Saturday 15 March 2025
Physicists have long been fascinated by the concept of time crystals, which are materials that exhibit periodic motion in time, just like regular crystals exhibit periodic patterns in space. But unlike regular crystals, time crystals don’t rely on external stimuli to maintain their rhythm – they do it all on their own.
Recently, researchers have made significant progress in understanding how to create these strange and fascinating materials. In a new study, scientists have proposed a general protocol for engineering dissipative time crystals in quantum open systems through symmetry-induced fragmentation and ergodicity breaking.
In traditional physics, time crystals are typically thought of as being created by periodically driving a system with an external force. But this approach has limitations – it’s only possible to create time crystals at very low temperatures, and even then, they’re prone to decay quickly.
The new protocol is different. It uses the concept of symmetry-induced fragmentation to break ergodicity in quantum systems. Ergodicity refers to the idea that a system will eventually settle into a uniform distribution of states over time – but in time crystals, this doesn’t happen. Instead, the system gets stuck in a periodic pattern.
The researchers start by creating a Liouvillian, which is a mathematical object that describes the dynamics of a quantum system. They then use symmetry-induced fragmentation to break ergodicity and create non-dissipative eigenmodes with purely imaginary eigenvalues. These modes give rise to long-time oscillations that break both ergodicity and time-translation symmetry.
The researchers illustrate their protocol using a dissipative lattice model, which is a simplified version of the real world. They show that even when the U(1) symmetry is broken, a prethermal time-crystal behavior survives – meaning that the system still exhibits periodic motion over long periods of time.
This prethermal time-crystal behavior is richly structured and derives from Fermi statistics and the Liouvillian skin effect of the model. The researchers show that excitations above the boundary-localized dark states can be mapped to the irreducible representations of the permutation group, which determines the branching rules of the system.
The implications of this research are significant – it could lead to the creation of new materials with unique properties that don’t exist in nature. Time crystals have already been proposed as a way to create ultra-stable clocks and memory devices, and this new protocol could make those possibilities a reality.
Cite this article: “Engineering Dissipative Time Crystals in Quantum Systems”, The Science Archive, 2025.
Time Crystals, Quantum Systems, Symmetry-Induced Fragmentation, Ergodicity Breaking, Liouvillian, Dissipative Eigenmodes, Oscillations, Prethermal Time-Crystal Behavior, Fermi Statistics, Liouvillian Skin Effect
Reference: Haowei Li, Wei Yi, “Symmetry-induced fragmentation and dissipative time crystal” (2025).
