TITLE:
Integrated Mathematical Modelling and AI-Driven Simulation of Nonlinear Quantum Dynamics under Complex Electromagnetic Fields
AUTHORS:
Kikmo Wilba Christophe, Mbogba Guy Leopold, Mah Charitos Serge, Batambock Samuel, Ngoma Jean Pierre, Abanda Andre
KEYWORDS:
Nonlinear Schrödinger Equation, Open Quantum Systems, Electromagnetic Fields, Bose-Einstein Condensates, Advanced Numerical Simulation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.9,
September
23,
2025
ABSTRACT: We present a novel integrated mathematical and numerical framework for the nonlinear Schrödinger equation in open quantum systems under electromagnetic fields, with a particular focus on Bose-Einstein condensates. To overcome limitations in modeling nonlinear dissipative effects and exogenous influences, we propose a non-Hermitian NLS formulation incorporating localized dissipation and complex electromagnetic couplings. Analytical tools, including generalized dissipative Strichartz estimates, variational methods, and spectral theory for non-self-adjoint operators, enable precise characterization of stability and dynamical behavior. A high-precision numerical platform, combining spectral discretization with semi-implicit Crank-Nicolson schemes and perfectly matched absorbing layers, was implemented to simulate multidimensional regimes. Machine learning modules, including convolutional neural networks, variational autoencoders, and sequential models (LSTM/Transformer), were employed to automatically explore critical regimes, predict temporal evolution, and identify phase transitions. Simulations revealed the formation of stable dissipative solitons and vortices, robust under environmental losses, and demonstrated that spatially structured dissipation combined with oscillating electromagnetic fields can stabilize quasi-stationary states. Quantitative analysis shows that topologically protected modes persist over long timescales and can be dynamically controlled via external fields, confirming the feasibility of encoding qubits and implementing basic quantum gates in dissipative quantum computing frameworks. By integrating nonlinear, dissipative, and topological effects within a unified framework, this approach provides new insights into the stability, coherence, and controllability of open quantum systems, offering a practical pathway for nanoscale device engineering and robust quantum state manipulation.