  We determine the dynamical dimer correlation functions of quantum dimer
models at the Rokhsar-Kivelson point on the bipartite square and cubic lattices
and the non-bipartite triangular lattice. Based on an algorithmic idea by
Henley, we simulate a stochastic process of classical dimer configurations in
continuous time and perform a stochastic analytical continuation to obtain the
dynamical correlations in momentum space and the frequency domain. This
approach allows us to observe directly the dispersion relations and the
evolution of the spectral intensity within the Brillouin zone beyond the
single-mode approximation. On the square lattice, we confirm analytical
predictions related to soft modes close to the wavevectors (pi,pi) and (pi,0)
and further reveal the existence of shadow bands close to the wavevector (0,0).
On the cubic lattice the spectrum is also gapless but here only a single soft
mode at (pi,pi,pi) is found, as predicted by the single mode approximation. The
soft mode has a quadratic dispersion at very long wavelength, but crosses over
to a linear behavior very rapidly. We believe this to be the remnant of the
linearly dispersing "photon" of the Coulomb phase. Finally the triangular
lattice is in a fully gapped liquid phase where the bottom of the dimer
spectrum exhibits a rich structure. At the M point the gap is minimal and the
spectral response is dominated by a sharp quasiparticle peak. On the other
hand, at the X point the spectral function is much broader. We sketch a
possible explanation based on the crossing of the coherent dimer excitations
into the two-vison continuum.
