Universality of the Gunn effect: self-sustained oscillations mediated by solitary waves

TL;DR

This paper demonstrates that Gunn-like oscillations, driven by solitary wave dynamics, are a universal phenomenon in certain classes of semiconductor models, supported by a new asymptotic analysis.

Contribution

It introduces a novel asymptotic analysis showing the universality of the Gunn effect across different model equations, including the constrained Cahn-Allen equation.

Findings

Gunn-like oscillations are shown to occur in specific mathematical models.

A new asymptotic method is developed for analyzing these oscillations.

The analysis includes an example related to the constrained Cahn-Allen equation.

Abstract

The Gunn effect consists of time-periodic oscillations of the current flowing through an external purely resistive circuit mediated by solitary wave dynamics of the electric field on an attached appropriate semiconductor. By means of a new asymptotic analysis, it is argued that Gunn-like behavior occurs in specific classes of model equations. As an illustration, an example related to the constrained Cahn-Allen equation is analyzed.