Companion software for the manuscript: "A Unified Spectral Framework Linking Deterministic Decoherence Forces to Engineered Environments and Adaptive Quantum Control"

This repository contains the Python scripts that generate and verify the numerical results reported in the manuscript. The central physical claim verified here is that the non-classical (quantum) component of the deterministic decoherence force is of second order in the system-environment coupling, F_quantum ~ c^2, and is therefore linearly suppressed relative to the classical component in the weak-coupling regime. This result underpins the validity of the unified spectral description developed in the paper. All scripts solve the two-dimensional time-dependent Schrodinger equation for a system (double-well) bilinearly coupled to an environmental oscillator (or a multi-mode bath), evaluate the Bohmian quantum potential Q = -(hbar^2/2m) (nabla^2 R)/R from the wavefunction amplitude R = |Psi|, and extract the resulting forces. They are self-contained and reproduce the tables and figures of the manuscript.本仓库收录了用于生成并验证该手稿中报告的数值结果的Python脚本。本工作验证的核心物理论断为：确定性退相干力 (deterministic decoherence force) 的非经典（量子）分量在系统-环境耦合 (system-environment coupling) 中呈二阶量级，即$F_{ ext{量子}} sim c^2$，因此在弱耦合区域 (weak-coupling regime) 中，其相对于经典分量呈现线性抑制效应。该结论为本文提出的统一光谱描述 (unified spectral description) 的合理性提供了支撑。 所有脚本均针对与环境振子 (environmental oscillator)（或多模热浴 (multi-mode bath)）双线性耦合的双势阱 (double-well) 系统，求解二维含时薛定谔方程 (two-dimensional time-dependent Schrodinger equation)；从波函数振幅 (wavefunction amplitude) $R=|Psi|$ 中计算玻姆量子势 (Bohmian quantum potential) $Q = -frac{hbar^2}{2m} cdot frac{ abla^2 R}{R}$，并提取对应的作用力。这些脚本具备自洽性，可复现该手稿中的所有表格与插图。