Continuous time crystals represent a novel state of many-body systems, self-organizing into time-periodic oscillations without the need for external periodic driving. Recent experiments have demonstrated the realization of such systems in dissipative solid-state materials, where persistent temporal order is autonomously sustained. A defining characteristic of time crystals is their robustness, signifying the ability to maintain rhythmic behavior despite various disturbances, including fluctuations in internal parameters and external noise., which is of both scientific value and potential for technological applications Although prior studies have established the existence of robustness in specific experimental parameters, a systematic framework for quantifying and predicting their resilience to perturbations is lacking, and the underlying physics of this robustness remains inadequately understood. Key unresolved questions include how nonlinear interactions and feedback mechanisms contribute to stability, and what the critical thresholds are for parameter variations beyond which temporal order collapses.This paper addresses these gaps by systematically analyzing how internal parameters and external influences affect the oscillation period and overall stability. Internally, the dynamics are dictated by dipole-dipole interactions and atomic transition strengths, which define the system’s emergent temporal symmetry breaking. Externally, the system’s response is controlled by the intensity of the optical driving field and the rates of energy dissipation. A key finding is the identification of an intrinsic feedback mechanism that dynamically stabilizes the time crystal. This mechanism acts as a restorative force, correcting for deviations caused by minor disturbances and maintaining the coherence of the oscillatory phase.Moreover, the system displays nonlinear dynamical behavior, characterized by two distinct regimes: one where stable oscillations continue under moderate disturbances, and another where stronger disturbances induce a dynamical phase transition, leading to disordered states or a switch between dynamically unstable and stable states. These results provide a thorough understanding of the diverse behaviors observed in continuous time crystals and create a vital theoretical foundation for exploiting their unique properties in advanced applications like quantum information processing and precision metrology.
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