Adiabatic-impulse approximation in the non-Hermitian Landau-Zener model

In the non-Hermitian Landau-Zener models, we investigate dynamical transition both in parity-time symmetric and symmetry-broken regimes. Taking into account complex nature of energy systems, absolute value gap was used to determine relaxation rate system. To show dynamics phase transitions, relative population is estimate topological defect density nonequilibrium rather than excitations corresponding Hermitian systems. The result shows that adiabatic-impulse approximation, which fundamental Kibble-Zurek mechanism, may be adapted models examine near critical point. most basic two-level with an exact solution exhibiting mechanism are presented. It would interesting extend this scenario quantum many-body such as Ising model.