  We prove several relations between spectrum and dynamics including wave trace
expansion, sharp/improved Weyl laws, propagation of singularities and quantum
ergodicity for the sub-Riemannian (sR) Laplacian in the four dimensional
quasi-contact case. A key role in all results is played by the presence of
abnormal geodesics and represents the first such appearance of these in
sub-Riemannian spectral geometry.
