Non-Hermitian dynamics of slowly varying Hamiltonians - Wang, Hailong (2018)
We develop a theoretical description of non-Hermitian time evolution that accounts for the breakdown of the adiabatic theorem. We obtain closed-form expressions for the time-dependent state amplitudes, involving the complex eigenenergies as well as interband Berry connections calculated using basis sets from appropriately chosen Schur decompositions. Using a two-level system as an example, we show that our theory accurately captures the phenomenon of “sudden transitions,” where the system state abruptly jumps from one eigenstate to another.