Single-molecule switches are a promising technology which can result in advances in nanoscale memristors and neuromorphic computing. While resistance-switching memristor-like phenomena induced by voltage bias have been documented in molecular junctions, the fundamental mechanisms governing these processes are not yet fully understood. IV-traces measured of 5 different rigid conjugated molecules (1-SAc, 2-SMe, 3-meta, 4-Hmeta, 5-Hpara) in a mechanically controlled break junction consist of complex features such as small conductance peaks which cannot be explained using the single-level model. Resistance-switching phenomena is studied to disentangle switches caused by mechanical origin related to the positioning of the molecule within the break junction, and those caused by a hypothetical proton-hopping mechanism which is expected to be a cause for switches in 4-Hmeta and 5-Hpara molecules. In this study, the molecule is modelled as a dipole consisting of 2 coupled sites with capacitive coupling, resulting in more accurate fits of the IV-traces compared to when using the single-level model. These small conductance peaks are found to be related to a very strong coupling Γ to the electrodes or a large coupling τ between the 2-sites within the dipole model. The dipole model is found to be insufficient to explain the entire shape of these IV traces and are found to be only partially able to fit the entire trace. Model inadequacies of the proposed dipole model are discussed extensively. Corrections to the dipole model are suggested such as in the form of a parallel resistance and inclusion of non-rectangular tunnelling barriers. The results of the curve fits using the dipole model point towards a step towards uncovering the origin of the memristive behaviour found in these IV-traces. ... Read more

As Wigner showed in 1939 for the Poincaré algebra, fundamental particles can be classified using symmetry algebras. In a universe including gravity, the Poincaré algebra cannot be the correct symmetry algebra, as this is the symmetry algebra for flat space. Instead, one should consider a symmetry algebra of asymptotic symmetries, which preserve only the asymptotic structure of gravity. Many of these asymptotic symmetries are not physically useful and are therefore considered 'trivial'. In this thesis we give a new, quantum, definition of trivial symmetries, namely that a symmetry is trivial if it does not change which fundamental particles are found in a classification. We then specialize to three-dimensional asymptotically Anti-de-Sitter space. To calculate which symmetries are trivial we first determine the second cohomology group of the asymptotic symmetries.
Using the second cohomology group it is then found that the useful asymptotic symmetry algebra is given by $\mathfrak w\oplus \mathfrak w\oplus \mathbb R$, where $\mathfrak w$ is the Witt (centerless Virasoro) algebra, whereas the standard definition of trivial symmetry gives $\mathfrak w\oplus \mathfrak w$ as the useful symmetry algebra. The extra factor of $\mathbb R$ is interpreted to be a kind of center-of-mass momentum. ... Read more

This bachelor thesis develops a four-stage machine-learning pipeline for pointwise conductance state classification in memristive current-voltage traces from mechanically controlled break junction experiments. The aim of this thesis is to improve data retention of hysteretic traces from the raw data set for downstream physics analysis despite an absence of ground truth pointwise state classifications and heterogeneous traces. The pipeline consists of an initial data filter, pseudo-labelling with a simple linear regression Hidden Markov Model (teacher), a Temporal Convolutional Network (student) capable of large-scale pointwise conductance classification, and a final hysteretic filter. The methodology is developed with data from three reference molecules expected to exhibit two-state behaviour, while two additional target molecules that are expected to show occasional three-conductance-state behaviour are used for comparison.

On the test set of unseen data, the Temporal Convolutional Network reproduces the teacher pseudo-labels with 98% pointwise agreement. The pipeline also identifies 8% of all traces in the available dataset as hysteretic, compared with the 5% resulting from the methodology used in previous work. Manual audit and plausibility analyses indicate that the increase in retained traces is achieved without losing physical plausibility for most molecules. Limitations include a lack of definitive ground truth and reduced robustness on complex three-conductance-state target molecules. ... Read more

In general relativity, mass cannot generally be defined as the volume integral over some density, as it is in Newtonian physics. This thesis investigates this question and how a spherically symmetric spacetime provides the tools to construct a volume integral expression for mass. However, the volume integral for this mass contains no ’curvature factor’, which would normally be expected for volume integral in a general relativistic setting. The static and dust solutions, important special cases of spherically symmetric spacetimes, are reviewed to demonstrate this peculiar property. In addition, we comment on the implications of this mass definition for the averaging procedures in cosmology. ... Read more