Researchers Find Dephasing Sustains Time Crystals

Local pure dephasing suppresses single-spin coherence, but it sustains continuous time-crystalline order in a fully connected ferromagnetic spin-1/2 ensemble with local decay. An exact operator identity elucidates the underlying mechanism; specifically, dephasing elevates the interaction energy, whereas energy relaxation occurring on a finite timescale transforms this charging into delayed feedback. Utilizing homogeneous mean-field theory, researchers rigorously prove that dephasing constitutes a necessity for sustained periodic motion within this model and that feedback precisely counteracts transverse damping across each complete cycle. Further investigation extends beyond the scope of mean field analysis to provide additional insights. A previously unobserved phenomenon, algebraically decreasing decay rates within fully connected ferromagnetic…