  Path integral-based simulation methodologies play a crucial role for the
investigation of nuclear quantum effects by means of computer simulations.
However, these techniques are significantly more demanding than corresponding
classical simulations. To reduce this numerical effort, we recently proposed a
method, based on a rigorous Hamiltonian formulation, which restricts the
quantum modeling to a small but relevant spatial region within a larger
reservoir where particles are treated classically. In this work, we extend this
idea and show how it can be implemented along with state-of-the-art path
integral simulation techniques, such as ring polymer and centroid molecular
dynamics, which allow the approximate calculation of both quantum statistical
and quantum dynamical properties. To this end, we derive a new integration
algorithm which also makes use of multiple time-stepping. The scheme is
validated via adaptive classical--path-integral simulations of liquid water.
Potential applications of the proposed multiresolution method are diverse and
include efficient quantum simulations of interfaces as well as complex
biomolecular systems such as membranes and proteins.
