Complex scaling method applied to the study of the Swanson Hamiltonian in the broken PT-symmetry phase

Abstract

In this work, we study the non-PT symmetry phase of the Swanson Hamiltonian in the framework ofthe Complex Scaling Method. By constructing a bi-orthogonality relation, we apply the formalism ofthe response function to analyse the time evolution of different initial wave packages. The WignerFunctions, mean value of operators, and the probabilities of survival and persistence for the differentwave packages are evaluated as a function of time. We analyse in detail the time evolution in theneighbourhood of Exceptional Points. We derive a continuity equation for the system. We comparethe results obtained using the Complex Scaling Method to the ones obtained by working in a RiggedHilbert Space.