Quantum Dynamical Phase Transitions at the Exceptional Point of Non-Hermitian Hamiltonians: their key rôle in molecular dissociation/formation and their persistence in density conserving dynamics

My own need to deal with exceptional points or spectral bifurcations appeared when we experimentally observed a Quantum Dynamical Phase Transition for a spin dimmer in the presence of a non-quiral spin environment [1]. In this case the effective Hamiltonian results nonHermitian. We further observed that spectral bifurcations (exceptional points) may appear in strictly positive dynamics, i.e. solutions of the Keldysh or Lindblad equations, even when the exceptional points are not present at the non-Hermitian Hamiltonian level [2]. I will start with an overview of these results.