Rabi transport and the other finite-size effects in one-dimensional discrete-time topological quantum walk

TL;DR

This paper explores how topological properties and finite sizes in one-dimensional quantum walks influence localized states and Rabi-like transport, revealing size-dependent transitions between ballistic, localized, and oscillatory behaviors.

Contribution

It introduces a detailed analysis of finite-size effects on topological quantum walks, demonstrating the emergence of Rabi transport and localized states due to boundary and size effects.

Findings

Finite systems exhibit localized and bilocalized states due to topology.

Rabi-like transport arises from degeneracy breaking in finite lattices.

Topological protection remains robust against disorder.

Abstract

This paper investigates Rabi transport and finite-size effects in one-dimensional discrete-time topological quantum walks. We demonstrate the emergence of localized states at boundaries between topologically distinct phases and analyze how finite system sizes influence quantum walk dynamics. For finite lattices, we show that topology induces localized and bilocalized states, leading to Rabi-like transport as a result of degeneracy breaking due to finite-size effects. The study bridges the gap between topological protection and size-dependent dynamics, revealing transitions from ballistic motion to localized or oscillatory behavior based on the system's topological properties. Analytical and numerical methods are employed to explore the spectra and dynamics of quantum walks, highlighting the robustness of Rabi transport against disorder. The findings provide insights into controlled quantum transport and potential applications in quantum information processing.