  Assemblies of interacting Rydberg atoms show promise for the quantum
simulation of transport phenomena, quantum chemistry and condensed matter
systems. Such schemes are typically limited by the finite lifetime of Rydberg
states. Circular Rydberg states have the longest lifetimes among Rydberg states
but lack the energetic isolation in the spectrum characteristic of low angular
momentum states. The latter is required to obtain simple transport models with
few electronic states per atom. Simple models can however even be realized with
circular states, by exploiting dipole-dipole selection rules or external
fields. We show here that this approach can be particularly fruitful for
scenarios where quantum transport is coupled to atomic motion, in adiabatic
excitation transport or quantum simulations of electron-phonon coupling in
light harvesting. Additionally, we explore practical limitations of flexible
Rydberg aggregates with circular states and to which extent interactions among
circular Rydberg atoms can be described using classical models.
