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Unified Framework and Engineering Pathways for Time Crystals: From Floquet Phases to Open System Limits, Quasiperiodic Drives, and Topological Protection

Haobo Ma, Wenlin Zhang

Published Nov 25, 2025• 0 citations
Publisher

Abstract

Construct unified time crystal theory penetrating closed and open quantum systems, periodic and quasiperiodic drives, and topological constraints. Using group representation and non-equilibrium statistics as foundation, propose operational order parameters, temporal correlations, and spectral criteria; at mathematical level via high-frequency Floquet--Magnus expansion, Lieb--Robinson bounds, and spectral pairing structure, prove rigidity and robustness of prethermal discrete time crystals on exp

DOI
10.5281/zenodo.17707726

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The classification of phases of matter has been revolutionised by topological order and non equilibrium phenomena such as time crystals. However, a unified framework connecting temporal order, topology, and dissipation remains elusive. Here we introduce the concept of "Time-Quasicrystals"—non-equilibrium topological phases that exhibit quasi-periodic temporal order protected by dissipative dynamics. These phases emerge in driven dissipative quantum systems through the interplay of Floquet engineering and non-local dissipation, leading to an effective non-Hermitian Floquet Hamiltonian with topological edge modes in the frequency domain. We demonstrate three hallmarks of Time-Quasicrystals: (1) fractal-like temporal correlations with multiple incommensurate frequencies, (2) a quantised topological invariant robust against disorder, and (3) algebraically decaying memory of phase perturbations. We provide explicit experimental realisations in Rydberg atom arrays and circuit quantum electrodynamics platforms. Our work establishes Time-Quasicrystals as a bridge between topological phases, time crystals, and quantum simulation, opening pathways to dissipative protected quantum memory and novel non-equilibrium quantum phenomena.
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