Loss, Gain, and Singular Points in Open Quantum Systems

Non-Hermitian quantum physics is used successfully for the description of different puzzling experimental results, which are observed in open quantum systems. Mostly, the influence of exceptional points on the dynamical properties of the system is studied. At these points, two complex eigenvalues of the non-Hermitian Hamiltonian coalesce (where is the energy and is the inverse lifetime of the state ). We show that also the eigenfunctions of the two states play an important role, sometimes even the dominant one. Besides exceptional points, other critical points exist in non-Hermitian quantum physics. At these points in the parameter space, the biorthogonal eigenfunctions of become orthogonal. For illustration, we show characteristic numerical results.