A Regularization Based Computational Method for Quantum Incommensurate Problems
Abstract
Quantum incommensurate systems have attracted widespread interest due to their unique physical properties. Related studies have made notable progress in recent years. To gain deeper insight, it is both significant and challenging to study a broader range of physical observables for these systems, which requires a comprehensive understanding of their spectral properties and wavefunction behavior. Based on the regularized model recently proposed, this work introduces a regularization framework, rendering physical observables for incommensurate systems mathematically well-defined and computationally accessible with theoretical guarantees. Based on this framework, taking the density of states and the electron density as representative examples, we establish their mathematical characterization, derive their planewave approximations, and provide a rigorous convergence analysis. Numerical experiments validate the effectiveness of our method, demonstrating its practical applicability for generic 1D and 2D incommensurate systems.
Related
- IQFEM: A quantum finite element method for heterogeneous problems with immersed boundaries
- Data-driven Smooth-to-hard Spectral Regularization for General Linear Inverse Problems
- Symmetry Regularization of 1D Generalized Coulomb Problems
- Physics-Guided Conditional Flow Matching with Energy Regularization for Robust PDE Inverse Problems
- Data-driven stochastic asymptotic regularization for ill-posed inverse problems with a posteriori and heuristic stopping
BibTeX
@misc{ding2026regularization,
title = {{A Regularization Based Computational Method for Quantum Incommensurate Problems}},
author = {Zhenan Ding and Yan Li and Aihui Zhou and Yuzhi Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29357},
eprint = {2609.29357},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29357},
}
RIS
TY - UNPB
TI - A Regularization Based Computational Method for Quantum Incommensurate Problems
AU - Zhenan Ding
AU - Yan Li
AU - Aihui Zhou
AU - Yuzhi Zhou
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29357
UR - https://arxiv.org/abs/2609.29357
AB - Quantum incommensurate systems have attracted widespread interest due to their unique physical properties. Related studies have made notable progress in recent years. To gain deeper insight, it is both significant and challenging to study a broader range of physical observables for these systems, which requires a comprehensive understanding of their spectral properties and wavefunction behavior. Based on the regularized model recently proposed, this work introduces a regularization framework, rendering physical observables for incommensurate systems mathematically well-defined and computationally accessible with theoretical guarantees. Based on this framework, taking the density of states and the electron density as representative examples, we establish their mathematical characterization, derive their planewave approximations, and provide a rigorous convergence analysis. Numerical experiments validate the effectiveness of our method, demonstrating its practical applicability for generic 1D and 2D incommensurate systems.
ER -