Discrete-time quantum walks with energy-dependent coins
Abstract
In this work, we extend the scattering quantum walk (SQW) framework to a lattice of energy-dependent point interactions. This yields, within the coined quantum walk (CQW) formalism, a coin operator that is directly related to the scattering matrix of zero-range potentials. The model thus provides a discrete-time quantum-walk (DTQW) analog of a periodic array of point interactions of the Kronig-Penney type, where the walker's wavenumber serves as a continuous, physically transparent control parameter for the coin operation. We analyze the spectra and the dynamics of position probability and entanglement, yielding distinct results for specific energies and point interactions. We relate the spectral structure to the spatial probability distribution and explicitly characterize the long-time entanglement behavior for each point interaction. The transmission modulus determines the quasienergy gap, bandwidth, and maximum group velocity, while also controlling the long-time coin-position entanglement for the initial state considered. The four families of one-dimensional point interactions (δ, δ', crossed and asymmetric) realize qualitatively distinct transmission profiles and span the full range of behavior, including enhanced or strongly suppressed spreading and oscillatory entanglement.
Related
- State Transfer in Discrete-Time Quantum Walks via Projected Transition Matrices
- Semi-discrete quadratic Wasserstein energy and state-dependent Langevin exploration
- Exponential functionals of two random walks and stationary measures of discrete growth processes
- Last-Coverage Probabilities of Random Walks on Cycle Graphs for Symmetric, Biased, and Time-Dependent Walks
- Spectral Criterion for Disorder-Free Localization of Quantum Walks on Hypercube: QBN Approach
BibTeX
@misc{santos2026discretetime,
title = {{Discrete-time quantum walks with energy-dependent coins}},
author = {Alana Spak dos Santos and Thiago T. Tsutsui and Fabiano M. Andrade},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03272},
eprint = {2609.03272},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03272},
}
RIS
TY - UNPB
TI - Discrete-time quantum walks with energy-dependent coins
AU - Alana Spak dos Santos
AU - Thiago T. Tsutsui
AU - Fabiano M. Andrade
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03272
UR - https://arxiv.org/abs/2609.03272
AB - In this work, we extend the scattering quantum walk (SQW) framework to a lattice of energy-dependent point interactions. This yields, within the coined quantum walk (CQW) formalism, a coin operator that is directly related to the scattering matrix of zero-range potentials. The model thus provides a discrete-time quantum-walk (DTQW) analog of a periodic array of point interactions of the Kronig-Penney type, where the walker's wavenumber serves as a continuous, physically transparent control parameter for the coin operation. We analyze the spectra and the dynamics of position probability and entanglement, yielding distinct results for specific energies and point interactions. We relate the spectral structure to the spatial probability distribution and explicitly characterize the long-time entanglement behavior for each point interaction. The transmission modulus determines the quasienergy gap, bandwidth, and maximum group velocity, while also controlling the long-time coin-position entanglement for the initial state considered. The four families of one-dimensional point interactions (δ, δ', crossed and asymmetric) realize qualitatively distinct transmission profiles and span the full range of behavior, including enhanced or strongly suppressed spreading and oscillatory entanglement.
ER -