Adaptive Variance-Reduced Grid-Free Monte Carlo Method for Electron-Phonon Transport Calculations

Source code accompanying the paper "Adaptive Variance-Reduced Grid-Free Monte Carlo Method for Electron-Phonon Transport Calculations" submitted to Computer Physics Communications (2025), Manuscript COMPHY-S-26-00402. This code implements an adaptive importance-sampling extension of the grid-free Monte Carlo framework for evaluating electron-phonon scattering integrals without Brillouin-zone grids or energy-broadening parameters. Features: - Complete implementation of Algorithm 1 (adaptive grid-free Monte Carlo) - Froehlich polar optical phonon model benchmark with analytical validation - Variance reduction analysis (R approximately 40) - Convergence and wall-clock efficiency benchmarks - Simplified ZnTe electron mobility calculation - Reproduces Figures 1, 2, 3, 6, 8, 10 and Table 2 from the paper Requirements: Python 3.7+, NumPy Usage: python main.py Runtime: approximately 20 seconds The Froehlich model benchmarks are fully self-contained. The full first-principles ZnTe results reported in the paper were computed using Quantum ESPRESSO, Wannier90, and EPW with DFPT electron-phonon couplings. Key results: - 10x fewer samples needed for 1% accuracy compared to uniform sampling - Variance reduction factor R approximately 30-40 - 5-10x wall-clock speedup at fixed precision - Optimal parameters: alpha = 0.3-0.5, N_per_iter = 50-200

• electron-phonon transport
• adaptive importance sampling
• variance reduction
• Brillouin zone sampling
• computational efficiency

• Physics of Superconductivity and Magnetism
• Markov Chains and Monte Carlo Methods
• Thermodynamic and Structural Properties of Metals and Alloys
• electron-phonon transport
• adaptive importance sampling
• variance reduction
• Brillouin zone sampling
• computational efficiency
• Condensed Matter Physics
• Statistics and Probability
• Mechanical Engineering
• Physics and Astronomy
• Mathematics
• Engineering