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Discrete time crystals are a many-body state of matter where the extensive system's dynamics are slower than the forces acting on it. Nowadays, there is a growing debate regarding the specific properties required to demonstrate such a…

Classical Physics · Physics 2019-09-25 Toni L. Heugel , Matthias Oscity , Alexander Eichler , Oded Zilberberg , R. Chitra

Discrete time crystals are periodically driven systems that display spontaneous symmetry breaking of time translation invariance in the form of indefinite subharmonic oscillations. We introduce a thermodynamically consistent model for a…

Statistical Mechanics · Physics 2021-01-20 Lukas Oberreiter , Udo Seifert , Andre C. Barato

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

The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: discrete time crystals (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay…

Statistical Mechanics · Physics 2020-04-21 Norman Y. Yao , Chetan Nayak , Leon Balents , Michael P. Zaletel

The spontaneous breaking of time translation symmetry has led to the discovery of a new phase of matter - the discrete time crystal. Discrete time crystals exhibit rigid subharmonic oscillations, which result from a combination of many-body…

Spontaneous symmetry breaking is one of the central organizing principles in physics. Time crystals have emerged as an exotic phase of matter, spontaneously breaking the time translational symmetry, and are mainly categorized as discrete or…

Quantum Physics · Physics 2026-01-16 Jan Carlo Schumann , Igor Lesanovsky , Parvinder Solanki

A time crystal is an exotic phase of matter where time-translational symmetry is broken; this phase differs from the spatial symmetry breaking induced in crystals in space. Lots of experiments report the transition from a thermal…

Discrete time crystal is a class of nonequilibrium quantum systems exhibiting subharmonic responses to external periodic driving. Here we propose a class of discrete time crystals enforced by nonsymmorphic dynamical symmetry. We start with…

Quantum Physics · Physics 2023-10-10 Zi-Ang Hu , Bo Fu , Xiao Li , Shun-Qing Shen

We simulate the dynamics of paramagnetic colloidal particles that are placed above a magnetic hexagonal pattern and exposed to an external field periodically changing its direction along a control loop. The conformation of three colloidal…

Soft Condensed Matter · Physics 2022-10-12 Adrian Ernst , Anna M. E. B. Rossi , Thomas M. Fischer

Many-body quantum systems, under suitable conditions, exhibit time-translation symmetry breaking and settle in a discrete time crystalline (DTC) phase -- an out-of-equilibrium quantum phase of matter. The defining feature of DTC is a robust…

Quantum Physics · Physics 2025-11-14 Gourab Das , Saptarshi Saha , Rangeet Bhattacharyya

Driven systems offer the potential to realize a wide range of non-equilibrium phenomena that are inaccessible in static systems, such as the discrete time crystals. Time rondeau crystals with a partial temporal order have been proposed as a…

Statistical Mechanics · Physics 2025-10-24 Zhuocheng Ma , Jin Yan , Hongzheng Zhao , Liang-You Peng

Spontaneous symmetry breaking is a fundamental concept in many areas of physics, ranging from cosmology and particle physics to condensed matter. A prime example is the breaking of spatial translation symmetry, which underlies the formation…

Two trains of light pulses at periods that are equally shifted from the harmonics of a missing fundamental, are combined in a nonlinear crystal. As a result of a noncollinear phase matched second order nonlinear generation, a new train of…

Other Condensed Matter · Physics 2016-08-16 Xavier Vidal , Pablo Balenzuela , Javier M. Buldú , Jordi Martorell , Jordi García-Ojalvo

The spontaneous breaking of symmetries is a widespread phenomenon in physics. When time translational symmetry is spontaneously broken, an exotic nonequilibrium state of matter in which the same structures repeat themselves in time can…

Soft Condensed Matter · Physics 2021-12-10 Marina Evers , Raphael Wittkowski

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

We demonstrate that the prethermal regime of periodically driven (Floquet), classical many-body systems can host nonequilibrium phases of matter. In particular, we show that there exists an effective Hamiltonian that captures the dynamics…

Quantum Physics · Physics 2021-10-04 Bingtian Ye , Francisco Machado , Norman Y. Yao

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

Time crystals are an eagerly sought phase of matter with broken time-translation symmetry. Quantum time crystals with discretely broken time-translation symmetry have been demonstrated in trapped ions, atoms and spins while continuously…

Optics · Physics 2023-08-03 Tongjun Liu , Jun-Yu Ou , Kevin F. MacDonald , Nikolay I. Zheludev

Time crystals constitute a novel phase of matter defined by the spontaneous breaking of timetranslation symmetry. Here we present a scheme to realize a continuous-time crystal of the vibrational phonon in the normal mode of two coupled…

Quantum Physics · Physics 2026-04-30 Yi-Ling Zhan , Chun-Fu Liu , J. -T. Bu , K. -F Cui , S. -L. Su , L. -L. Yan , Gang Chen

Floquet (periodically driven) systems can give rise to unique non-equilibrium phases of matter without equilibrium analogs. The most prominent example is the realization of discrete time crystals. An intriguing question emerges: what other…

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