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Time crystals are nonequilibrium phases of matter characterized by the emergence of temporal ordering, in which an interacting many-body system develops robust structure in its time evolution that is not trivially dictated by the external…

Quantum Physics · Physics 2026-05-27 Gonzalo Camacho , Benedikt Fauseweh

Time crystals are quantum many-body systems which, due to interactions between particles, are able to spontaneously self-organize their motion in a periodic way in time by analogy with the formation of crystalline structures in space in…

Quantum Gases · Physics 2018-04-04 Krzysztof Giergiel , Artur Miroszewski , Krzysztof Sacha

Time crystals are quantum many-body systems which are able to self-organize their motion in a periodic way in time. Discrete time crystals have been experimentally demonstrated in spin systems. However, the first idea of spontaneous…

Quantum Gases · Physics 2018-07-16 Krzysztof Giergiel , Arkadiusz Kosior , Peter Hannaford , Krzysztof Sacha

Time crystals correspond to a phase of matter where time-translational symmetry (TTS) is broken. Up to date, they are well studied in open quantum systems, where external drive allows to break discrete TTS, ultimately leading to Floquet…

Quantum Physics · Physics 2019-11-27 Valerii K. Kozin , Oleksandr Kyriienko

When the discrete time-translation symmetry of isolated, periodically driven systems is spontaneously broken, a new phase of matter can emerge. We review some recent developments on both the theoretical underpinnings and experimental…

Quantum Physics · Physics 2018-11-28 Norman Y. Yao , Chetan Nayak

Understanding different aspects of time is at the core of many areas in theoretical physics. Minimal models of continuous stochastic and quantum clocks have been proposed to explore fundamental limitations on the performance of timekeeping…

Quantum Physics · Physics 2026-03-31 Ludmila Viotti , Marcus Huber , Rosario Fazio , Gonzalo Manzano

Time crystals are quantum systems which are able to reveal condensed matter behavior in the time domain. It is known that crystalization in time can be observed in a periodically driven many-body system when interactions between particles…

Quantum Gases · Physics 2019-04-02 Pawel Matus , Krzysztof Sacha

Time crystals are an enigmatic phase of matter in which a quantum mechanical system displays repetitive, observable motion - they spontaneously break the time translation symmetry. On the other hand optomechanical systems, where mechanical…

Quantum Physics · Physics 2025-10-20 J. T. Mäkinen , P. J. Heikkinen , S. Autti , V. V. Zavjalov , V. B. Eltsov

Continuous time crystals, i.e., nonequilibrium phases with a spontaneously broken continuous time-translational symmetry, have been studied and recently observed in the long-time dynamics of open quantum systems. Here, we investigate a…

Quantum Physics · Physics 2025-09-15 Felix Russo , Thomas Pohl

Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems is those which do not thermalize under…

Strongly Correlated Electrons · Physics 2022-10-05 Dominic V. Else , Christopher Monroe , Chetan Nayak , Norman Y. Yao

We argue that time crystal properties naturally arise from phase-space noncommutative quantum mechanics. In order to exemplify our point we consider the 2-dimensional noncommutative quantum harmonic oscillator and show that it exibihits…

Quantum Physics · Physics 2024-02-29 Orfeu Bertolami , A. E. Bernardini

Crystals spontaneously break the continuous translation symmetry in space, despite the invariance of the underlying energy function. This has triggered suggestions of time crystals analogously lifting translational invariance in time.…

Mesoscale and Nanoscale Physics · Physics 2024-02-29 A. Greilich , N. E. Kopteva , A. N. Kamenskii , P. S. Sokolov , V. L. Korenev , M. Bayer

Open many-body quantum systems can exhibit intriguing nonequilibrium phases of matter, such as time crystals. In these phases, the state of the system spontaneously breaks the time-translation symmetry of the dynamical generator, which…

Discrete time crystals are a special phase of matter in which time translational symmetry is broken through a periodic driving pulse. Here, we first propose and characterize an effective mechanism to generate a stable discrete time crystal…

Quantum Physics · Physics 2025-03-31 Rozhin Yousefjani , Krzysztof Sacha , Abolfazl Bayat

In analogy with crystalline solids around us, Wilczek recently proposed the idea of "time crystals" as phases that spontaneously break the continuous time translation into a discrete subgroup. The proposal stimulated further studies and…

Statistical Mechanics · Physics 2015-06-26 Haruki Watanabe , Masaki Oshikawa

A time crystal is a macroscopic quantum system in periodic motion in its ground state, stable only if isolated from energy exchange with the environment. For this reason, coupling separate time crystals is challenging, and time crystals in…

Motivated by the Generalized Uncertainty Principle, covariance, and a minimum measurable time, we propose a deformation of the Heisenberg algebra and show that this leads to corrections to all quantum mechanical systems. We also demonstrate…

General Physics · Physics 2016-01-27 Mir Faizal , Mohammed M. Khalil , Saurya Das

Time crystals are unexpected states of matter that spontaneously break time translation symmetry either in a discrete or continuous manner. However, spatially-mesoscale space-time crystals that break both the space and time symmetries have…

Soft Condensed Matter · Physics 2025-07-24 Hanqing Zhao , Ivan I. Smalyukh

Time crystal is defined as a phase of matter spontaneously exhibiting a periodicity in time. Previous studies focused on discrete quantum time crystals under periodic drive. Here, we propose a time crystal model based on a levitated charged…

Quantum Physics · Physics 2020-08-27 Yi Huang , Qihao Guo , Anda Xiong , Tongcang Li , Zhang-qi Yin

Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous time-translation symmetry in static systems is proved impossible for the equilibrium state, the…

Quantum Gases · Physics 2020-08-19 Lingzhen Guo , Pengfei Liang
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