Another example of finite speed propagation techniques
is described in On-diagonal estimates on Schrödinger
and reduced heat kernels.
Using the wave equation techniques I obtained on-diagonal bounds for
heat kernels corresponding to the Schrödinger operators
with magnetic field under the
assumption of polynomial growth of the potential.
I also obtained off-diagonal
estimates as a direct consequence of on-diagonal estimates.
These results complement the earlier results of
Davies and Simon.