Suppression of quantum-mechanical reflection by environmental decoherence

Abstract

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.