Wavepacket dynamics in non Hermitian systems

 Berry phases strongly affect 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 using the bi-orthogonal formalism have been argued to characterize the topology of these systems. Since non-Hermitian Hamiltonians could be relevant for many types of open and lossy systems it is important to understand how these new quantities enter equations of motion for semi-classical wavepackets. Since generally for non-Hermitian systems the adiabatic theorem fails, this poses a challenge to the theory. I will discuss how to define observables and the conditions under which we can still apply the single band limit, and introduce the type of anomalous terms that may appear in the equation of motion and are present already in one-dimensional systems. I will also discuss the conditions for observing these anomalous contributions and potential extensions of the formalism to include complex electric fields, and magnetic fields.