Kondo effect in three-dimensional Dirac and Weyl systems

Magnetic impurities in three-dimensional Dirac and Weyl systems are shown to exhibit a fascinatingly diverse range of Kondo physics, with distinctive experimental spectroscopic signatures. When the Fermi level is precisely at the Dirac point, Dirac semimetals are in fact unlikely candidates for a Kondo effect due to the pseudogapped density of states. However, the influence of a nearby quantum critical point leads to the unconventional evolution of Kondo physics for even tiny deviations in the chemical potential. Separating the degenerate Dirac nodes produces a Weyl phase: time-reversal symmetry-breaking precludes Kondo due to an effective impurity magnetic field, but different Kondo variants are accessible in time-reversal invariant Weyl systems.Comment: 4+ pages, 2 figure

Real-time Planning as Decision-making Under Uncertainty

In real-time planning, an agent must select the next action to take within a fixed time bound. Many popular real-time heuristic search methods approach this by expanding nodes using time-limited A* and selecting the action leading toward the frontier node with the lowest f value. In this thesis, we reconsider real-time planning as a problem of decision-making under uncertainty. We treat heuristic values as uncertain evidence and we explore several backup methods for aggregating this evidence. We then propose a novel lookahead strategy that expands nodes to minimize risk, the expected regret in case a non-optimal action is chosen. We evaluate these methods in a simple synthetic benchmark and the sliding tile puzzle and find that they outperform previous methods. This work illustrates how uncertainty can arise even when solving deterministic planning problems, due to the inherent ignorance of time-limited search algorithms about those portions of the state space that they have not computed, and how an agent can benefit from explicitly meta-reasoning about this uncertainty

Real-space renormalization group flow in quantum impurity systems: local moment formation and the Kondo screening cloud

The existence of a length-scale $\xi_K\sim 1/T_K$ (with $T_K$ the Kondo temperature) has long been predicted in quantum impurity systems. At low temperatures $T\ll T_K$, the standard interpretation is that a spin-$\tfrac{1}{2}$ impurity is screened by a surrounding `Kondo cloud' of spatial extent $\xi_K$. We argue that renormalization group (RG) flow between any two fixed points (FPs) results in a characteristic length-scale, observed in real-space as a crossover between physical behaviour typical of each FP. In the simplest example of the Anderson impurity model, three FPs arise; and we show that `free orbital', `local moment' and `strong coupling' regions of space can be identified at zero temperature. These regions are separated by two crossover length-scales $\xi_{\text{LM}}$ and $\xi_K$, with the latter diverging as the Kondo effect is destroyed on increasing temperature through $T_K$. One implication is that moment formation occurs inside the `Kondo cloud', while the screening process itself occurs on flowing to the strong coupling FP at distances $\sim \xi_K$. Generic aspects of the real-space physics are exemplified by the two-channel Kondo model, where $\xi_K$ now separates `local moment' and `overscreening' clouds.Comment: 6 pages; 5 figure

Quantum phase transitions and thermodynamics of the power-law Kondo model

We revisit the physics of a Kondo impurity coupled to a fermionic host with a diverging power-law density of states near the Fermi level, $\rho(\omega) \sim |\omega|^r$, with exponent $-1<r<0$. Using the analytical understanding of several fixed points, based partially on powerful mappings between models with bath exponents $r$ and $(-r)$, combined with accurate numerical renormalization group calculations, we determine thermodynamic quantities within the stable phases, and also near the various quantum phase transitions. Antiferromagnetic Kondo coupling leads to strong screening with a negative zero-temperature impurity entropy, while ferromagnetic Kondo coupling can induce a stable fractional spin moment. We formulate the quantum field theories for all critical fixed points of the problem, which are fermionic in nature and allow for a perturbative renormalization-group treatment.Comment: 13 pages, 11 figure

Reliability of an experimental method to analyse the impact point on a golf ball during putting

This study aimed to examine the reliability of an experimental method identifying the location of the impact point on a golf ball during putting. Forty trials were completed using a mechanical putting robot set to reproduce a putt of 3.2 m, with four different putter-ball combinations. After locating the centre of the dimple pattern (centroid) the following variables were tested; distance of the impact point from the centroid, angle of the impact point from the centroid and distance of the impact point from the centroid derived from the X, Y coordinates. Good to excellent reliability was demonstrated in all impact variables reflected in very strong relative (ICC = 0.98–1.00) and absolute reliability (SEM% = 0.9–4.3%). The highest SEM% observed was 7% for the angle of the impact point from the centroid. In conclusion, the experimental method was shown to be reliable at locating the centroid location of a golf ball, therefore allowing for the identification of the point of impact with the putter head and is suitable for use in subsequent studies