Description
Quantum tunnelling underpins important phenomena ranging from scanning tunnelling microscopy to the formation of heavy elements in stars. For stellar fusion to occur, nuclei must overcome the barrier formed by the competition between the nuclear and Coulomb forces. The best models of fusion underestimate the reaction rates at energies far below the barrier, predicting that reactions like $^{12}\text{C} + ^{12}\text{C}$ should not occur at the rates observed. One suspected cause is the neglect of the many-body nature of the nucleus. Because modelling each interacting nucleon is computationally expensive, mean-field methods are used instead, approximating the interactions between particles as a single effective potential. However, mean-field dynamics fail to capture tunnelling behaviour at exactly these below barrier energies, instead predicting the particles are entirely reflected.
To restore tunnelling to mean-field models, the system can be transformed into imaginary time by Wick rotation ($t \rightarrow i\tau$). This imaginary time rotation causes the potential term of the Hamiltonian to flip, meaning potential barriers that are energetically forbidden in the mean-field become potential wells. This allows the particles to traverse across the barrier in imaginary time, and thus recovers the correct tunnelling behaviour. Whilst this technique has previously been applied to a simple two-state system, it was found to be computationally intractable for the times required for realistic systems. Novel directions are explored using Floquet theory to decompose the system into a periodic and exponentially decaying part, allowing more realistic systems to be modelled.
| I am the presenting author | Yes |
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