Compound transfer matrices: Constructive and destructive interference

TL;DR

This paper investigates how wave interference effects in compound barriers influence transmission probabilities, revealing bounds and phase-related phenomena that differ from classical particle scattering.

Contribution

It provides a detailed analysis of interference effects in wave scattering through compound barriers, deriving bounds on transmission and quantum excitation processes.

Findings

Transmission probability oscillates due to interference effects.

Derived bounds on quantum excitation via parametric resonance.

Contrasts classical and wave scattering behaviors.

Abstract

Scattering from a compound barrier, one composed of a number of distinct non-overlapping sub-barriers, has a number of interesting and subtle mathematical features. If one is scattering classical particles, where the wave aspects of the particle can be ignored, the transmission probability of the compound barrier is simply given by the product of the transmission probabilities of the individual sub-barriers. In contrast if one is scattering waves (whether we are dealing with either purely classical waves or quantum Schrodinger wavefunctions) each sub-barrier contributes phase information (as well as a transmission probability), and these phases can lead to either constructive or destructive interference, with the transmission probability oscillating between nontrivial upper and lower bounds. In this article we shall study these upper and lower bounds in some detail, and also derive bounds on the closely related process of quantum excitation (particle production) via parametric resonance.