Modelling and structure-preserving discretization of the Schrödinger as a port-Hamiltonian system, and simulation of a controlled quantum box. (English) Zbl 1536.81081
Nielsen, Frank (ed.) et al., Geometric science of information. 6th international conference, GSI 2023, St. Malo, France, August 30 – September 1, 2023. Proceedings. Part II. Cham: Springer. Lect. Notes Comput. Sci. 14072, 392-401 (2023).
Summary: The modelling of the Schrödinger Equation as a port-Hamitonian 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.
For the entire collection see [Zbl 1528.53002].
For the entire collection see [Zbl 1528.53002].
MSC:
| 81Q93 | Quantum control |
| 81S22 | Open systems, reduced dynamics, master equations, decoherence |
| 70H05 | Hamilton’s equations |
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 39A12 | Discrete version of topics in analysis |
| 57R67 | Surgery obstructions, Wall groups |
| 47D06 | One-parameter semigroups and linear evolution equations |
| 32M15 | Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
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