Lyapunov exponents explain disorder-induced polarization and soliton teleportation in a mechanical Markov system

TL;DR

This paper introduces a Lyapunov exponent-based framework to understand wave localization, polarization, and soliton teleportation phenomena in disordered 1D mechanical systems modeled as mechanical Markov systems, revealing new nonlinear dynamics.

Contribution

It develops a novel Lyapunov exponent approach to explain disorder-induced polarization and soliton dynamics in mechanical Markov systems, bridging stochastic processes and wave localization.

Findings

Disorder induces polarization of zero modes explained by Lyapunov exponents.

Zero modes become mobile solitons in nonlinear regimes despite localization.

Discovery of reflectionless, chirality-dependent soliton teleportation phenomena.

Abstract

Using a mapping between spatial disorder and temporal stochasticity, we develop a new framework using Lyapunov exponents to explain exotic wave localization and mobility phenomena in disordered one-dimensional (1D) mechanical systems that can be constructed via a spatial analog of a Markov process, which we call ``mechanical Markov systems.'' We show that disorder induces robust polarization of zero modes (ZMs) in these mechanical Markov systems, and this phenomenon is explained using Lyapunov exponents. Remarkably, these ZMs become mobile solitons in the nonlinear regime despite the disorder-controlled localization of all other modes, and display a set of new nonlinear dynamics features including reflectionless chirality-dependent teleportation, which can also be explained using Lyapunov exponents. Our results establish the Markov formalism as a powerful tool to explain and design localization and dynamics in disordered mechanical systems, opening opportunities for programmable metamaterials with novel linear and nonlinear responses.