We present the ghost-free infinite-derivative extensions of Spherically-Reduced Gravity (SRG) and Callan-Giddings-Harvey-Strominger (CGHS) theories in two space-time dimensions. For case SRG, we specify Schwarzschild-type gauge diagonalise quadratic action for field perturbations after taking background fields to be those flat-space solution with a linear dilaton. Using obtained diagonalisation...

A canonical particle definition via the diagonalisation of the Hamiltonian for a quantum field theory in specific curved space-times is presented. Within the provided approach radial ingoing or outgoing Minkowski particles do not exist. An application of this formalism to the Rindler metric recovers the well-known Unruh effect. For the situation of a black hole the Hawking temperature exhibits ...

Due to its fourfold spin-valley degeneracy, graphene in a strong magnetic field may be viewed as a four-component quantum Hall system. We investigate the consequences of this particular structure on a possible, yet unobserved, fractional quantum Hall effect in graphene within a trial-wavefunction approach and exact-diagonalisation calculations. This trial-wavefunction approach generalises an or...

We introduce a self-consistent theory of mobility edges in nearest-neighbour tight-binding chains with quasiperiodic potentials. Demarcating boundaries between localised and extended states the space system parameters energy, are generic systems which lack energy-independent self-duality commonly studied Aubry-Andr\'e-Harper model. The potentials such strongly infinite-range correlated, reflect...

We obtain constraints on the topology of families smooth $4$-manifolds arising from a finite dimensional approximation Seiberg-Witten monopole map. Amongst other results these include generalisation Donaldson's diagonalisation theorem and Furuta's $10/8$ theorem. As an application we construct examples continuous $\mathbb{Z}_p$-actions for any odd prime $p$, which can not be realised smoothly. ...

Many areas of scientific research are underpinned by computational methods that require ever increasing levels of computer performance. In order to meet this demand high-performance systems are rapidly heading towards Petascale performance levels with planned systems typically consisting of O(100,000) processors. We are investigating whether current applications used in the UK are capable of sc...