An experimental setup of three coupled PT -symmetric wave guides showing the characteristics of a third-order exceptional point (EP3) has been investigated in an idealized model of three deltafunctions wave guides in W. D. Heiss and G. Wunner, J. Phys. A 49, 495303 (2016). Here we extend these investigations to realistic, extended wave guide systems. We place major focus on the strong parameter sensitivity rendering the discovery of an EP3 a challenging task. We also investigate the vicinity of the EP3 for further branch points of either cubic or square root type behavior.

Abstract. In open double-well Bose-Einstein condensate systems which balance in-and outfluxes of atoms and which are effectively described by a non-hermitian PT -symmetric Hamiltonian PT -symmetric states have been shown to exist. PTsymmetric states obey parity and time reversal symmetry. We tackle the question of how the in-and outfluxes can be realized and introduce a hermitian system in which two PT -symmetric subsystems are embedded. This system no longer requires an inand outcoupling to and from the environment. We show that the subsystems still have PT -symmetric states. In addition we examine what degree of detail is necessary to correctly model the PT -symmetric properties and the bifurcation structure of such a system. We examine a four-mode matrix model and a system described by the full Gross-Pitaevskii equation in one dimension. We see that a simple matrix model correctly describes the qualitative properties of the system. For sufficiently isolated wells there is also quantitative agreement with the more advanced system descriptions. We also investigate which properties the wave functions of a system must fulfil to allow for PT -symmetric states. In particular the requirements for the phase difference between different parts of the system are examined.

Abstract.We study theoretical models of three coupled wave guides with a PT -symmetric distribution of gain and loss. A realistic matrix model is developed in terms of a three-mode expansion. By comparing with a previously postulated matrix model it is shown how parameter ranges with good prospects of finding a third-order exceptional point (EP3) in an experimentally feasible arrangement of semiconductors can be determined. In addition it is demonstrated that continuous distributions of exceptional points, which render the discovery of the EP3 difficult, are not only a feature of extended wave guides but appear also in an idealised model of infinitely thin guides shaped by delta functions.

We reveal limitations of several standard coupled-cluster (CC) methods with perturbation-theory based noniterative or approximate iterative treatments of triple excitations when applied to the determination of highly accurate potential energy curves (PECs) of ionic dimers, such as the XΣg+2 electronic ground state of Rb2+. Such computations are of current interest for the understanding of ion–atom interactions in the ultracold regime. We demonstrate that these CC methods lead to an unphysical long-range barrier for the Rb2+ system. The barrier is small but spoils the long-range behavior of the PEC. The effect is also found for other X2+ systems, such as X = Li, Na, and K. Calculations using a flexible framework for obtaining leading perturbative triples corrections derived using an analytic CC singles and doubles energy derivative formulation demonstrate that the origin of this problem lies in the use of T̂3 amplitudes obtained from approximate CC singles, doubles, and triples amplitude equations. It is shown that the unphysical barrier is related to a symmetry instability of the underlying Hartree–Fock mean-field solution, leading to orbitals representing two +0.5-fold charged ions in the limit of separated fragments. This, in turn, leads to a wrong 1/R asymptote of the interaction potential computed by perturbation-based CC approximations. Physically meaningful perturbative corrections in the long-range tail of the PEC may instead be obtained using symmetry-broken reference determinants.