Interplay of disorder and nonlinearity in Klein-Gordon models: Immobile kinks

TL;DR

This paper investigates how spatial disorder affects immobile kinks in Klein-Gordon models, revealing a crossover in kink width behavior depending on their statistical distribution and system size.

Contribution

It demonstrates the dependence of kink properties on their statistical distribution over potential minima and identifies a crossover in behavior influenced by disorder and system size.

Findings

Kink width behavior depends on statistical distribution over minima.

A crossover from monotonic to non-monotonic dependence on disorder.

System size influences the occurrence of the crossover.

Abstract

We consider Klein-Gordon models with a $\delta$-correlated spatial disorder. We show that the properties of immobile kinks exhibit strong dependence on the assumptions as to their statistical distribution over the minima of the effective random potential. Namely, there exists a crossover from monotonically increasing (when a kink occupies the deepest potential well) to the non-monotonic (at equiprobable distribution of kinks over the potential minima) dependence of the average kink width as a function of the disorder intensity. We show also that the same crossover may take place with changing size of the system.