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

Abstract

There is currently great 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 here with an emphasis on their geometrical thermodynamics properties.