Intermittent time-crystalline dynamics under stochastic measurements
Phys. Rev. A 114, 032422 – Published 9 September, 2026
DOI: https://doi.org/10.1103/y9yn-x6x2
Abstract
Discrete time crystals are nonequilibrium states of periodically driven quantum matter characterized by robust subharmonic responses. We investigate how such temporal order behaves in the presence of stochastic measurements. Using trajectory-resolved simulations of a monitored Floquet-Ising model, we identify an intermediate regime in which the local subharmonic response survives only intermittently in time. The dynamics develops finite-lived temporal plateaus of locally coherent subharmonic response punctuated by stochastic disruptions correlated with projective measurements. While local temporal staggering remains robust over broad intervals, the spectral coherence of the subharmonic response exhibits substantially stronger fluctuations, revealing a temporally fragmented dynamics not fully captured by global long-time observables alone. The resulting plateau statistics are further consistent with an effective two-state kinetic description based on finite-rate stochastic disruption events. These results show that monitored dynamics can support fluctuating local synchronization in which finite temporal domains repeatedly emerge and disappear along individual quantum trajectories, without establishing globally persistent discrete time-crystalline order under stochastic monitoring.
