On the adiabatic theorem for nonself-adjoint Hamiltonians

Abstract

The authors consider the evolution of a two-level system driven by a nonself-adjoint Hamiltonian H( in t) and treat the adiabatic limit in to 0. While adiabatic theorem-like results do not hold true in general for this case, they prove that they are still valid for the subspace corresponding to the eigenvalue having the largest imaginary part (least dissipative eigenvalue). The theory gives the full asymptotic expansion of the evolution restricted to this subspace. The first correction beyond Berry's phase is to their best knowledge given explicitly for the first time.