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Inversion and time reversal are essential symmetries for the structure of Cooper pairs in superconductors. The loss of one or both leads to modifications to this structure and can change the properties of the superconducting phases in…

Superconductivity · Physics 2023-03-21 Mark H Fischer , Manfred Sigrist , Daniel F Agterberg , Youichi Yanase

A spacetime crystal is a phase of matter that spontaneously develops periodic order in both space and time. Spacetime crystals have been experimentally observed in microscopic quantum many-body systems and, very recently, in a mesoscopic…

Soft Condensed Matter · Physics 2026-03-11 Guoqing Liu , Jimin Bai , Matteo Baggioli , Jie Zhang

A choreographic time crystal is a dynamic lattice structure in which the points comprising the lattice move in a coordinated fashion. These structures were initially proposed for understanding the motion of synchronized satellite swarms.…

Soft Condensed Matter · Physics 2024-04-23 Andras Libal , Tunde Balazs , C. Reichhardt , C. J. O. Reichhardt

By including appropriate Riemman cubic invariants, we find that the dynamics of classical time crystals can be straightforwardly realized in Einstein gravity on the FLRW metric. The time reflection symmetry is spontaneously broken in the…

High Energy Physics - Theory · Physics 2020-11-25 Xing-Hui Feng , Hyat Huang , Shou-Long Li , H. Lu , Hao Wei

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

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

Superconductivity and magnetism are antagonistic states of matter. The presence of spontaneous magnetic fields inside the superconducting state is, therefore, an intriguing phenomenon prompting extensive experimental and theoretical…

Due to the fact that only matter fields have phase, frequently is believed that the gauge principle can induce gauge fields only in quantum systems. But this is not necessary. This paper, of pedagogical scope, presents a classical system…

High Energy Physics - Theory · Physics 2007-05-23 Luis Alberto Sanchez , Jorge Mahecha

Spontaneous symmetry breaking is responsible for the rich phenomena in equilibrium physics. Driving a system out-of-equilibrium can significantly enrich the possibility of spontaneous symmetry breaking, which occurs not only in space, but…

Statistical Mechanics · Physics 2023-07-06 Mingxi Yue , Zi Cai

Colloidal particles can self-assemble into various ordered structures in fluid flows that have potential applications in biomedicine, materials synthesis and encryption. These dynamic processes are also of fundamental interest for probing…

Soft Condensed Matter · Physics 2017-01-31 Yu Abe , Bo Zhang , Leonardo Gordillo , Alireza Mohammad Karim , Lorraine F. Francis , Xiang Cheng

In this work, we analyze a scalar field model which gives rise to stable bound states in field space characterized by nonzero motion that breaks the underlying time translation symmetry of its Hamiltonian, known as time crystals. We…

High Energy Physics - Phenomenology · Physics 2025-09-12 Laura Mersini-Houghton

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

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

Moir\'e physics has transcended spatial dimensions, extending into synthetic domains and enabling novel quantum phenomena. We propose a theoretical model for a two-dimensional (2D) Moir\'e time crystal formed by ultracold atoms, induced by…

Quantum Gases · Physics 2026-03-03 Weijie Liang , Weiping Zhang , Keye Zhang

We introduce the time glass, a non-periodic analogue of the discrete time crystal that arises in periodically driven dissipative quantum many-body systems. This phase is defined by two key features: (i) spatial long-range order arising from…

Statistical Mechanics · Physics 2026-03-11 Taiki Haga

A new class of self-similar ordered structures with non-crystallographic point symmetries is presented. Each of these structures, named superquasicrystals, is given as a section of a higher-dimensional "crystal" with recursive superlattice…

Materials Science · Physics 2007-05-23 Komajiro Niizeki , Nobuhisa Fujita

The competition between thermal fluctuations and potential forces is the foundation of our understanding of phase transitions and matter in equilibrium. Driving matter out of equilibrium allows for a new class of interactions which are…

Spontaneous symmetry breaking has revolutionized the understanding in numerous fields of modern physics. Here, we theoretically demonstrate the spontaneous time-reversal symmetry breaking in a cavity quantum electrodynamics system in which…

Quantum Physics · Physics 2018-08-01 Yu-Kun Lu , Pai Peng , Qi-Tao Cao , Da Xu , Jan Wiersig , Qihuang Gong , Yun-Feng Xiao

Phase crystals are a class of nonuniform superconducting ground states characterized by spontaneous phase gradients of the superconducting order parameter. These phase gradients nonlocally drive periodic currents and magnetic fields, thus…

Time crystallization is a hallmark of superfluidity, indicative of the fundamental fact that along with breaking the global U(1) symmetry, superfluids also break time-translation symmetry. While the standard discussion of the time…

Statistical Mechanics · Physics 2019-02-20 Nikolay V. Prokof'ev , Boris V. Svistunov
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