Classical Time Crystals

Abstract

We consider the possibility that classical dynamical systems display motion in their lowest energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary orbits of an angular variable as lowest-energy trajectories for nonsingular Lagrangian systems. Dynamics within orbits of broken symmetry provide a natural arena for formation of time crystals. We exhibit models of that kind, including a model with traveling density waves.

5 pages, 1 figure

References in corpus (2)

• Quantum Time Crystals
• Branched Quantization

Cited by in corpus (227)

• Floquet Time Crystals
• Quantum Time Crystals
• Non-reciprocal phase transitions
• Photonics of Time-Varying Media
• Time crystals: a review
• Modeling spontaneous breaking of time-translation symmetry
• Discrete Time Crystals
• Pre-thermal phases of matter protected by time-translation symmetry
• Observation of a dissipative time crystal
• Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
• Floquet time crystal in the Lipkin-Meshkov-Glick model
• Observation of a continuous time crystal
• Observation of a many-body-localized discrete time crystal with a programmable spin-based quantum simulator
• Colloquium: Quantum and Classical Discrete Time Crystals
• Space-time crystals of trapped ions
• Observation of anomalous π modes in photonic Floquet engineering
• Discrete time crystals in the absence of manifest symmetries or disorder in open quantum systems
• Dicke time crystals in driven-dissipative quantum many-body systems
• Classical Discrete Time Crystals
• Clean Floquet Time Crystals: Models and Realizations in Cold Atoms
• Quantum Time Crystals from Hamiltonians with Long-Range Interactions
• Limit cycle phase in driven-dissipative spin systems
• Floquet time crystals in clock models
• Emergent limit cycles and time crystal dynamics in an atom-cavity system
• Superfluidity and Space-Time Translation Symmetry Breaking
• Period-$n$ discrete time crystals and quasicrystals with ultracold bosons
• Shattered Time: Can a Dissipative Time Crystal Survive Many-Body Correlations?
• Review: Quantum Metrology and Sensing with Many-Body Systems
• Superradiance Lattice
• Discrete Time Quasi-Crystals
• Dissipative time crystal in a strongly interacting Rydberg gas
• Exact solution of a boundary time-crystal phase transition: time-translation symmetry breaking and non-Markovian dynamics of correlations
• Quantum metrology with boundary time crystals
• Time crystals in a shaken atom-cavity system
• Integrable nonlocal Hirota equations
• Topologically protected braiding in a single wire using Floquet Majorana modes
• Dynamical phases and quantum correlations in an emitter-waveguide system with feedback
• Condensed Matter Physics in Time Crystals
• Topological Time Crystals
• Nonequilibrium many-body quantum engine driven by time-translation symmetry breaking
• Minimalist approach to the classification of symmetry protected topological phases
• Classical Stochastic Discrete Time Crystals
• Integrability and chemical potential in the (3+1)-dimensional Skyrme model
• Optically trapped polariton condensates as semiclassical time crystals
• Motion in time-periodic backgrounds with applications to ultralight dark matter haloes at galactic centers
• Continuous time crystal in an electron-nuclear spin system: stability and melting of periodic auto-oscillations
• Nonreciprocal Ising model
• Fractional Time Crystals
• Time Crystals from Minimum Time Uncertainty
• Building continuous time crystals from rare events
• Correlated photon dynamics in dissipative Rydberg media
• The goldstone and goldstino of supersymmetric inflation
• On quantum time crystals and interacting gauge theories in atomic Bose-Einstein condensates
• Symmetry-breaking dynamics of the finite-size Lipkin-Meshkov-Glick model near ground state
• Inflation in Motion: Unitarity Constraints in Effective Field Theories with Broken Lorentz Symmetry
• Observations of a PT-like phase transition and limit cycle oscillations in non-reciprocally coupled optomechanical oscillators levitated in vacuum
• Branched Quantization
• An instanton-like excitation of a discrete time crystal
• Mode softening in time-crystalline transitions of open quantum systems
• Perspective on Reversible to Irreversible Transitions in Periodic Driven Many Body Systems and Future Directions For Classical and Quantum Systems
• Generalized phase transitions in Lovelock gravity
• Analytic (3+1)-dimensional gauged Skyrmions, Heun and Whittaker-Hill equations and resurgence
• Experimental observation of the spontaneous breaking of the time-reversal symmetry in a synchronously-pumped passive Kerr resonator
• Photonic Floquet time crystals
• Analytic topologically non-trivial solutions of the (3+1)-dimensional $U(1)$ gauged Skyrme model and extended duality
• On the integration of fields and quanta in time dependent backgrounds
• Casimir effect for mixed fields
• Synthesizing Lattice Structure in Phase Space
• 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
• Suppressing Quantum Fluctuations in Classicalization
• Consistent Quantization of Nearly Singular Superconducting Circuits
• Scale invariance vs conformal invariance
• Torsion in quantum field theory through time-loops on Dirac materials
• Oscillatory Attractors: A New Cosmological Phase
• Analytic Studies of Static and Transport Properties of (Gauged) Skyrmions
• Dynamics of Magnus Dominated Particle Clusters, Collisions, Pinning and Ratchets
• Dynamics of a Space-Time Crystal in an Atomic Bose-Einstein Condensate
• Bistability and time crystals in long-ranged directed percolation
• Particle models with self sustained current
• Stationary uphill currents in locally perturbed Zero Range Processes
• Dynamical phase transitions in the nonreciprocal Ising model
• Stochastic discrete time crystals: Entropy production and subharmonic synchronization
• Dissipative time crystal in an atom-cavity system: Influence of trap and competing interactions
• Nonequilibrium Criticality at the Onset of Time-Crystalline Order
• Coherent dynamics in frustrated coupled parametric oscillators
• Realizing time crystals in discrete quantum few-body systems
• Models of Topology Change
• Temporal boundaries in electromagnetic materials
• Synchronisation and liquid crystalline order in soft active fluids
• Rotating Casimir systems: magnetic-field-enhanced perpetual motion, possible realization in doped nanotubes, and laws of thermodynamics
• Time Quasilattices in Dissipative Dynamical Systems
• Realization of an inherent time crystal in a dissipative many-body system
• Six-dimensional time-space crystalline structures
• Homogeneous Floquet time crystal from weak ergodicity breaking
• One-parameter families of supersymmetric isospectral potentials from Riccati solutions in function composition form
• Critical properties of the prethermal Floquet Time Crystal
• Universal presence of time-crystalline phases and period-doubling oscillations in one-dimensional Floquet topological insulators
• Stable Cosmic Time Crystals
• Anharmonic classical time crystals: A coresonance pattern formation mechanism
• Exploring eternal stability with the simple harmonic universe
• Imaginary time crystal of thermal quantum matter
• On the role of constraints and degrees of freedom in the Hamiltonian formalism
• Time Glass: A Fractional Calculus Approach
• Resolving the issue of branched Hamiltonian in modified Lanczos-Lovelock gravity
• Critical properties of the Floquet time crystal within the Gaussian approximation
• Space-time crystalline order of a high-critical-temperature superconductor with intrinsic Josephson junctions
• Space-Time Quasicrystal Structures and Inflationary and Late Time Evolution Dynamics in Accelerating Cosmology
• Time Crystal in a Single-mode Nonlinear Cavity
• Time-crystalline Topological Superconductors
• Colloidal Dynamics on a Choreographic Time Crystal
• Canonical structure of higher derivative theories
• Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: Application to squeezed parametric oscillation beyond the rotating-wave approximation
• Effective Field Theory for Spontaneously Broken Symmetry
• Algebraic Time Crystallization in a Two-dimensional Superfluid
• Truncated Dynamics, Ring Molecules and Mechanical Time Crystals
• Temporally, Spatially or Light-like Modulated Vacua in Lorentz Invariant Theories
• Time Crystals in the Driven Transverse Field Ising Model under Quasiperiodic Modulation
• Torsion at different scales: from materials to the Universe
• Emergent symmetries in prethermal phases of periodically driven quantum systems
• Autonomous quantum clocks using athermal resources
• Exploring nonlinear dynamics in periodically driven time crystal: from synchronized to chaotic motion
• Emergent Continuous Time Crystal in Dissipative Quantum Spin System without Driving
• Inflation and late-time accelerated expansion driven by $k$-essence degenerate dynamics
• Branched Hamiltonians and Supersymmetry
• The Phantom of the New Oscillatory Cosmological Phase
• Thermal melting of discrete time crystals: a dynamical phase transition induced by thermal fluctuations
• Discreteness of time in the evolution of the universe
• On the long-term stability of space-time crystals
• Nonlocal discrete time crystals in periodically driven surface codes
• Continuous Space-Time Crystal State Driven by Nonreciprocal Optical Forces
• Time Crystals transforming Frequency Combs in Tunable Photonic Oscillators
• Symmetric Satellite Swarms and Choreographic Crystals
• Spectral signatures of symmetry-breaking dynamical phase transitions
• Self-Organized Higgs Criticality
• Topological Polarisation States
• Thermodynamics and Phase Transition in Shapere-Wilczek {\it fgh} model: Cosmological Time Crystal in Quadratic Gravity
• Tuning, Ergodicity, Equilibrium and Cosmology
• Provenance of classical Hamiltonian time crystals
• Absolutely stable time crystals at finite temperature
• Magnetization oscillations in a periodically driven transverse field Ising chain
• Tunable Spatiotemporal Orders in Driven Insulators
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• Exploring Branched Hamiltonians for a Class of Nonlinear Systems
• Space- and time-crystallization effects in multicomponent superfluids
• Liquid Time Crystals
• From prethermalization to chaos in periodically driven coupled rotors
• Yet another time about time - Part I
• Programmable Hamiltonian engineering with quadratic quantum Fourier transform
• Dynamic phase transition theory
• Spontaneous Symmetry Breaking of Time-Reversal-Symmetry and Time-Crystal States in Chiral Atomic Systems
• Classical and quantum time crystals in a levitated nanoparticle without drive
• Non-trivial time crystal-like ground state for gravitational perturbation in quadratic gravity
• Non-Hermitian quantum gases: a platform for imaginary time crystals
• Spatio-temporal Symmetry - Point Groups with Time Translations
• Time crystals made of electron-positron pairs
• Boundary Time Crystals Induced by Local Dissipation and Long-Range Interactions
• Topological carbon allotropes: paradigm shift for materials innovation
• Nanoscopic time crystal obtained by nonergodic spin dynamics
• Basis for time crystal phenomena in ultra-cold atoms bouncing on an oscillating mirror
• Topologically ordered time crystals
• Kaluza--Klein gravity & cosmology emerging from G. Perelman's entropy functionals and quantum geometric information flows
• Dynamical dimensional reduction in multi-valued Hamiltonians
• Swapping Floquet time crystal
• Continuous time crystal from a spontaneous many-body Floquet state
• Time crystal and chaos in the hybrid atom-optomechanics system
• Cosmological Time Crystals From Einstein-Cubic Gravities
• A reappraisal of Lagrangians with non-quadratic velocity dependence and branched Hamiltonians
• Vortex precession and exchange in a Bose-Einstein condensate
• Parametric-resonance based phenomenology of gravitating axion configurations
• Eight-dimensional topological systems simulated using time-space crystalline structures
• Ground state and the spin precession of the Dirac electron in counterpropagating plane electromagnetic waves
• A Solvable Model for Discrete Time Crystal Enforced by Nonsymmorphic Dynamical Symmetry
• A metronome spin stabilizes time-crystalline dynamics
• Spontaneous emission decay and excitation in photonic time crystals
• Landau meets Newton: time translation symmetry breaking in classical mechanics
• Emergent time crystal from a fractional Langevin equation with white and colored noise
• Ground state fractal crystals
• Breaking of Time Translation Symmetry and Ergodicity, and Entropy decrease in a Continuous Time Crystal Driven by Nonreciprocal Optical Forces
• Localized solutions of the Dirac equation in free space and electromagnetic space-time crystals
• Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows
• Dynamical sectors of a relativistic two particle model
• Counter-flow induced clustering: Exact results
• Discrete Lorentz symmetry and discrete time translational symmetry
• Dirac electron in a chiral space-time crystal created by counterpropagating circularly polarized plane electromagnetic waves
• Time Crystals from single-molecule magnet arrays
• Relativistic spacetime crystals
• Programmable time crystals from higher-order packing fields
• Discrete Lorentz symmetry and discrete spacetime translational symmetry in two- and three-dimensional crystals
• Time crystals in primordial perturbations
• Travelling Surface Plasmons with Interference Envelope and A Vision for Time Crystals
• Cosmology in $R^2$-gravity: Effects of a Higher Derivative Scalar Condensate Background
• Spacetime Metamaterials
• K-nonizing
• Quantization and Renormalization and the Casimir Energy of a Scalar Field Interacting with a Rotating Ring
• The Symmetry Principle in Condensed Matter Physics (I)
• Cosmological Time Crystals from Gauss-Bonnet Gravity in Four Dimensions
• Critical behavior of a programmable time-crystal lattice gas
• Nonlinear dynamics determines the thermodynamic instability of condensed matter in vacuo
• The Nakano-Nishijima-Gell-Mann Formula From Discrete Galois Fields
• Observation of tunable discrete time crystalline phases
• Dark Energy from Time Crystals
• Classical periodic trajectories and quantum scars in many-spin systems
• Degeneracy Index and Poincaré-Hopf Theorem
• Emergent Time Crystal with Tunable Period in the Uniaxial Random Field XY Magnet
• Correlations in Circular Quantum Cascades
• Condensed matter physics in big discrete time crystals
• Effects of leakage on the realization of a discrete time crystal in a chain of singlet-triplet qubits
• Heat Superconductivity
• The Nature of Phantom Dark Energy and its Relation to Time Crystals
• Time dispersion in bound states
• Discrete time crystal order in spin chains enabled by Floquet flat bands
• Peratic Phase Transition by Bulk-to-Surface Response
• Many-body state and dynamic behaviour of the pair-correlation function of a small Bose-Einstein condensate confined in a ring potential
• Quantum repetition codes as building blocks of large period discrete time crystals
• Frequency Comb Behavior of Time Crystals in an RF-Driven Dissipative Rydberg System
• Autoresonant excitation of space-time quasicrystals in plasma
• Adiabatic and irreversible classical discrete time crystals
• Localized structures in two-field systems: exact solutions in the presence of Lorentz symmetry breaking and explicit connection with geometric constraints
• Intrinsic space-time crystalline order in a hybrid Josephson junction
• Non canonical polarizations of Gravitational Waves
• Dynamics of spontaneous symmetry breaking in a space-time crystal
• Construction of the classical time crystal Lagrangians from Sisyphus dynamics and duality description with the Liénard type equation
• Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1+1)$-dimensional Gross-Neveu model in the mean-field approximation
• Logarithmic quantum time crystal
• Metamaterial model of a time crystal
• The role of atomic interactions in cavity-induced continuous time crystals