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Time crystals form when arbitrary physical states of a periodically driven system spontaneously break discrete time-translation symmetry. We introduce one-dimensional time-crystalline topological superconductors, for which time-translation…

Mesoscale and Nanoscale Physics · Physics 2020-03-11 Aaron Chew , David F. Mross , Jason Alicea

Photonic time crystals are a class of artificial materials that have only recently been explored. They are characterized by the ultrafast modulation of the material properties in time, causing a momentum bandgap for light that propagates…

Following the recent realisation that periodically driven quantum matter can support new types of spatiotemporal order, now known as discrete time crystals (DTCs), we consider the stability of this phenomenon. Motivated by its conceptual…

Statistical Mechanics · Physics 2017-05-24 Achilleas Lazarides , Roderich Moessner

Time crystal is a class of non-equilibrium phases with broken time-translational symmetry. Here we demonstrate the time crystal in a single-mode nonlinear cavity. The time crystal originates from the self-oscillation induced by a linear…

Quantum Physics · Physics 2024-12-05 Yaohua Li , Chenyang Wang , Yuanjiang Tang , Yong-Chun Liu

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

Non-equilibrium driving systems provide fertile ground for exploring intriguing spontaneous symmetry breaking phenomena. In this study, we report on the intertwined discrete spacetime translational symmetry breaking in a driven-dissipative…

Statistical Mechanics · Physics 2024-06-25 Xingdong Luo

Photonic space time crystals (PSTCs) are emerging materials characterized by periodic variations in electromagnetic parameters with respect to both space and time. To date, research on PSTCs remains theoretical, with no practical…

Applied Physics · Physics 2025-11-14 Onta Shahriar , M. R. C. Mahdy

An acoustic standing wave acts as a lattice of evenly spaced potential energy wells for sub-wavelength-scale objects. Trapped particles interact with each other by exchanging waves that they scatter from the standing wave. Unless the…

Soft Condensed Matter · Physics 2026-02-10 Mia C. Morrell , Leela Elliott , David G. Grier

Moving media break time-reversal symmetry and exhibit intriguing optical nonreciprocity. This nonreciprocity is usually weak due to the much lower moving speed of media relative to the speed of light. We demonstrate that strong optical…

Optics · Physics 2026-03-13 Hengzhi Li , Wanyue Xiao , Junho Jung , Hao Pan , Shubo Wang

Photonic Time crystals (PTC) arise in time-modulated media when the frequency of modulation of permittivity is on the order of twice the frequency of light and are manifested by the generation and amplification of so-called time reversed…

Optics · Physics 2024-04-01 Jacob B Khurgin

The rich dynamics and phase structure of driven systems includes the recently described phenomenon of the "discrete time crystal" (DTC), a robust phase which spontaneously breaks the discrete time translation symmetry of its driving…

Quantum Physics · Physics 2018-05-18 Jared Rovny , Robert L. Blum , Sean E. Barrett

It has been argued recently that an inhomogeneous system could rotate spontaneously in its ground state - hence a 'time crystal' which is periodic in time. In this note we present a very simple example: a superfluid ring threaded by a…

Quantum Physics · Physics 2015-06-16 Philippe Nozières

We describe a possible general and simple paradigm in a classical thermal setting for discrete time crystals (DTCs), systems with stable dynamics which is subharmonic to the driving frequency thus breaking discrete time-translational…

Statistical Mechanics · Physics 2020-01-22 F. M. Gambetta , F. Carollo , A. Lazarides , I. Lesanovsky , J. P. Garrahan

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

Topological edge states in systems of two (or more) dimensions offer scattering-free transport, exhibiting robustness to inhomogeneities and disorder. In a different domain, time-modulated systems, such as photonic time crystals (PTCs),…

Photonic time crystals (PhTCs) are spatially uniform media whose material parameters vary periodically in time, opening momentum bandgaps within which the fields of electromagnetic modes can grow exponentially in time. To date, PhTCs have…

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 present a theoretical study of the interaction between an atom characterized by a degenerate ground state and a reciprocal environment, such as a semiconductor nanoparticle, without the presence of external bias. Our analysis reveals…

Quantum Physics · Physics 2024-03-22 Mário G. Silveirinha , Hugo Terças , Mauro Antezza

The breaking of the continuous time-translation symmetry manifests, in Markovian open quantum systems, through the emergence of non-stationary dynamical phases. Systems that display nonequilibrium transitions into these phases are referred…

Statistical Mechanics · Physics 2022-05-04 Federico Carollo , Igor Lesanovsky

Discrete time crystals (DTCs) are non-equilibrium phases in periodically driven systems that exhibit spontaneous breaking of discrete time-translation symmetry. The stabilization of most DTC phases is achieved via the disorder-induced…

Quantum Physics · Physics 2025-12-19 Jian-Jia Wang , Ling-Zhi Tang , Yan-Xiong Du , Dan-Wei Zhang
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