Metastable discrete time-crystal resonances in a dissipative central spin system

We consider the non-equilibrium behavior of a central spin system where is periodically reset to its ground state. The quantum mechanical evolution under this effectively dissipative dynamics described by discrete-time map. Despite simplicity problem shows surprisingly complex dynamical features. In particular, we identify several metastable time-crystal resonances. Here does not relax rapidly stationary state but undergoes long-lived oscillations with period that an integer multiple period. At these resonances becomes restricted low-dimensional space within which periodic motion. Generalizing theory metastability in open systems, develop effective description for subspace and show long-time limit approached. Our study links timely questions concerning emergent collective 'prethermal' stage many-body may establish intriguing link phenomenon synchronization.