Time crystals: a review

Abstract

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 verifications of discrete (or Floquet) time crystals -- the structures that appear in the time domain due to spontaneous breaking of discrete time translation symmetry. The struggle to observe discrete time crystals is reviewed here together with propositions that generalize this concept introducing condensed matter like physics in the time domain. We shall also revisit the original Wilczek's idea and review strategies aimed at spontaneous breaking of continuous time translation symmetry.

VIDEO ABSTRACT: https://youtu.be/5uaUEWH0x60

References in corpus (18)

• Many body localization and thermalization in quantum statistical mechanics
• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• Equilibrium states of generic quantum systems subject to periodic driving
• Many-body localization in periodically driven systems
• Absence of Quantum Time Crystals
• Equilibration and Order in Quantum Floquet Matter
• Floquet time crystal in the Lipkin-Meshkov-Glick model
• Comment on "Quantum Time Crystals": a new paradigm or just another proposal of perpetuum mobile?
• Floquet Topological Order in Interacting Systems of Bosons and Fermions
• Nonequilibrium Quantum Phase Transitions in the Ising Model
• Anderson localization and Mott insulator phase in the time domain
• The role of real-space micromotion for bosonic and fermionic Floquet fractional Chern insulators
• Quantum phase transition and critical fluctuations of an attractive Bose gas in a double well potential
• Anderson localization of a Rydberg electron along a classical orbit
• Rotating Casimir systems: magnetic-field-enhanced perpetual motion, possible realization in doped nanotubes, and laws of thermodynamics

Cited by in corpus (354)

• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
• Boundary time crystals
• Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 XY Magnets
• Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System
• Observation of a dissipative time crystal
• Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
• Engineered Dissipation for Quantum Information Science
• Quantum Many-Body Scars: A Quasiparticle Perspective
• Observation of time quasicrystal and its transition to superfluid time crystal
• Tailoring quantum gases by Floquet engineering
• Colloquium: Quantum and Classical Discrete Time Crystals
• Observation of a space-time crystal in a superfluid quantum gas
• Discrete time crystals in the absence of manifest symmetries or disorder in open quantum systems
• Quantum Many-Body Scars and Space-Time Crystalline Order from Magnon Condensation
• Towards quantum simulation with circular Rydberg atoms
• Many-Body Localization in the Age of Classical Computing
• Quantum Time Crystals from Hamiltonians with Long-Range Interactions
• Floquet Higher-Order Topological Insulators with Anomalous Dynamical Polarization
• Robust Dynamic Hamiltonian Engineering of Many-Body Spin Systems
• Observation of a symmetry-protected topological time crystal with superconducting qubits
• The isolated Heisenberg magnet as a quantum time crystal
• Floquet prethermalization in a Bose-Hubbard system
• Floquet dynamical quantum phase transitions
• Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation
• Simulation of non-Abelian braiding in Majorana time crystals
• Many-body physics in the NISQ era: quantum programming a discrete time crystal
• Emergent limit cycles and time crystal dynamics in an atom-cavity system
• Higher-order and fractional discrete time crystals in clean long-range interacting systems
• Coherent and dissipative dynamics at quantum phase transitions
• Period-$n$ discrete time crystals and quasicrystals with ultracold bosons
• Classical many-body time crystals
• A Tutorial on Quantum Master Equations: Tips and tricks for quantum optics, quantum computing and beyond
• A dissipative time crystal in an asymmetric non-linear photonic dimer
• ${}^{31}$P NMR study of discrete time-crystalline signatures in an ordered crystal of ammonium dihydrogen phosphate
• Shattered Time: Can a Dissipative Time Crystal Survive Many-Body Correlations?
• Counting Rules of Nambu-Goldstone Modes
• Review: Quantum Metrology and Sensing with Many-Body Systems
• Floquet topological phases in a spin-1/2 double kicked rotor
• Discrete Time Quasi-Crystals
• Dissipative time crystal in a strongly interacting Rydberg gas
• Time crystal platform: from quasi-crystal structures in time to systems with exotic interactions
• Prethermalization without temperature
• Time crystals: analysis of experimental conditions
• From a continuous to a discrete time crystal in a dissipative atom-cavity system
• Dynamical quantum phase transitions in discrete time crystals
• AC Josephson effect between two superfluid time crystals
• Emergent prethermalization signatures in out-of-time ordered correlations
• Continuous sensing and parameter estimation with the boundary time-crystal
• Exact solution of a boundary time-crystal phase transition: time-translation symmetry breaking and non-Markovian dynamics of correlations
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Persistent coherent beating in coupled parametric oscillators
• Discrete time crystal in globally driven interacting quantum systems without disorder
• Driven Bose-Hubbard dimer under nonlocal dissipation: A bistable time crystal
• Feedback-Induced Quantum Phase Transitions Using Weak Measurements
• Probing many-body localization phase transition with superconducting circuits
• Symmetries and conserved quantities of boundary time crystals in generalized spin models
• Quantum metrology with boundary time crystals
• Time crystals in a shaken atom-cavity system
• Tuning anomalous Floquet topological bands with ultracold atoms
• Dynamical phases and quantum correlations in an emitter-waveguide system with feedback
• Condensed Matter Physics in Time Crystals
• Topological Time Crystals
• Boundary time crystals in collective $d$-level systems
• Period-doubling in period-$1$ steady states
• Non-Hermitian Floquet Topological Matter -- A Review
• Stability of many-body localization in Floquet systems
• Bounds in Nonequilibrium Quantum Dynamics
• Classical Stochastic Discrete Time Crystals
• Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals
• Observation of a critical prethermal discrete time crystal created by two-frequency driving
• Measurement Induced Continuous Time Crystals
• Floquet Time Spirals and Stable Discrete Time Quasi-Crystals in Quasi-Periodically Driven Quantum Many-Body Systems
• Quantum state control of a Bose-Einstein condensate in an optical lattice
• Discrete time-crystalline response stabilized by domain-wall confinement
• Optically trapped polariton condensates as semiclassical time crystals
• Creation and Characterization of Matter-Wave Breathers
• Simulating complex quantum networks with time crystals
• Long-lived period-doubled edge modes of interacting and disorder-free Floquet spin chains
• Fractional Time Crystals
• Nonreciprocal Ising model
• Theory of coupled parametric oscillators beyond coupled Ising spins
• Dissipative time crystals with long-range Lindbladians
• Building continuous time crystals from rare events
• Semiclassical roots of universality in many-body quantum chaos
• On quantum time crystals and interacting gauge theories in atomic Bose-Einstein condensates
• Floquet Many-body Engineering: Topological and Many-body Physics in Phase Space Lattices
• Floquet time-crystals as sensors of AC fields
• Symmetry-breaking dynamics of the finite-size Lipkin-Meshkov-Glick model near ground state
• Creating and controlling global Greenberger-Horne-Zeilinger entanglement on quantum processors
• Non-reciprocal frustration: time crystalline order-by-disorder phenomenon and a spin-glass-like state
• Nonreciprocal Synchronization of Active Quantum Spins
• Quantum Information Scrambling in Quantum Many-body Scarred Systems
• Quantum trajectories of dissipative time-crystals
• Mesoscopic limit cycles in coupled nanolasers
• Observations of a PT-like phase transition and limit cycle oscillations in non-reciprocally coupled optomechanical oscillators levitated in vacuum
• Discrete time crystal in a finite chain of Rydberg atoms without disorder
• Dynamical quantum phase transitions in systems with broken continuous time and space translation symmetries
• Mode softening in time-crystalline transitions of open quantum systems
• Correlations and dynamical quantum phase transitions in an interacting topological insulator
• Creating big time crystals with ultracold atoms
• Tunable space-time crystal in room-temperature magnetodielectrics
• Perspective on Reversible to Irreversible Transitions in Periodic Driven Many Body Systems and Future Directions For Classical and Quantum Systems
• Driving-induced multiple $\mathcal{P}\mathcal{T}$-symmetry breaking transitions and reentrant localization transitions in non-Hermitian Floquet quasicrystals
• Rigorous bounds on dynamical response functions and time-translation symmetry breaking
• Statistical Mechanics of Floquet Quantum Matter: Exact and Emergent Conservation Laws
• A dissipative time crystal with or without ${\mathbb{Z}}_2$ symmetry breaking
• Dynamical quantum phase transitions in collapse and revival oscillations of a quenched superfluid
• Solid-state continuous time crystal with a built-in clock
• Synthetic dimensions for topological and quantum phases: Perspective
• Signatures of discrete time-crystallinity in transport through an open Fermionic chain
• Square-root Floquet topological phases and time crystals
• Casimir effect for mixed fields
• Nonlinear two-level dynamics of quantum time crystals
• An eternal discrete time crystal beating the Heisenberg limit
• Discrete Time Crystal Phase as a Resource for Quantum Enhanced Sensing
• Discrete time crystals in many-body quantum chaos
• Cosmological Time Crystal: Cyclic Universe with a small $\Lambda$ in a toy model approach
• Entangled time-crystal phase in an open quantum light-matter system
• Phase diagram and optimal control for n-tupling discrete time crystal
• Driven-dissipative time crystalline phases in a two-mode bosonic system with Kerr nonlinearity
• Efficient algorithm to compute the second Chern number in four dimensional systems
• Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder
• Floquet dynamical quantum phase transitions in periodically quenched systems
• Floquet Scalar Dynamics in Global AdS
• Analytical solutions for a boundary driven XY chain
• The optimal frequency window for Floquet engineering in optical lattices
• Dynamics of a Space-Time Crystal in an Atomic Bose-Einstein Condensate
• Genuine Multipartite Correlations in a Boundary Time Crystal
• Stochastic discrete time crystals: Entropy production and subharmonic synchronization
• Dynamical phase transitions in the nonreciprocal Ising model
• Comment on "Quantum Time Crystals and Interacting Gauge Theories in Atomic Bose-Einstein Condensates"
• Photo-Induced Anomalous Hall Effect in Two-Dimensional Transition-Metal Dichalcogenides
• Proof of the absence of long-range temporal orders in Gibbs states
• Coherent dynamics in frustrated coupled parametric oscillators
• Measurement induced transitions in non-Markovian free fermion ladders
• Higgs time crystal in a high-$T_c$ superconductor
• Realizing time crystals in discrete quantum few-body systems
• Chimera Time-Crystalline order in quantum spin networks
• Sufficient condition for gapless spin-boson Lindbladians, and its connection to dissipative time-crystals
• Relaxation dynamics and dissipative phase transition in quantum oscillators with period tripling
• Temporal boundaries in electromagnetic materials
• Emergence and Dynamical Stability of Charge Time-Crystal in a Current-Carrying Quantum Dot Simulator
• Critical properties of the prethermal Floquet Time Crystal
• Six-dimensional time-space crystalline structures
• A Decade of Time Crystals: Quo Vadis?
• Spin-controlled photonics via temporal anisotropy
• Boundary Time Crystals as AC sensors: enhancements and constraints
• Open Quantum-System Simulation of Faraday's Induction Law via Dynamical Instabilities
• Quantum thermodynamics of boundary time-crystals
• Self-organized Limit Cycles in Red-detuned Atom-cavity Systems
• Lack of a genuine time crystal in a chiral soliton model
• Nonequilibrium transition between dissipative time crystals
• Polynomial filter diagonalization of large Floquet unitary operators
• Stroboscopic aliasing in long-range interacting quantum systems
• Many-Body Effects and Quantum Fluctuations for Discrete Time Crystals in Bose-Einstein Condensates
• Imaginary time crystal of thermal quantum matter
• Single-particle localization in dynamical potentials
• Quantum frequency locking and down-conversion in a driven cavity-qubit system
• Prethermalization and entanglement dynamics in interacting topological pumps
• Nonequilibrium thermodynamics and power generation in open quantum optomechanical systems
• Towards quantum internet and non-local communication in position based qubits
• Unified Light-Matter Floquet Theory and its Application to Quantum Communication
• Critical properties of the Floquet time crystal within the Gaussian approximation
• Strong zero modes in integrable quantum circuits
• Nonequilibrium phases of ultracold bosons with cavity-induced dynamic gauge fields
• Analytical theory of cat scars with discrete time crystalline dynamics in Floquet systems
• Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: Application to squeezed parametric oscillation beyond the rotating-wave approximation
• Space-time crystalline order of a high-critical-temperature superconductor with intrinsic Josephson junctions
• Exotic synchronization in continuous time crystals outside the symmetric subspace
• Space-Time Quasicrystal Structures and Inflationary and Late Time Evolution Dynamics in Accelerating Cosmology
• Colloidal Dynamics on a Choreographic Time Crystal
• Entanglement Transitions in Unitary Circuit Games
• Tuning between continuous time crystals and many-body scars in long-range XYZ spin chains
• Time Crystals in the Driven Transverse Field Ising Model under Quasiperiodic Modulation
• Truncated Dynamics, Ring Molecules and Mechanical Time Crystals
• Universality classes of thermalization for mesoscopic Floquet systems
• Simulation of many body localization and time crystals in two dimensions with the neighborhood tensor update
• Quantum dynamics of Dissipative Kerr solitons
• Emergent symmetries in prethermal phases of periodically driven quantum systems
• Magnon Bose-Einstein condensates: from time crystals and quantum chromodynamics to vortex sensing and cosmology
• Emergent strong zero mode through local Floquet engineering
• Bose-Hubbard realization of fracton defects
• Flow Equations for Disordered Floquet Systems
• Parametric resonance of a Bose-Einstein condensate in a ring trap with periodically driven interactions
• Exploring nonlinear dynamics in periodically driven time crystal: from synchronized to chaotic motion
• Signatures of Many-Body Localization in the Dynamics of Two-Level Systems in Glasses
• Topological and dynamical features of periodically driven spin ladders
• Autonomous quantum clocks using athermal resources
• Emergent Continuous Time Crystal in Dissipative Quantum Spin System without Driving
• Dynamical Freezing in Exactly Solvable Models of Driven Chaotic Quantum Dots
• Spontaneous symmetry breaking in a driven-dissipative system
• Tuning the universality class of phase transitions by feedback: Open quantum systems beyond dissipation
• Unitary Subharmonic Response and Floquet Majorana Modes
• Driving-induced metamorphosis of transport in arrays of coupled resonators
• Integrable Floquet Hamiltonian for a Periodically Tilted 1D Gas
• Ergodic-localized junctions in periodically-driven systems
• Experimental observation of a time rondeau crystal: Temporal Disorder in Spatiotemporal Order
• Time-crystal ground state and production of gravitational waves from QCD phase transition
• Nonlocal discrete time crystals in periodically driven surface codes
• Spatiotemporally ordered patterns in a chain of coupled dissipative kicked rotors
• Self-similar phase diagram of the Fibonacci-driven quantum Ising model
• Quantum Physics in Connected Worlds
• Non-Abelian geometric phases in periodically driven systems
• Anderson Localization in Photonic Time Crystals
• Driven anti-Bragg subradiant states in waveguide quantum electrodynamics
• Feasible model for photo-induced interband pairing
• Overcoming dispersive spreading of quantum wave packets via periodic nonlinear kicking
• Continuous simultaneous measurement of position and momentum of a particle
• Criticality and Rigidity of Dissipative Discrete Time Crystals in Solids
• Shortcuts to adiabatic state transfer in time-modulated two-level non-Hermitian systems
• Controlled preparation of phases in two-dimensional time crystals
• Reconstructing effective Hamiltonians from nonequilibrium (pre-)thermal steady states
• Inseparable time-crystal geometries on the Möbius strip
• Exploring Dynamical Phase Transitions in the XY Chain through Linear Quench: Early and Long-term Perspectives
• Nonreciprocal interactions induce frequency shifts in superradiant lasers
• Spectral signatures of symmetry-breaking dynamical phase transitions
• Long-lived coherence in driven spin systems: from two to infinite spatial dimensions
• Gaussian-state Ansatz for the non-equilibrium dynamics of quantum spin lattices
• Provenance of classical Hamiltonian time crystals
• Many-body localization crossover is sharper in quasiperiodic spin chains
• Sensing with discrete time crystals
• Fractional resonances and prethermal states in Floquet systems
• Thermodynamics and Phase Transition in Shapere-Wilczek {\it fgh} model: Cosmological Time Crystal in Quadratic Gravity
• Route to Extend the Lifetime of a Discrete Time Crystal in a Finite Spin Chain Without Disorder
• Two-dimensional Thouless pumping in time-space crystalline structures
• Robust spectral $\pi$ pairing in the random-field Floquet quantum Ising model
• Anderson Molecules
• Two Nambu-Goldstone zero modes for rotating Bose-Einstein condensates
• Space- and time-crystallization effects in multicomponent superfluids
• Instabilities of interacting matter waves in optical lattices with Floquet driving
• Neural network enhanced hybrid quantum many-body dynamical distributions
• Prethermalization in aperiodically driven classical spin systems
• Coherent multiple-period states in a resonantly driven qubit
• Clean two-dimensional Floquet time-crystal
• Spontaneous Symmetry Breaking of Time-Reversal-Symmetry and Time-Crystal States in Chiral Atomic Systems
• Crossover from the discontinuous to continuous phase transitions in dissipative spin system with collective decay
• Perturbative Framework for Engineering Arbitrary Floquet Hamiltonian
• Classical and quantum time crystals in a levitated nanoparticle without drive
• Observation of period doubling and higher multiplicities in a driven single-spin system
• Designing open quantum systems for enabling quantum enhanced sensing through classical measurements
• Floquet chiral hinge modes and their interplay with Weyl physics in a three-dimensional lattice
• Time-crystalline behavior in central-spin models with Heisenberg interactions
• Boundary Time Crystals Induced by Local Dissipation and Long-Range Interactions
• Symmetries & Correlations in Continous Time Crystals
• Non-trivial time crystal-like ground state for gravitational perturbation in quadratic gravity
• Transport in a periodically driven tilted lattice via the extended reservoir approach: Stability criterion for recovering the continuum limit
• Non-Hermitian quantum gases: a platform for imaginary time crystals
• Can a bright soliton model reveal a genuine time crystal for a finite number of bosons?
• Nanoscopic time crystal obtained by nonergodic spin dynamics
• Non-spreading matter-wave packets in a ring
• Time crystals made of electron-positron pairs
• Quantum Pairing Time Orders
• Dynamical density wave order in an atom-cavity system
• Prolonging a discrete time crystal by quantum-classical feedback
• Exact density profile in a tight-binding chain with dephasing noise
• Formation of Spatial Patterns by Spin-selective Excitations of Interacting Fermions
• Unveiling clean two-dimensional discrete time crystals on a digital quantum computer
• Classical Phase Space Crystals in an Open Environment
• Basis for time crystal phenomena in ultra-cold atoms bouncing on an oscillating mirror
• Impurity Screening and Friedel Oscillations in Floquet-driven Two-dimensional Metals
• Cosmological Time Crystals From Einstein-Cubic Gravities
• Swapping Floquet time crystal
• Thermodynamics and Protection of Discrete-Time Crystals
• Quantum sensing with ultracold simulators in lattice and ensemble systems: a review
• Quantum metrology with Bloch Oscillations in Floquet phase space
• Eight-dimensional topological systems simulated using time-space crystalline structures
• A Solvable Model for Discrete Time Crystal Enforced by Nonsymmorphic Dynamical Symmetry
• Powering an autonomous clock with quantum electromechanics
• Steering spin fluctuations in lattice systems via two-tone Floquet engineering
• Non-dispersing wave packets in lattice Floquet systems
• Prethermalization in the PXP Model under Continuous Quasiperiodic Driving
• Emergent time crystal from a fractional Langevin equation with white and colored noise
• Modulation-induced long-range magnon bound states in one-dimensional optical lattices
• Spin bath dynamics and dynamical Renormalization Group
• Dephasing-induced growth of discrete crystalline order in spin networks
• Fragility to quantum fluctuations of classical Hamiltonian period doubling
• Temporal localization of optical waves supported by a copropagating quasiperiodic structure
• Time Crystals from single-molecule magnet arrays
• Dynamics of one-dimensional quantum many-body systems in time-periodic linear potentials
• Topologically protected quantized changes of the distance between atoms
• Quantum metamorphism
• Programmable time crystals from higher-order packing fields
• Tunable quantum interference effects in Floquet two- and three-level systems
• Subharmonic spin correlations and spectral pairing in Floquet time crystals
• Stable many-body resonances in open quantum systems
• Time dispersion in quantum electrodynamics
• Observation of Fermi acceleration with cold atoms
• Nonexistence of spontaneous symmetry breakdown of time-translation symmetry on general quantum systems: Any macroscopic order parameter moves not!
• Generalized criteria of symmetry breaking. A strategy for quantum time crystals
• Floquet dynamics of Rabi model beyond the counterrotating hybridized rotating wave method
• Proposal for realizing anomalous Floquet insulators via Chern band annihilation
• Non-Abelian geometric potentials and spin-orbit coupling for periodically driven systems
• Time crystal optomechanics
• Cosmology in $R^2$-gravity: Effects of a Higher Derivative Scalar Condensate Background
• Cosmological Time Crystals from Gauss-Bonnet Gravity in Four Dimensions
• Walsh-Floquet Theory of Periodic Kick Drives
• Quasi-Discrete Time Crystals in the quasiperiodically driven Lipkin-Meshkov-Glick model
• Symmetry-induced fragmentation and dissipative time crystal
• Correlations in Circular Quantum Cascades
• Persistent oscillation of a Cooper-pair condensate of topological defects in a nonintegrable quantum Ising chain
• Nonperturbative decay of bipartite discrete time crystals
• Continuous time crystals as a PT symmetric state and the emergence of critical exceptional points
• Chiral supersolid and dissipative time crystal in Rydberg-dressed Bose-Einstein condensates with Raman-induced spin-orbit coupling
• Dark Energy from Time Crystals
• Critical behavior of a programmable time-crystal lattice gas
• Condensed matter physics in big discrete time crystals
• Discrete time crystals detected by time-translation twist
• Exact analysis of AC sensors based on Floquet time crystals
• Long-time properties of generic Floquet systems are approximately periodic with the driving period
• Strong and almost strong modes of Floquet spin chains in Krylov subspaces
• Electronic Mechanism that Quenches Field-Driven Heating as Illustrated with the Static Holstein Model
• Observation of tunable discrete time crystalline phases
• Seeding crystallization in time
• Cosmology from Strong Interactions
• Effective dynamics and quantum state engineering by periodic kicks
• The Nakano-Nishijima-Gell-Mann Formula From Discrete Galois Fields
• Flavored extended instanton in QCD
• $2+1$ dimensional Floquet systems and lattice fermions: Exact bulk spectral equivalence
• Classical periodic trajectories and quantum scars in many-spin systems
• Rydberg Atoms in a Ladder Geometry: Quench Dynamics and Floquet Engineering
• Discrete time crystals in Bose-Einstein Condensates and symmetry-breaking edge in a simple two-mode theory
• Localized structures in two-field systems: exact solutions in the presence of Lorentz symmetry breaking and explicit connection with geometric constraints
• Fock space prethermalization and time-crystalline order on a quantum processor
• Frequency Comb Behavior of Time Crystals in an RF-Driven Dissipative Rydberg System
• Charge waves and dynamical signatures of topological phases in Su-Schrieffer-Heeger chains
• Topological Molecules and Topological Localization of a Rydberg Electron on a Classical Orbit
• Quantum Boomerang Effect in Time-Crystalline Structures
• Floquet dynamical quantum phase transitions in periodically flux-quenched systems
• Giant Kohn anomaly and chiral phonons in the charge density wave phase of 1H-NbSe${}_2$
• Pre-Floquet states facilitating coherent subharmonic response of periodically driven many-body systems
• Phase transitions from Heating to non-heating in SU(1, 1) quantum dynamics: applications to Bose-Einstein condensates and periodically driven coupled oscillators
• Formation of Complex Discrete Time Crystals with Ultracold Atoms
• The Nature of Phantom Dark Energy and its Relation to Time Crystals
• Suppression of scattering from slow to fast subsystems and application to resonantly Floquet-driven impurities in strongly interacting systems
• Emergent time crystals from phase-space noncommutative quantum mechanics
• Floquet-engineered system-reservoir interaction in the transverse field Ising model
• Harmonic oscillator kicked by spin measurements: a Floquet-like system without classical analogous
• Quantum dynamics of a spin model with an extensive degeneracy
• Time dispersion in bound states
• Logarithmic quantum time crystal
• Quantum fingerprints of self-organization in spin chains coupled to a Kuramoto model
• Unpolarized prethermal discrete time crystal
• Discrete time crystal for periodic-field sensing with quantum-enhanced precision
• Realizing Topological Quantum Walks on NISQ Digital Quantum Computer
• Scattering of two particles in a 1D lattice
• Time Glasses: Symmetry Broken Chaotic Phase with a Finite Gap
• Symmetry properties of the ground state of the system of interacting spinless bosons
• Time Crystal from Self-Amplification of Spontaneous Analog Hawking Radiation
• Quantum repetition codes as building blocks of large period discrete time crystals
• Many-body state and dynamic behaviour of the pair-correlation function of a small Bose-Einstein condensate confined in a ring potential
• Eight-fold classification of superconducting orders
• Time Crystals in Actively Mode-locked Lasers
• Adiabatic and irreversible classical discrete time crystals
• Harnessing Floquet dynamics for selective metrology in few-qubit systems