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smooth-windowing-quantum

Companion code for the paper:

Parameter-Free Absorbing Boundaries for Pseudo-Spectral Quantum Dynamics via C∞ Windowing David Ariza-Ruiz Computer Physics Communications (2026)

Overview

This repository provides a self-contained Python implementation of a parameter-free absorbing boundary condition for FFT-based split-step solvers of the one-dimensional time-dependent Schrodinger equation. The boundary treatment consists of multiplying the wave function at each time step by a compactly supported C-infinity bump function that equals unity on an interior plateau and vanishes smoothly at the computational boundaries, exploiting the super-algebraic convergence guarantees established by Bergold and Lasser (2020).

Repository contents

File Description
smooth_windowing_abc.py Main script: runs all 13 numerical experiments and generates figures 1--14
pml_convergence_study.py PML convergence study with spatial refinement, higher-order stencils (FD2/FD4/FD6), and ultra-refined reference solutions
convergence_extended.py Extended convergence analysis using 80-digit (mpmath) arithmetic
convergence_extended.csv Pre-computed convergence data (80-digit precision)
figure_1.pdf -- figure_14.pdf All figures reported in the paper
requirements.txt Python dependencies
CITATION.cff Citation metadata
LICENSE MIT license

Numerical experiments (main script)

The 13 experiments in smooth_windowing_abc.py are:

  1. Fourier approximation and Gibbs suppression
  2. Wave packet absorption
  3. Plateau parameter study
  4. Window regularity comparison
  5. Complex absorbing potential (CAP) comparison
  6. CAP robustness test across momenta
  7. Temporal convergence
  8. Gaussian barrier scattering (above-barrier)
  9. Gaussian barrier scattering (tunneling)
  10. Comprehensive tunneling and strong-barrier campaign with barrier-shape universality
  11. Delta-t anomaly diagnosis
  12. 1D PML benchmark (single traversal)
  13. Multiple-reflection benchmark (C-infinity windowing vs PML)

Requirements

  • Python 3.8+
  • NumPy >= 1.22
  • Matplotlib >= 3.5
  • mpmath >= 1.3
  • SciPy >= 1.10 (required for PML finite-difference solves; optional for main script)

Install all dependencies:

pip install -r requirements.txt

Usage

Run the main experiments:

python smooth_windowing_abc.py

Run the PML convergence study:

python pml_convergence_study.py

Run the extended convergence analysis (computationally intensive):

python convergence_extended.py

All figures are saved as figure_X.pdf in the working directory.

License

MIT License. See LICENSE.

Citation

If you use this code in your research, please cite:

@article{ArizaRuiz2026,
  author  = {Ariza-Ruiz, David},
  title   = {Parameter-Free Absorbing Boundaries for Pseudo-Spectral Quantum
             Dynamics via {$C^\infty$} Windowing},
  journal = {Computer Physics Communications},
  year    = {2026}
}