Symmetry breaking in driven and strongly damped pendulum

TL;DR

This paper investigates the occurrence of symmetry breaking bifurcations in a strongly damped, driven pendulum, revealing that such phenomena can persist at high dissipation levels and are relevant to semiconductor superlattice behaviors.

Contribution

It demonstrates the existence of symmetry breaking phases in strongly damped pendulums and clarifies their parameter space, contrasting previous assumptions about their rarity.

Findings

Symmetry breaking can occur at high damping levels.

Symmetry broken solutions occupy smaller parameter regions than previously thought.

Relevance established to dynamic symmetry breaking in semiconductor superlattices.

Abstract

We examine the conditions for appearance of symmetry breaking bifurcation in damped and periodically driven pendulum in the case of strong damping. We show that symmetry breaking, unlike other nonlinear phenomena, can exist at high dissipation. We prove that symmetry breaking phases exist between phases of symmetric normal and symmetric inverted oscillations. We find that symmetry broken solutions occupy a sufficiently smaller region of pendulum's parameter space in comparison to the statements made in earlier considerations [McDonald and Plischke, Phys. Rev. B 27 (1983) 201]. Our research on symmetry breaking in a strongly damped pendulum is relevant to an understanding of phenomena of dynamic symmetry breaking and rectification in a pure ac driven semiconductor superlattices.