Bird, Senan (2026) Modelling Exciton Dissipation via the Numerical Integration of the Schrödinger Equation. Master's Thesis / Essay, Physics.
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Abstract
Numerical Integration of the Schrödinger Equation is a methodology used to simulate exciton transfer in molecular aggregates. By treating the electronic system and the nuclear bath within a mixed quantum-classical framework, Numerical Integration of the Schrödinger Equation simplifies the complexity of these interactions by assuming a high-temperature limit. The system Hamiltonian is propagated via a wavefunction that evolves according to an Ornstein–Uhlenbeck process, which simulates environmental noise and system-bath coupling. However, this classical approximation does not fully capture the thermalisation of molecular interactions or the Stokes shift. Unlike numerically exact methods, such as Hierarchy of Pure States or Hierarchical Equations of Motion, standard Numerical Integration of the Schrödinger Equation fails to reach a proper Boltzmann distribution. This thesis implements two computationally efficient schemes to incorporate the Stokes shift into the Numerical Integration of the Schrödinger Equation framework. The first method utilises a Linear Reorganisation Shift within the Hamiltonian, updated at each propagation step. The second method employs a memory kernel, allowing the Hamiltonian to retain a temporary "memory" of the dissipative effects. Both modifications demonstrate improved accuracy relative to the standard Numerical Integration of the Schrödinger Equation model. The memory kernel, in particular, yields superior long-term results as the system reaches the steady state, while the Linear Reorganisation Shift offers occasional improvements under specific parameter sets in the short/medium term before the system/bath has stabilised. These methods provide a scalable solution for simulating large-scale molecular networks, significantly enhancing accuracy with limited additional computational overhead.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Jansen, T.L.C. |
| Degree programme: | Physics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 06 May 2026 12:49 |
| Last Modified: | 06 May 2026 12:49 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37306 |
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