Modelling and Structure-Preserving Discretization of the Schrödinger as a Port-Hamiltonian System, and Simulation of a Controlled Quantum Box

The modelling of the Schrödinger Equation as a port-Hamil-tonian system is addressed. We suggest two Hamiltonians for the model, one based on the probability of presence and the other on the energy of the quantum system in a time-independent potential. In order to simulate the evolution of the quantum system, we adapt the model to a bounded domain. The model is discretized thanks to the structure-preserving Partitioned Finite Element Method (PFEM). Simulations of Rabi oscillations to control the state of a system inside a quantum box are performed. Our numerical experiments include the transition between two levels of energy and the generation of Schrödinger cat states.

To cite this paper:
Verrier Gabriel, Haine Ghislain, Matignon Denis (2023) Modelling and Structure-Preserving Discretization of the Schrödinger as a Port-Hamiltonian System, and Simulation of a Controlled Quantum Box. In: Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science; 14072:392–401. Springer, Cham. St. Malo, France.

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