Structural Hamiltonian Reconstruction for Quantum Dynamicsin the IDSFramework

This work redefines quantum dynamics through a structure-driven Hamiltonian generator within the Information Dynamical Sys-tem (IDS) framework. We propose a non-Hermitian, wavefunction-dependent Hamiltonian, 𝐻IDS [𝜓] = −12 𝜕2𝑥 + 𝜙res (𝑥, 𝑡; 𝜓) + 𝑖Γ(𝑥, 𝑡; 𝜓),which encodes entropy-driven dissipation and structural time emer-gence. A numerical solver using finite-difference discretization andRunge-Kutta 45 (RK45) integration models a free particle with aGaussian wave packet, incorporating dynamic potentials and adap-tive absorbing boundaries. Simulations reveal asymmetric spectralevolution and controlled norm decay, aligning with IDS’s structuralattractor at 𝐾 = 1. This approach achieves numerical stability andcomputational efficiency, offering a breakthrough in modeling irre-versible quantum dynamics without external reservoirs.