  Time evolution of tunneling phenomena in medium is studied using a standard
model of environment interaction. A semiclassical formula valid at low, but
finite temperatures is derived in the form of integral transform for the
reduced Wigner function, and the tunneling probability in thermal medium is
calculated for a general tunneling potential of one dimensional system. Effect
of dissipation, its time evolution in particular, depends on the behavior of
the potential far beyond the barrier.
