A Unified View on Geometric Phases and Exceptional Points in Adiabatic Quantum Mechanics

We present a formal geometric framework for the study of adiabatic quantum mechanics arbitrary finite-dimensional non-degenerate Hamiltonians. This generalizes earlier holonomy interpretations phase to non-cyclic states appearing non-Hermitian start with an investigation space operators on state space. then show how energy bands Hamiltonian family form covering Likewise, we that eigenrays bundle, generalization principal which admits natural connection yielding (generalized) phase. bundle provides in addition tensor and derived tensors, it can incorporate non-geometric dynamical as well. finish by demonstrating be recast so both phases permutations eigenstates expressed simultaneously means standard theory.