  The van der Waals (vdW) interaction plays a prominent role between neutral
objects at separations where short ranged chemical forces are negligible. This
type of dispersive coupling is determined by the interplay between geometry and
response properties of the materials making up the objects. Here, we
investigate the vdW interaction between 1D, 2D, and 3D standard and Dirac
materials within the Random Phase Approximation, which takes into account
collective excitations originating from the electronic Coulomb potential. A
comprehensive understanding of characteristic functionalities and scaling laws
are obtained for systems with parabolic energy dispersion (standard materials)
and crossing linear bands (Dirac materials). By comparing the quantum
mechanical and thermal limits the onset of thermal fluctuations in the vdW
interaction is discussed showing that thermal effects are significantly
pronounced at smaller scales in reduced dimensions.
