  In quantum mechanics an incoming particle wave packet with sufficient energy
will undergo both transmission and reflection when encountering a barrier of
lower energy, but in classical mechanics there is no reflection, only
transmission. In this paper we seek to explain the disappearance of
quantum-mechanical reflection in the quasi-classical limit, using standard
methods of decoherence through environmental interaction. We consider two
models. In the first, the incoming particle is classicalized by coupling it to
an environment described by a standard Lindblad master equation diagonalizing
in position. We find, however, that suppression of reflection is achieved only
for environmental interaction so strong that large fluctuations in momentum are
generated which blurs the distinction between incoming and reflected wave
packets. This negative conclusion also holds for a complex potential which has
similar implications for attempts to understand the suppression of the Zeno
effect using the same mechanism (discussed in more detail in another paper). A
different Lindblad master diagonalizing in momentum is shown to be successful
in suppressing reflection without large fluctuations but such a master equation
is unphysical. We consider a second model in which the barrier is modelled
quantum-mechanically by a massive target particle coupled to an environment to
maintain it in a quasi-classical state. This avoids the fluctuations problem
since the incoming particle is not coupled to the environment directly. We find
that reflection is significantly suppressed as long as the decoherence
timescale of the target particle is much smaller than certain characteristic
scattering timescales of the incoming particle, or equivalently, as long as the
velocity fluctuations in the target are larger than the velocity of the
incoming particle.
