A quantum Peierls-Nabarro barrier

TL;DR

This paper explores how quantum effects induce a lattice-periodic potential for static kinks in discrete nonlinear Klein-Gordon systems, even when classical barriers are absent, using a computationally efficient method.

Contribution

It introduces the concept of a quantum Peierls-Nabarro potential and provides a simple numerical approach to calculate it in specific nonlinear systems.

Findings

Quantum effects create a confining potential for kinks without classical barriers.

The quantum Peierls-Nabarro potential can be computed efficiently using the proposed algorithm.

Application to a two-parameter substrate family demonstrates the method's effectiveness.

Abstract

Kink dynamics in spatially discrete nonlinear Klein-Gordon systems is considered. For special choices of the substrate potential, such systems support continuous translation orbits of static kinks with no (classical) Peierls-Nabarro barrier. It is shown that these kinks experience, nevertheless, a lattice-periodic confining potential, due to purely quantum effects anaolgous to the Casimir effect of quantum field theory. The resulting ``quantum Peierls-Nabarro potential'' may be calculated in the weak coupling approximation by a simple and computationally cheap numerical algorithm, which is applied, for purposes of illustration, to a certain two-parameter family of substrates.