Modelling and Structure-Preserving Discretization of the Schrödinger Equation as a Port-Hamiltonian System

Explore the modelling and structure-preserving discretization of the Schrödinger equation as a port-Hamiltonian system in this 15-minute conference talk. Delve into two proposed Hamiltonians for the model, one based on probability of presence and the other on the energy of quantum systems in time-independent potentials. Learn how the model is adapted to bounded domains and discretized using the Partitioned Finite Element Method (PFEM). Examine simulations of Rabi oscillations for controlling quantum box states, including transitions between energy levels and generation of Schrödinger cat states.

Modelling and structure-preserving discretization of the Schrödinger equation as aport-Hamiltonian