How “Berry Phase” Analysis of Non-adiabatic Non Hermitian Systems Reflects Their Geometry

This is the authors' abstract. We don't add key points for this paper.

There is great current interest in systems represented by non-Hermitian Hamiltonians, including a wide variety of real systems that may be dissipative and whose behaviour can be represented by a "phase" parameter that characterises the way "exceptional points" (singularities of various sorts) determine the system. These systems are briefly reviewed with an emphasis on their geometrical thermodynamics properties.