Theoretical Physics Project Prize and medal for 5 level Theoretical Physics - Dylan Houston

 Awarded for the best final year MPhys Theoretical Physics project for a project entitled: ‘Modelling Quasiparticle Interference in Twisted Bilayer Graphene’

Supervisors: Prof Peter Wahl and Dr Luke Rhodes

The 5^th level medal is awarded to the best performance in fifth level Theoretical Physics.

Twisted bilayer graphene is a fascinating material, by twisting two layers of graphene by just one degree with respect to each other it is possible to induce superconductivity in a conventionally non-superconducting material. Currently, the mechanism behind this formation of superconductivity is an important open question. 

Dylan performed a fantastic piece of work identifying how to relate the electronic properties of twisted bilayer graphene to experimental observables, namely quasiparticle interference measurements probed by scanning tunnelling microscopy (STM).  

From his work we learnt how different twist angles produce unique spectroscopic signatures within STM which are not present in regular graphene, and using this we can now explicitly look for these signatures in the ultra low vibration laboratories here in St Andrews.

We are currently in the process of writing up these findings with dylan in a formal publication. 

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Astrophysics BSc Project Prize - Peter Robertson

 Awarded for the best final year BSc Astrophysics project for a project entitled: ‘Simulations of Extreme Trans-Neptunian Objects as a test of Milgromian Gravity’

Supervisors: Dr Hongsheng Zhao and Dr Indranil Banik

Peter explored the hypothesis known as Milgromian dynamics (MOND), a modified gravity theory that can explain the unexpectedly fast and flat rotation curves of galaxies without resort to hypothetical dark matter, which has eluded decades of careful searches and is not required by particle physics. The main postulate of MOND is that gravity starts following an inverse distance law around an isolated point mass instead of the usual inverse square law once the strength of gravity drops below some threshold. This occurs several thousand light years away from a galaxy, but for a single star, the transition occurs only a few thousand times further away than the Earth-Sun distance. Consequently, MOND predicts subtle effects on the orbits of extreme trans-Neptunian objects, which are small bodies in the outer Solar System that lie beyond the orbit of the most distant planet (Neptune) even when they approach the Sun most closely.

Peter explored how the subtle MOND effects build up over millions of years using a special custom code in Fortran to integrate the orbital elements (size, shape, and orientation), instead of the usual approach of integrating the motion of each body around the Sun. This drastically reduced the computational cost and allowed the exploration of many hundreds of thousands of objects over the full 4.6 billion year history of the Solar System. The main reason for unusual effects in MOND is its non-linearity coupled with the external gravitational field due to the rest of the Galaxy, which is more or less directed towards its centre. A crucial detail is that as the Sun rotates around the Galaxy, the direction towards the Galactic centre changes, with the Sun completing about twenty Galactic revolutions thus far. Since the MOND effects are very subtle, the time needed to significantly alter an orbit is actually longer than the time needed for the Galactic external field to change direction. This violates a key assumption in the study of Brown & Mathur (2023), who used analytic arguments without any trajectory integrations to argue that certain statistical properties of extreme trans-Neptunian objects favour MOND. It is now thought that selection effects are largely responsible for the observations, especially the fact that objects are easier to discover when they are close to the Sun and located away from the direction towards the Galactic centre, which is a very crowded region of the sky.

 

Shortly after Peter completed his project, a preprint appeared in which Nesvorny et al. explored the same issues in much more detail (arxiv.org/abs/2403.09555). Their conclusions were similar, indicating that Peter's results were correct and the Brown & Mathur (2023) study was wrong. Peter's project report was shared with the Nesvorny et al. authors. They indicated that Peter obtained some deep insights into the behaviour of extreme trans-Neptunian objects in MOND, insights which they had missed. The much simpler approach used by Peter was better able to pinpoint what exactly was wrong with the Brown & Mathur study. This is very helpful when discussing with researchers who still hold on to its conclusions that MOND is favoured by the distribution of objects in the outer Solar System, observations of which actually decisively reject MOND with high confidence in multiple different ways.

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Astrophysics MPhys Project Prize – Jay Anderson

 

Awarded for the best final year MPhys Astrophysics project for a project entitled: ‘Precision vs Cadence: Simulating Observation of Weak Planetary Signals in Microlensing Events’

Supervisor: Dr Martin Dominik

Gravitational microlensing events, characterised by a transient brightening of an observed star due to the bending of its light by intervening massive bodies, harbour the potential of detecting extra-solar planets of Earth mass or below. The detectability however critically hinges on the quality of the photometric measurements that can be obtained. Given that higher photometric precision requires longer exposure times, there needs to be a trade-off against the cadence of the observations. So what is more relevant, the photometric precision or the cadence? Jay Anderson carried out a range of simulations of elaborate observing strategies for investigating this, taking into account that correlated noise in particular substantially limits the return of increased cadence at some point and drives up false positives. Strikingly, it turns out that strategies similar to current efforts with telescopes of 1m to 2m diameter aiming at photometric precisions between 0.5% and 1.5% perform rather well.

 

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Physics BSc Project Prize – Daisy Matthews

 Awarded for the best final year BSc Physics project for a project entitled: ‘Integer factorisation in a logarithmic quantum potential’

Supervisor: Dr Donatella Cassettari

This project explored a method to factorise a natural number N using a quantum particle confined within a two-dimensional potential, where the energy spectra along the two degrees of freedom are the logarithms of the primes and the logarithms of the integers. This potential is constructed using supersymmetric quantum mechanics. By applying a time-dependent perturbation, the particle is excited to a state with energy corresponding to the number N to be factorised. A measurement of energy along the degree of freedom corresponding to the logarithms of the primes yields a prime factor of N. The project focussed on the preparation of single and superposition states with suitable choices of perturbation.