Nonlinear quantum evolution in post-selected non-Hermitian dynamics.

Open systems with gain and loss are described by non-Hermitian Hamiltonians that act as generators of time evolution. They are realized in open quantum systems through subspace-trace-preserving post-selection on no-quantum-jump trajectories. By construction, such post-selection is accompanied by an anti-Hermitian nonlinear term in the equations of motion for a quantum state (or the density matrix). We present analytical and numerical results for different nonlinearities that can be introduced in this fashion, and quantify their effect on the dynamics of small systems by using fixed points of such nonlinear Hamiltonians.