Exact diffusion coefficients for quantum--classical hybrid walks
Abstract
One-dimensional quantum--classical hybrid walks are introduced by combining quantum and classical steps under periodic and random protocols. Exact diffusion coefficients are derived for both protocols throughout the diffusive regime. The exact results show how diffusion depends on the average frequency and temporal arrangement of classical steps. As the average frequency approaches zero, both diffusion coefficients diverge inversely with the frequency. At matched average frequencies, the ratio of the diffusion coefficients for the random and periodic protocols approaches two. A finite-mode approximation is also developed and tested against the exact diffusion coefficient for the random protocol. The exact results for the one-dimensional model provide a foundation for future studies of more general quantum--classical hybrid walks.
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BibTeX
@misc{kim2026exact,
title = {{Exact diffusion coefficients for quantum--classical hybrid walks}},
author = {Cook Hyun Kim and Jaesub Park and Namshik Han},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01951},
eprint = {2609.01951},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01951},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact diffusion coefficients for quantum--classical hybrid walks
AU - Cook Hyun Kim
AU - Jaesub Park
AU - Namshik Han
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.01951
UR - https://arxiv.org/abs/2609.01951
AB - One-dimensional quantum--classical hybrid walks are introduced by combining quantum and classical steps under periodic and random protocols. Exact diffusion coefficients are derived for both protocols throughout the diffusive regime. The exact results show how diffusion depends on the average frequency and temporal arrangement of classical steps. As the average frequency approaches zero, both diffusion coefficients diverge inversely with the frequency. At matched average frequencies, the ratio of the diffusion coefficients for the random and periodic protocols approaches two. A finite-mode approximation is also developed and tested against the exact diffusion coefficient for the random protocol. The exact results for the one-dimensional model provide a foundation for future studies of more general quantum--classical hybrid walks.
ER -