Topological chiral random walker

TL;DR

The paper introduces the topological chiral random walker (TCRW), a model that leverages topological features to achieve robust edge currents and improve efficiency in maze solving and self-assembly tasks despite noise and disorder.

Contribution

It presents the TCRW model that connects topological dynamics with robust edge currents, demonstrating improved maze solving and self-assembly performance.

Findings

TCRW outperforms diffusive motion in maze solving.

TCRW reduces self-assembly times by about 80%.

Topological features enable robustness against defects and disorder.

Abstract

Understanding how biological and synthetic systems achieve robust function in noisy environments remains a fundamental challenge across the physical and life sciences. To connect robust behavior with non-trivial topological features present already in the dynamics of individual units, here we introduce the topological chiral random walker (TCRW) model. While exploring the system, a TCRW locates edges and boundaries in the system and develops topologically protected edge currents even in the presence of defects and disorder. Drawing on the bulk-boundary correspondence found in hard condensed matter systems allows us to rationalize the emergence of robust edge currents through topological features of the dynamic spectrum. We show that chiral motion and rotational noise with opposite chirality are two crucial components in our inherently non-Hermitian model. As proofs of principle, we first show that a topological walker outperforms diffusive motion to efficiently solve complex mazes due to its property of remaining on the edge with some rare detachments. Second, we use this model to design building blocks that can perform efficient self-assembly overcoming the timescale bottlenecks of diffusion-limited growth and reducing self-assembly times by approximately 80%.