13 research outputs found
Modeling Bound States in the Continuum for Multiple Electrons in a Quantum Dot Pair
The bound eigenstates of an electron inside a pair of quantum dots embedded on an infinite quantum wire are examined using the method of particular solutions. The eigenstates of a two-electron system in the same structure are examined perturbatively using wavefunction expansions for the one-electron eigenstates. The stability of the two-electron eigenstates is evaluated and compared with other theoretical results. It is found that stable bound states in the continuum exist for two electrons confined to this geometry
Entanglement and hall viscosity
This dissertation studies quantum entanglement in relation to the geometric response known as Hall viscosity. We begin by reviewing geometric response in the quantum Hall effect in comparison to its well-known electromagnetic response, Hall conductivity. We develop an understanding of momentum transport due to Hall viscosity in analogy to charge transport under Hall conductivity. We apply our momentum transport argument to continuum and lattice models of the quantum Hall effect. We also leverage this insight to reveal a previously-unrecognized manifestation of Hall viscosity: the acoustic Faraday effect in superfluid Helium-3 B. We suggest that the acoustic Faraday effect is a new platform for the direct observation of Hall viscosity in Helium-3 B and other systems. We then turn our focus to the entanglement spectrum. We calculate the momentum polarization of lattice models of the quantum Hall effect to determine the Hall viscosity based on the entanglement spectrum, revealing the close connection between geometric response and entanglement. Finally, we turn away from the quantum Hall effect to consider other topological insulators; we use the entanglement spectrum to develop a topological classification of composite systems comprising components of topological phases in different dimensions. Our composite topological index generalizes classification of weak and antiferromagnetic topological insulators. We predict the presence of topological bound states localized to defects in systems that are trivial under all other topological classifications
Reengineering Aircraft Structural Life Prediction Using a Digital Twin
Reengineering of the aircraft structural life prediction process to fully exploit advances in very high performance digital computing is proposed. The proposed process utilizes an ultrahigh fidelity model of individual aircraft by tail number, a Digital Twin, to integrate computation of structural deflections and temperatures in response to flight conditions, with resulting local damage and material state evolution. A conceptual model of how the Digital Twin can be used for predicting the life of aircraft structure and assuring its structural integrity is presented. The technical challenges to developing and deploying a Digital Twin are discussed in detail