SciPost Physics

SciPost Phys. 5, 001 (2018) · published 3 July 2018

• doi: 10.21468/SciPostPhys.5.1.001
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

We establish the existence of 'time quasilattices' as stable trajectories in dissipative dynamical systems. These tilings of the time axis, with two unit cells of different durations, can be generated as cuts through a periodic lattice spanned by two orthogonal directions of time. We show that there are precisely two admissible time quasilattices, which we term the infinite Pell and Clapeyron words, reached by a generalization of the period-doubling cascade. Finite Pell and Clapeyron words of increasing length provide systematic periodic approximations to time quasilattices which can be verified experimentally. The results apply to all systems featuring the universal sequence of periodic windows. We provide examples of discrete-time maps, and periodically-driven continuous-time dynamical systems. We identify quantum many-body systems in which time quasilattices develop rigidity via the interaction of many degrees of freedom, thus constituting dissipative discrete 'time quasicrystals'.

• Gambetta et al., Classical stochastic discrete time crystals
  Phys. Rev. E 100, 060105 (2019) [Crossref]
• Peng et al., Time-quasiperiodic topological superconductors with Majorana multiplexing
  Phys. Rev. B 98, 220509 (2018) [Crossref]
• Keßler et al., Emergent limit cycles and time crystal dynamics in an atom-cavity system
  Phys. Rev. A 99, 053605 (2019) [Crossref]
• Libál et al., Colloidal Dynamics on a Choreographic Time Crystal
  Phys. Rev. Lett. 124, 208004 (2020) [Crossref]
• Zaletel et al., Colloquium : Quantum and classical discrete time crystals
  Rev. Mod. Phys. 95, 031001 (2023) [Crossref]
• Giergiel et al., Discrete time quasicrystals
  Phys. Rev. B 99, 220303 (2019) [Crossref]
• Snegirev, Lagrangian formulation for perfect fluid equations with the ℓ -conformal Galilei symmetry
  Phys. Rev. D 110, 045003 (2024) [Crossref]
• Nagaoka et al., Quasicrystalline materials from non-atom building blocks
  Matter 6, 30 (2023) [Crossref]
• Kosior et al., Dynamical quantum phase transitions in systems with broken continuous time and space translation symmetries
  Phys. Rev. A 98, 023612 (2018) [Crossref]
• Cosme et al., Time crystals in a shaken atom-cavity system
  Phys. Rev. A 100, 053615 (2019) [Crossref]
• Zaporski et al., Superconvergence of topological entropy in the symbolic dynamics of substitution sequences
  SciPost Phys. 7, 018 (2019) [Crossref]
• Flicker et al., Classical Dimers on Penrose Tilings
  Phys. Rev. X 10, 011005 (2020) [Crossref]
• Bhowmick et al., Discrete time crystal made of topological edge magnons
  Phys. Rev. B 108, 014434 (2023) [Crossref]
• Syrwid et al., Lack of a genuine time crystal in a chiral soliton model
  Phys. Rev. Research 2, 032038 (2020) [Crossref]
• Pizzi et al., Period- n Discrete Time Crystals and Quasicrystals with Ultracold Bosons
  Phys. Rev. Lett. 123, 150601 (2019) [Crossref]
• Matus et al., Fractional time crystals
  Phys. Rev. A 99, 033626 (2019) [Crossref]
• Planat et al., Graph Coverings for Investigating Non Local Structures in Proteins, Music and Poems
  Sci 3, 39 (2021) [Crossref]
• Sacha,
  114, 39 (2020) [Crossref]
• Moniri et al., Limit cycles and their period detection via numeric and symbolic hybrid computations
  Communications in Nonlinear Science and Numerical Simulation 83, 105107 105107 (2020) [Crossref]
• Nicolaou et al., Anharmonic classical time crystals: A coresonance pattern formation mechanism
  Phys. Rev. Research 3, 023106 (2021) [Crossref]