Berry phases are known to significantly alter the properties of crystalline materials, giving rise to modifications of the semiclassical equations of motion that govern wave-packet dynamics. In non-Hermitian systems, generalizations of the Berry connection have been analyzed and have been shown to have novel effect on dynamics and transport.
In this work, we expand upon these results by deriving the full set of semiclassical equations of motion for wave-packet dynamics in a non-Hermitian system subject to complex external electric fields.
We show that the non-Hermiticities of both the bare Hamiltonian and the external potential give rise to anomalous weight rate and velocity terms which depend on the geometric properties of the eigenfunctions. These analytical results are compared with numerical lattice simulations which reveal these anomalous terms even in one-dimension.
Our work expands the range of phenomena expected to be detectable in experimental setups, which should be realizable in currently available metamaterials for classical wave systems, including mechanical, acoustic, and optical.