Stefani Mancas

Expertise in the theory of special functions with direct applications to Quantum Information and Cryptographic Systems including the design and modeling of qubits, quantum logic gates, and digital-analog architectures for scalable quantum computing. Focused on the development and simulation of quantum algorithms with applications in optimization, simulation, and secure communication. Advanced mathematical and high-precision numerical methods integrated with complex analysis frameworks and global optimization algorithms to investigate supersymmetric quantum mechanical systems which address challenges in characterizing potential energy landscapes, solving eigenvalue problems, and modeling symmetry-preserving dynamical evolutions within SUSY-invariant formulations. Specialized in the analytical treatment of nonlinear, dissipative, and time-dependent evolution equations, with an emphasis on methods that preserve underlying physical structure. Expertise includes the application of Darboux transformations and related supersymmetric techniques to systematically reduce complex differential equations to Riccati or Abel forms, enabling exact or quasi-exact solutions. Particular focus is given to Schrödinger-type equations arising in quantum field theory, supersymmetric quantum mechanics, and curved spacetime formulations within general relativity, including the study of scattering processes, bound states, and stability criteria in gravitational and gauge field backgrounds.