Inelastic quantum tunneling through disordered potential barrier

TL;DR

This paper investigates how inelastic scattering influences quantum tunneling through a disordered barrier, revealing conditions where inelastic processes dominate despite their small probability, with implications for understanding tunneling in complex systems.

Contribution

It provides a detailed analysis of inelastic tunneling probabilities in disordered barriers, including asymptotic behaviors and energy intervals where inelastic effects surpass elastic tunneling.

Findings

Inelastic tunneling probability can exceed elastic probability under certain conditions.

Asymptotic expressions for tunneling probabilities are derived for various impurity configurations.

Identifies energy intervals where inelastic processes dominate elastic tunneling.

Abstract

The effect of inelastic scattering on quantum tunneling through a rectangular potential barrier, of length $L$, containing randomly distributed impurities, is considered. It is shown that, despite the fact that the inelastic transition probability $\mathcal{T}_{\mathrm{inelastic}}$ is exponentially small, it may be greater than that of the elastic in the out of resonance conditions for some energy interval $\triangle E$ (the energy of the incident particle is far from the spectrum of the random Hamiltonian). The asymptotic of the tunnelling transition probability for various impurity configurations are found and the energy interval $\triangle E$ where $\mathcal{T}_{\mathrm{elastic}}\sim\exp(-L/L^{*})\lesssim\mathcal{T}_{\mathrm{i nelastic}}$ is determined.