Quantum geometry of non-Hermitian systems

The geometry of quantum states determines their response to external perturbations, their noise, and wave packets dynamic. For example, the Berry curvature gives anomalous velocity of wave packets and the Hall conductivity of extended systems, thereby linking these observables to topological invariants. In non-Hermitian systems, wave packet dynamics are enriched by additional anomalous terms arising from generalizations of the Berry curvature to non-orthogonal eigenstates. In this work, we contextualize these anomalous contributions by showing that they directly arise from the geometry of the underlying quantum states. We discuss possible generalizations of the quantum geometric tensor, which we relate to the localization of qunatum states and wave packets. We discuss experimental signatures in terms of response functions and transport signatures.