Resonance Trapping and Dynamical Phase Transitions

Abstract

In the non-Hermitian quantum physics, resonance trapping occurs due to width bifurcation in the regime of overlapping resonances. It causes dynamical phase transitions in many-level quantum systems. In the present contribution, three different examples, observed experimentally, are considered. In any case, resonance trapping breaks the symmetry characteristic of the system at low level density due to the alignment of a few states with the scattering states of the environment.Keywords Exceptional points · Dynamical phase transitions · PT symmetry breaking · Phase lapses · Spin swapping Most interesting features of non-Hermitian quantum physics occur in the regime of overlapping resonances. Here, the phases of the eigenfunctions of the Hamiltonian are not rigid [1]. It is possible therefore that some eigenstates of the system align with the scattering states of the environment, while the other ones decouple (more or less) from the environment. This phenomenon, called resonance trapping, is known for many years [2]. It is caused by width bifurcation. Due to this mechanism, non-Hermitian quantum physics is able to describe environmentally induced effects.Some years ago, the question has been studied [3] whether or not the resonance trapping phenomenon is related to some type of phase transition. The study is performed by using the toy modelin the one-channel case and with the assumption that (almost) all crossing (exceptional) points accumulate in one point [4]. It has been found that resonance trapping may be understood, in this case, as a second-order phase transition. The calculations are performed I. Rotter ( )