  In computer simulations, quantum delocalization of atomic nuclei can be
modeled making use of the Path Integral (PI) formulation of quantum statistical
mechanics. This approach, however, comes with a large computational cost. By
restricting the PI modeling to a small region of space, this cost can be
significantly reduced. In the present work we derive a Hamiltonian formulation
for a bottom-up, theoretically solid simulation protocol that allows molecules
to change their resolution from quantum-mechanical to classical and vice versa
on the fly, while freely diffusing across the system. This approach renders
possible simulations of quantum systems at constant chemical potential. The
validity of the proposed scheme is demonstrated by means of simulations of low
temperature parahydrogen. Potential future applications include simulations of
biomolecules, membranes, and interfaces.
