# Quantum time crystals.

@article{Wilczek2012QuantumTC, title={Quantum time crystals.}, author={Frank Wilczek}, journal={Physical review letters}, year={2012}, volume={109 16}, pages={ 160401 } }

Some subtleties and apparent difficulties associated with the notion of spontaneous breaking of time-translation symmetry in quantum mechanics are identified and resolved. A model exhibiting that phenomenon is displayed. The possibility and significance of breaking of imaginary time-translation symmetry is discussed.

## 421 Citations

Quantum physics: Time crystals

- Physics, EducationNature
- 2013

Physicists have come up with the mind-boggling concept of a time crystal based on the notion of broken time-translation symmetry, which might open up a whole new field of research.

Equilibration and order in quantum Floquet matter

- Physics
- 2017

Over the past decade, remarkable progress has occurred in the physics of closed quantum systems away from equilibrium, culminating in the recent experimental realization of so-called time crystals.…

Imaginary Time Crystal of Thermal Quantum Matter

- PhysicsChinese Physics Letters
- 2020

Spontaneous symmetry breaking is responsible for rich quantum phenomena from crystalline structures to superconductivity. This concept was boldly extended to the breaking of time translation, opening…

Condensed-matter physics: Marching to a different quantum beat

- PhysicsNature
- 2017

Two experiments have found evidence for a Floquet time crystal, which is characterized by persistent in‐phase oscillations, and this work aims to characterize this crystal as aperiodic oscillator.

Boundary Time Crystals.

- PhysicsPhysical review letters
- 2018

This work introduces boundary time crystals and analyzes in detail a solvable model where an accurate scaling analysis can be performed.

Dynamical nonlocality in quantum time via modular operators

- Physics, MathematicsPhysical Review A
- 2022

We formalize the concept of the modular energy operator within the Page and Wootters timeless framework. As a result, this operator is elevated to the same status as the more studied modular…

Nonlocality in quantum time via modular operators

- Physics, Mathematics
- 2021

The concept of the modular energy operator is formalized within the Page and Wooters timeless framework and is elevated to the same status as the more studied modular operators of position and momentum.

A dissipative time crystal with or without Z2 symmetry breaking

- PhysicsNew Journal of Physics
- 2020

We study an emergent semiclassical time crystal composed of two interacting driven-dissipative bosonic modes. The system has a discrete Z2 spatial symmetry which, depending on the strength of the…

Quantum time crystals with programmable disorder in higher dimensions

- Physics
- 2020

We present fresh evidence for the presence of discrete quantum time crystals in two spatial dimensions. Discrete time crystals are intricate quantum systems that are concomitant with spontaneous…

Relativistic spacetime crystals

- PhysicsActa crystallographica. Section A, Foundations and advances
- 2021

By appropriate reformulation of relativistic spacetime geometry, a direct mapping to Euclidean space crystals is shown and hidden symmetries in relativist spacetime crystals are uncovered.

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