Mass Dependence of Granular Noise in a Schr¨odinger–Poisson–Gross–Pitaevskii Model for Fuzzy Dark Matter Using a GPU Fourier Solver

We present a GPU‑accelerated numerical solver for the Schrödinger–Poisson–Gross–Pitaevskii system describing fuzzy dark matter (FDM) with a repulsive self‑interaction in an expanding cosmological background. The code employs a Fourier pseudospectral method with Strang splitting and is implemented in PyTorch for efficient execution on CUDA‑enabled devices. We perform extensive verification of individual components: fast Fourier transforms, spectral Laplacian, Poisson solver, free Schrödinger evolution, cosmological background integration, and the accuracy of the analytical norm‑decay law. We apply the solver to a controlled mass scan over three representative masses: μ = 1, 10, 100 (m = 10⁻²², 10⁻²¹, 10⁻²⁰ eV), with five independent realisations each. The granular noise is measured as the fractional high‑frequency potential RMS above a fixed spectral cut k_cut = 0.5 kpc⁻¹. The results show that this metric grows with mass and is consistent with saturation for μ ≳ 10, with this behaviour reproducible across all realisations. The code reproduces the expected cosmological norm decay with relative error below 10⁻⁷ for all masses. The numerical pipeline is publicly available.