Environment-effect on the Berry phase of a driven G32⊗ϵ(t) system in a magnetic field by the square-root method

The method is here applied to incorporate Lindblad-type processes into the evolution of a degenerate quantum system. Specifically, the effect of a dissipative environment on the topological or Berry phase (BP) is here studied for a system consisting of a spin-doubly degenerate orbital (E), belonging to the cubic G32 or Γ8 representation, subject to time-periodically varying stress and magnetic fields. The environmental effects redistribute the component amplitude of the initial wave packet and, with a general precessional motion of the magnetic field, change the BP markedly. The changes in the BP are suppressed for the magnetic field precessing on a large circle, in accordance with previous results (D.M. Tong et al., Phys. Rev. Lett. 93 (2004) 080405).