Chains of topological oscillators with instantons and calculable topological observables in topological quantum mechanics

TL;DR

This paper develops an extended chain model of topological oscillators in quantum mechanics, revealing computable topological invariants and zero modes, and supports the idea that supersymmetric quantum mechanics aids understanding of complex physical systems.

Contribution

It introduces a possibly infinite chain of topological oscillators with computable invariants, extending previous toy models to explore topological quantum properties.

Findings

The model confirms the existence of zero modes and topological invariants.

It supports the conjecture that supersymmetric quantum mechanics helps analyze topological properties.

The system exhibits absence of ground states and mass gaps, characteristic of topological quantum systems.

Abstract

We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang-Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al.) and condensed matter properties (Kane et al.), where trajectories of effective models are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.