Synchronization Induced by Ultralight Dark Matter

We study the possibility of ultralight bosonic dark matter (UlDM) to induce a synchronized behaviour on randomly evolving oscillators. We introduce a new interaction between UlDM and the oscillators and further demonstrate the occurence of the phase transition from disordered oscillators state into ordered state. For UlDM within the mass range of $10^{-14}\,\text{eV}/c^{2} \leq m_{\phi} \leq 1 \,\text{eV}/c^{2}$ as well as the white noise strength lower than 0.01 Hz, the synchronization of randomly distributed oscillators with the mean angular frequency $1$ Hz and the corresponding standard deviation 0.1 Hz occurs when the coupling strength between UlDM and oscillators lies within $10 \geq g_{\omega} \geq 10^{-13}$. This offers an alternative method to unveil the nature of UlDM with respect to the established experiments.