Diffusive real-time dynamics of a particle with Berry curvatures

We study theoretically the influence of Berry phase on the real-time dynamics of the single particle focusing on the diffusive dynamics, i.e., the time-dependence of the distribution function. Our model can be applied to the real-time dynamics of intraband relaxation and diffusion of optically excited excitons, trions or particle-hole pair. We found that the dynamics at the early stage is deeply influenced by the Berry curvatures in real-space ($B$), momentum-space ($\Omega$), and also the crossed space between these two ($C$). For example, it is found that $\Omega$ induces the rotation of the wave packet and causes the time-dependence of the mean square displacement of the particle to be linear in time $t$ at the initial stage; it is qualitatively different from the $t^3$ dependence in the absence of the Berry curvatures. It is also found that $\Omega$ and $C$ modifies the characteristic time scale of the thermal equilibration of momentum distribution. Moreover, the dynamics under various combinations of $B$, $\Omega$ and $C$ shows singular behaviors such as the critical slowing down or speeding up of the momentum equilibration and the reversals of the direction of rotations. The relevance of our model for time-resolved experiments in transition metal dichalcogenides is also discussed.