

Abstract

Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.