Multidimensional Splitting of Electron Wavefunctions via Spacetime Phase Resolution Modulation Induced by Inhomogeneous Magnetic Curl Fields

This paper establishes a novel electron optics paradigm by generalizing the inhomogeneous magnetic field mechanism of the Stern-Gerlach experiment into a spatiotemporally modulated traveling magnetic lattice. Rather than treating the vacuum as a static background, we define a localized Spacetime Phase Resolution Metric ( Ξ̅ ) governed directly by the dynamic transverse curl of the magnetic field ( ∇ × B⃗ ).By resolving prior algebraic ambiguities through exact Jacobi-Anger identities, we mathematically demonstrate that an incident electron wave packet undergoing this Spacetime Phase Resolution Modulation (SPRM) splits into an infinite tree-like bifurcation of discrete, phase-locked energy-momentum channels. Within this framework, we derive the quantum chaos suppression and dynamical localization phenomena under a periodic Floquet-Aubry-André lattice drive protocol, ensuring strict continuous unitary time evolution while blocking unphysical equipotential diffusion.Furthermore, we develop a reverse-engineered Quantum Dissipation Control Algorithm that regulates the local rate of quantum decoherence through a bound-preserving, real-valued Lindblad master equation. This architecture guarantees that the external control parameter Γ(x) remains strictly positive and real-valued ( Γ(x) ∈ ℝ⁺ ) across all spatial coordinates, resolving previous non-physical complex parameter boundaries.To bridge the gap between 1D micro-control and 3D volumetric synthesis, we introduce a rigorous coordinate transformation governed by the Jacobian determinant ( det(J) ), which models the spatial scaling behavior of the emergent particle cloud. Finally, we verify that by algorithmically tuning the local spacetime phase resolution density, the spatial probability distribution of unconstrained electrons can be deterministically sculpted and printed into arbitrary target nanoscale morphologies from vacuum fluctuations.