Topological Blocking in Quantum Quench Dynamics

We study the non-equilibrium dynamics of quenching through a quantum critical point in topological systems, focusing on one of their defining features: ground state degeneracies and associated topological sectors. We present the notion of 'topological blocking', experienced by the dynamics due to a mismatch in degeneracies between two phases and we argue that the dynamic evolution of the quench depends strongly on the topological sector being probed. We demonstrate this interplay between quench and topology in models stemming from two extensively studied systems, the transverse Ising chain and the Kitaev honeycomb model. Through non-local maps of each of these systems, we effectively study spinless fermionic $p$-wave paired superconductors. Confining the systems to ring and toroidal geometries, respectively, enables us to cleanly address degeneracies, subtle issues of fermion occupation and parity, and mismatches between topological sectors. We show that various features of the quench, which are related to Kibble-Zurek physics, are sensitive to the topological sector being probed, in particular, the overlap between the time-evolved initial ground state and an appropriate low-energy state of the final Hamiltonian. While most of our study is confined to translationally invariant systems, where momentum is a convenient quantum number, we briefly consider the effect of disorder and illustrate how this can influence the quench in a qualitatively different way depending on the topological sector considered.Comment: 18 pages, 11 figure

Optimised control of an advanced hybrid powertrain using combined criteria for energy efficiency and driveline vibrations

This thesis discusses a general approach to hybrid powertrain control based on optimisation and optimal control techniques. A typical strategy comprises a high level non-linear control for optimised energy efficiency, and a lower level Linear Quadratic Regulator (LQR) to track the high-level demand signals and minimise the first torsional vibration mode. The approach is demonstrated in simulation using a model of the Toyota Prius hybrid vehicle, and comparisons are made with a simpler control system which uses proportional integral (PI) control at the lower level. The powertrain of the Toyota Prius has a parallel configuration, comprising a motor, engine and generator connected via an epicyclic gear train. High level control is determined by a Power Efficient Controller (PE C) which dynamically varies the operating demands for the motor, engine and generator. The PEC is an integrated nonlinear controller based on an iterative downhill search strategy for optimising energy efficiency and battery state of charge criteria, and fully accounts for the non-linear nature of the various efficiency maps. The PEC demand signals are passed onto the LQR controller where a cost function balances the importance of deviations from these demands against an additional criterion relating to the amplitude of driveline vibrations. System non-linearity is again accounted for at the lower level through gain scheduling of the LQR controller. Controller performance is assessed. in simulation, the results being compared with a reference system that uses simple PI action to deliver low-level control. Consideration is also given to assessing performance against that of a more general, fully non-linear dynamic optimal controller

Arm cavity resonant sideband control for laser interferometric gravitational wave detectors

We present a new optical control scheme for a laser interferometric gravitational wave detector that has a high degree of tolerance to interferometer spatial distortions and noise on the input light. The scheme involves resonating the rf sidebands in an interferometer arm cavity

Topological Degeneracy and Vortex Manipulation in Kitaev's Honeycomb Model

The classification of loop symmetries in Kitaev's honeycomb lattice model provides a natural framework to study the Abelian topological degeneracy. We derive a perturbative low-energy effective Hamiltonian that is valid to all orders of the expansion and for all possible toroidal configurations. Using this form we demonstrate at what order the system's topological degeneracy is lifted by finite size effects and note that in the thermodynamic limit it is robust to all orders. Further, we demonstrate that the loop symmetries themselves correspond to the creation, propagation, and annihilation of fermions. We note that these fermions, made from pairs of vortices, can be moved with no additional energy cost

Exact results for the star lattice chiral spin liquid

We examine the star lattice Kitaev model whose ground state is a a chiral spin liquid. We fermionize the model such that the fermionic vacua are toric code states on an effective Kagome lattice. This implies that the Abelian phase of the system is inherited from the fermionic vacua and that time reversal symmetry is spontaneously broken at the level of the vacuum. In terms of these fermions we derive the Bloch-matrix Hamiltonians for the vortex free sector and its time reversed counterpart and illuminate the relationships between the sectors. The phase diagram for the model is shown to be a sphere in the space of coupling parameters around the triangles of the lattices. The abelian phase lies inside the sphere and the critical boundary between topologically distinct Abelian and non-Abelian phases lies on the surface. Outside the sphere the system is generically gapped except in the planes where the coupling parameters are zero. These cases correspond to bipartite lattice structures and the dispersion relations are similar to that of the original Kitaev honeycomb model. In a further analysis we demonstrate the three-fold non-Abelian groundstate degeneracy on a torus by explicit calculation.Comment: 7 pages, 8 figure

Dynamical properties of the delta-kicked harmonic oscillator

We propose an efficient procedure for numerically evolving the quantum dynamics of delta-kicked harmonic oscillator. The method allows for longer and more accurate simulations of the system as well as a simple procedure for calculating the system’s Floquet eigenstates and quasienergies. The method is used to examine the dynamical behavior of the system in cases where the ratio of the kicking frequency to the system’s natural frequency is both rational and irrational

Rigorous Calculations of Non-Abelian Statistics in the Kitaev Honeycomb Model

We develop a rigorous and highly accurate technique for calculation of the Berry phase in systems with a quadratic Hamiltonian within the context of the Kitaev honeycomb lattice model. The method is based on the recently found solution of the model which uses the Jordan-Wigner-type fermionization in an exact effective spin-hardcore boson representation. We specifically simulate the braiding of two non-Abelian vortices (anyons) in a four vortex system characterized by a two-fold degenerate ground state. The result of the braiding is the non-Abelian Berry matrix which is in excellent agreement with the predictions of the effective field theory. The most precise results of our simulation are characterized by an error on the order of $10^{-5}$ or lower. We observe exponential decay of the error with the distance between vortices, studied in the range from one to nine plaquettes. We also study its correlation with the involved energy gaps and provide preliminary analysis of the relevant adiabaticity conditions. The work allows to investigate the Berry phase in other lattice models including the Yao-Kivelson model and particularly the square-octagon model. It also opens the possibility of studying the Berry phase under non-adiabatic and other effects which may constitute important sources of errors in topological quantum computation.Comment: 27 pages, 9 figures, 3 appendice

Model of Thermal Wavefront Distortion in Interferometric Gravitational-Wave Detectors I: Thermal Focusing

We develop a steady-state analytical and numerical model of the optical response of power-recycled Fabry-Perot Michelson laser gravitational-wave detectors to thermal focusing in optical substrates. We assume that the thermal distortions are small enough that we can represent the unperturbed intracavity field anywhere in the detector as a linear combination of basis functions related to the eigenmodes of one of the Fabry-Perot arm cavities, and we take great care to preserve numerically the nearly ideal longitudinal phase resonance conditions that would otherwise be provided by an external servo-locking control system. We have included the effects of nonlinear thermal focusing due to power absorption in both the substrates and coatings of the mirrors and beamsplitter, the effects of a finite mismatch between the curvatures of the laser wavefront and the mirror surface, and the diffraction by the mirror aperture at each instance of reflection and transmission. We demonstrate a detailed numerical example of this model using the MATLAB program Melody for the initial LIGO detector in the Hermite-Gauss basis, and compare the resulting computations of intracavity fields in two special cases with those of a fast Fourier transform field propagation model. Additional systematic perturbations (e.g., mirror tilt, thermoelastic surface deformations, and other optical imperfections) can be included easily by incorporating the appropriate operators into the transfer matrices describing reflection and transmission for the mirrors and beamsplitter.Comment: 24 pages, 22 figures. Submitted to JOSA

A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers

We present a solution of Kitaev's spin model on the honeycomb lattice and of related topologically ordered spin models. We employ a Jordan-Wigner type fermionization and find that the Hamiltonian takes a BCS type form, allowing the system to be solved by Bogoliubov transformation. Our fermionization does not employ non-physical auxiliary degrees of freedom and the eigenstates we obtain are completely explicit in terms of the spin variables. The ground-state is obtained as a BCS condensate of fermion pairs over a vacuum state which corresponds to the toric code state with the same vorticity. We show in detail how to calculate all eigenstates and eigenvalues of the model on the torus. In particular, we find that the topological degeneracy on the torus descends directly from that of the toric code, which now supplies four vacua for the fermions, one for each choice of periodic vs. anti-periodic boundary conditions. The reduction of the degeneracy in the non-Abelian phase of the model is seen to be due to the vanishing of one of the corresponding candidate BCS ground-states in that phase. This occurs in particular in the fully periodic vortex-free sector. The true ground-state in this sector is exhibited and shown to be gapped away from the three partially anti-periodic ground-states whenever the non-Abelian phase is gapped.Comment: 10 pages, 4 figure

Federal agency perspectives and funding opportunities for weed and invasive plant research

Weeds and invasive plants know no borders and have collectively impacted many ecosystems worldwide, including croplands, forests, grasslands, rangelands, wetlands, and riparian areas. Losses continue to mount, affecting yield and productivity, species diversity, and ecosystem services, with both short- and long-term repercussions on the sustainability of plant and animal communities and the livelihoods of many. New and emerging invasive plants, along with many of the most intractable weeds, have undermined even the best control efforts, serving as a reminder of the constant need for improvements in science, application, and technology. One of the main reasons for the success of weeds and invasive plants is their ability to adapt to abiotic and biotic conditions, and research suggests that this will continue with minimal change. Despite the challenges posed by weeds and invasive plants, integrated management techniques, several effective chemistries, and the development of new technology are a signal that ongoing and renewed efforts are worthwhile. National coordination is needed across the sectors of weed and invasive plant sciences to achieve common goals. Federal agencies have the largest land holdings—which are infested with weeds and invasive plants—and work with a diverse group of stakeholders comprising managers, researchers, and regulators. Thus, there is an urgent and pressing need to facilitate dialogue between federal agencies specific to weed and invasive plant science to (1) serve as a starting point for summarizing current knowledge and identifying information gaps and (2) re-engage national program leaders and representatives to better coordinate programs in addressing common challenges. Federal departments and agencies with expertise in weed and invasive plant science were brought together at a symposium held during the Weed Science Society of America’s 63rd Annual Meeting in Washington, DC. Individuals from the Animal and Plant Health Inspection Service (APHIS), Agricultural Research Service (ARS), National Institute of Food and Agriculture (NIFA), Office of Pest Management Policy (OPMP), Natural Resources Conservation Service (NRCS), U.S. Forest Service (USFS), Bureau of Land Management (BLM), U.S. Geological Survey (USGS), National Park Service (NPS), Department of Defense (DOD), Army Corps of Engineers (ACOE), National Aeronautics and Space Administration (NASA), and National Science Foundation (NSF) shared current research and management efforts and participated in a discussion focused on the identification of funding opportunities and other issues pertaining to research gaps and management needs among this society’s membership