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Time-variant systems have recently garnered considerable attention due to their unique potentials in manipulating electromagnetic waves. Here, a novel class of topological spacetime crystals is introduced, with a traveling-wave modulation…

Optics · Physics 2025-09-24 João C. Serra , Mário G. Silveirinha

A discrete time crystal is a recently discovered non-equilibrium phase of matter that has been shown to exist in disordered, periodically driven Ising spin chains. In this phase, if the system is initially prepared in one of a certain class…

Quantum Physics · Physics 2019-01-30 Edwin Barnes , John M. Nichol , Sophia E. Economou

A time crystal is a time dependent physical system that does not reach a standstill, even in state of minimum energy. Here we show that the stability of a time crystal can be enhanced by its topology. For this we simulate time crystals made…

Pattern Formation and Solitons · Physics 2019-10-31 Jin Dai , Xubiao Peng , Antti J. Niemi

Non-stationary long-time dynamics was recently observed in a driven two-component Bose-Einstein condensate coupled to an optical cavity [N. Dogra, et al. arXiv:1901.05974] and analyzed in mean-field theory. We solve the underlying model in…

Quantum Physics · Physics 2020-01-01 Berislav Buca , Dieter Jaksch

We investigate the transverse field Ising model subject to a two-step periodic driving protocol and quasiperiodic modulation of the Ising couplings. Analytical results on the phase boundaries associated with Majorana edge modes and…

Disordered Systems and Neural Networks · Physics 2020-11-17 Pengfei Liang , Rosario Fazio , Stefano Chesi

Topological phase transitions, characterized by the closing and reopening of band gaps and a concomitant change in topological invariants, have played a central role in topological physics. However, such transitions have so far been…

Optics · Physics 2025-12-19 Zebin Zhu , Bolun Huang , Siqi Xu , Jingming Chen , Yan Meng , Zhenxiao Zhu , Xiang Xi , Zhen Gao

Time crystals are time-periodic self-organized structures postulated by Frank Wilczek in 2012. While the original concept was strongly criticized, it stimulated at the same time an intensive research leading to propositions and experimental…

Quantum Physics · Physics 2018-01-19 Krzysztof Sacha , Jakub Zakrzewski

Understanding how temporal order degrades in quantum systems remains a central issue in nonequilibrium physics. Here we study the melting of discrete time crystals in a periodically driven holographic system, where a distinct (discrete)…

High Energy Physics - Theory · Physics 2026-04-16 Yu-Qi Lei , Xian-Hui Ge , Yu Tian , Shao-Feng Wu

We introduce a boundary condition twisted by time translation as a novel probe to characterize dynamical phases in periodically driven (Floquet) quantum systems. Inspired by twisted boundary conditions in equilibrium systems, this approach…

Statistical Mechanics · Physics 2025-11-17 Ryota Nakai , Taozhi Guo , Shinsei Ryu

Discrete-Time Crystals (DTC) are a non-equilibrium phase of matter characterized by the breaking of time-translation symmetry in periodically driven quantum systems. In this work, we present a detailed thermodynamic analysis of a DTC in a…

We introduce a space-time Floquet operator, a generalization of the conventional Floquet operator, that captures the long-time behavior of space-time crystals - systems where spatial and temporal periodicities are intrinsically intertwined.…

Other Condensed Matter · Physics 2025-10-21 Abhijeet Melkani , Jayson Paulose

We have constructed and characterised an instrument to study gravitationally bouncing droplets of fluid, subjected to periodic driving force. Our system incorporates a droplet printer that enables an on-demand computer controlled deposition…

Fluid Dynamics · Physics 2024-03-12 Tapio Simula

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

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

Periodic modulation of the material index in time opens momentum gaps. Such systems are regarded as the temporal analogue of common spatial crystals, wherein the bandgaps open in the frequency space. Recent studies have also led to the…

Optics · Physics 2024-12-13 Mingwei Li , Jianwei Liu , Xulong Wang , Wenjie Chen , Guancong Ma , Jianwen Dong

Periodically driven quantum systems manifest various non-equilibrium features which are absent at equilibrium. For example, discrete time-translation symmetry can be broken in periodically driven quantum systems leading to an exotic phase…

Quantum Physics · Physics 2020-04-09 C. M. Dai , Z. C. Gu , X. X. Yi

We present a quantum circuit with measurements and post-selection that exhibits a panoply of space- and/or time-ordered phases, from ferromagnetic order to spin-density waves to time crystals. Unlike the time crystals that have been found…

Statistical Mechanics · Physics 2022-05-03 Sankhya Basu , Daniel P. Arovas , Sarang Gopalakrishnan , Chris A. Hooley , Vadim Oganesyan

We present the theory of spontaneous symmetry breaking (SSB) of discrete time translations as recently realized in the space-time crystals of an atomic Bose-Einstein condensate. The non-equilibrium physics related to such a…

Quantum Gases · Physics 2021-11-10 J. N. Stehouwer , J. Smits , P. van der Straten , H. T. C. Stoof

We consider a dissipative quantum Ising model periodically driven by a train of $\pi$-pulses and investigate dissipative discrete time crystals (DTCs) in solids. In this model, the interaction between the spins spontaneously breaks the…

Statistical Mechanics · Physics 2022-06-01 Koki Chinzei , Tatsuhiko N. Ikeda

Quantum time crystals are systems characterised by spontaneously emerging periodic order in the time domain. A range of such phases has been reported. The concept has even been discussed in popular literature, and deservedly so: while the…