Diffusive real-time dynamics of a particle with Berry curvatures

Motivated by the recent developments of time-resolved experiments, we study theoretically the influence of Berry phase on the real-time dynamics focusing on the diffusive dynamics, i.e., the time-dependence of the distribution function. We found that the dynamics at the early stage is deeply influenced by the Berry curvatures in real-space (B), momentum-space (Ω), and also the crossed space between these two (C). For example, it is found that Ω 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 t³ dependence in the absence of the Berry curvatures. It is also found that Ω and C modifies the characteristic time scale of the thermal equilibration of momentum distribution. Moreover, the dynamics under various combinations of B, Ω 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. These results offer yet another method to disentangle Berry curvatures in terms of time-resolved experiments. Possible experimental observations for excitons and trions in transition metal dichalcogenides are also discussed.