Control of trapped-ion quantum states with optical pulses

We present new results on the quantum control of systems with infinitely large Hilbert spaces. A control-theoretic analysis of the control of trapped ion quantum states via optical pulses is performed. We demonstrate how resonant bichromatic fields can be applied in two contrasting ways -- one that makes the system completely uncontrollable, and the other that makes the system controllable. In some interesting cases, the Hilbert space of the qubit-harmonic oscillator can be made finite, and the Schr\"{o}dinger equation controllable via bichromatic resonant pulses. Extending this analysis to the quantum states of two ions, a new scheme for producing entangled qubits is discovered.Comment: Submitted to Physical Review Letter

The influence of clearance on friction, lubrication and squeaking in large diameter metal-on-metal hip replacements

Large diameter metal-on-metal bearings (MOM) are becoming increasingly popular, addressing the needs of young and more active patients. Clinical data has shown excellent short-to-mid-term results, though incidences of transient squeaking have been noted between implantation and up to 2 years post-operative. Geometric design features, such as clearance, have been significant in influencing the performance of the bearings. Sets of MOM bearings with different clearances were investigated in this study using a hip friction simulator to examine the influence of clearance on friction, lubrication and squeaking. The friction factor was found to be highest in the largest clearance bearings under all test conditions. The incidence of squeaking was also highest in the large clearance bearings, with all bearings in this group squeaking throughout the study. A very low incidence of squeaking was observed in the other two clearance groups. The measured lubricating film was found to be lowest in the large clearance bearings. This study suggests that increasing the bearing clearance results in reduced lubricant film thickness, increased friction and an increased incidence of squeaking

PEEK and CFR-PEEK as alternative bearing materials to UHMWPE in a fixed bearing total knee replacement: An experimental wear study

New bearing materials for total joint replacement have been explored as the need to improve longevity and enhance performance is driven by the changing demands of the patient demographic. Carbon-reinforced PEEK has demonstrated good wear characteristics in experimental wear simulation in both simple geometry pin-on-plate studies and in total hip joint replacement. Carbon reinforced PEEK CFR-PEEK has the potential to reduce tibial insert thickness and preserve bone in the knee. This study investigated the wear performance of PEEK and CFR-PEEK in a low conformity total knee replacement configuration. Custom-made flat inserts were tested against cobalt-chromium femoral bearings in a knee wear simulation for a period of three million cycles. Wear was assessed gravimetrically at intervals throughout the study. The wear rates of both PEEK and CFR-PEEK were very high and almost two orders of magnitude higher than the wear rate of UHMWPE under comparable conditions. Evidence of mechanical failure of the materials, including surface cracking and delamination was observed in both materials. This study highlights that these materials may not be suitable alternatives for UHMWPE in low-conformity designs

Inverse moment problem for elementary co-adjoint orbits

We give a solution to the inverse moment problem for a certain class of Hessenberg and symmetric matrices related to integrable lattices of Toda type.Comment: 13 page

Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer

Many coherence transfer experiments in Nuclear Magnetic Resonance Spectroscopy, involving network of coupled spins, use temporary spin-decoupling to produce desired effective Hamiltonians. In this paper, we show that significant time can be saved in producing an effective Hamiltonian, if spin-decoupling is avoided. We provide time optimal pulse sequences for producing an important class of effective Hamiltonians in three spin networks. These effective Hamiltonians are useful for coherence transfer experiments and implementation of quantum logic gates in NMR quantum computing. It is demonstrated that computing these time optimal pulse sequences can be reduced to geometric problems that involve computing sub-Riemannian geodesics on Homogeneous spaces

Engagement in the digital age:Understanding “what works” for participatory technologies in environmental decision-making

Effective engagement is crucial for enhancing environmental decision-making processes, fostering more sustainable and equitable outcomes. However, the success of engagement is highly variable and context-dependent. While theoretical frameworks have been developed to explain outcome variance in engagement in environmental decision-making, they have not yet been tested in digital contexts, leaving their applicability to digital engagement processes unclear. More broadly, there are unanswered questions about the effectiveness of digital tools in achieving the goals of engagement, which have become increasingly pertinent amidst growing concerns about the potential of digital technologies for exacerbating exclusions, ethical issues, and systematically undermining democratic progress. This paper addresses this evidence gap by presenting findings from interviews with practitioners in UK public, private, and third sector organisations. Our results provide empirical insights into the technical, ethical, and inclusivity debates surrounding digital tools and their effectiveness in promoting accessible engagement, high-quality social interaction, place-based decision-making, and more trustworthy and credible outcomes. Our findings indicate that while current engagement theories are applicable to digital environments, the key explanatory factors acquire new dimensions in digital compared to in-person contexts. Drawing on the findings, this study contributes novel insights to expand current theory for explaining “what works” in engagement in environmental decisions, enhancing its relevance and applicability in the digital age. The paper concludes with evidence-led recommendations for environmental practitioners to improve engagement processes in digital and remote settings.</p

Engagement in the digital age:Understanding “what works” for participatory technologies in environmental decision-making

Effective engagement is crucial for enhancing environmental decision-making processes, fostering more sustainable and equitable outcomes. However, the success of engagement is highly variable and context-dependent. While theoretical frameworks have been developed to explain outcome variance in engagement in environmental decision-making, they have not yet been tested in digital contexts, leaving their applicability to digital engagement processes unclear. More broadly, there are unanswered questions about the effectiveness of digital tools in achieving the goals of engagement, which have become increasingly pertinent amidst growing concerns about the potential of digital technologies for exacerbating exclusions, ethical issues, and systematically undermining democratic progress. This paper addresses this evidence gap by presenting findings from interviews with practitioners in UK public, private, and third sector organisations. Our results provide empirical insights into the technical, ethical, and inclusivity debates surrounding digital tools and their effectiveness in promoting accessible engagement, high-quality social interaction, place-based decision-making, and more trustworthy and credible outcomes. Our findings indicate that while current engagement theories are applicable to digital environments, the key explanatory factors acquire new dimensions in digital compared to in-person contexts. Drawing on the findings, this study contributes novel insights to expand current theory for explaining “what works” in engagement in environmental decisions, enhancing its relevance and applicability in the digital age. The paper concludes with evidence-led recommendations for environmental practitioners to improve engagement processes in digital and remote settings.</p

Hamiltonian statistical mechanics

A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward those of the reference Hamiltonian. The nonlinear double-bracket equation governing the flow is such that the eigenvalues of the initial Hamiltonian remain unperturbed. The space of Hamiltonians is foliated by compact invariant subspaces, which permits the construction of statistical distributions over the Hamiltonians. In two dimensions, an explicit dynamical model is introduced, wherein the density function on the space of Hamiltonians approaches an equilibrium state characterised by the canonical ensemble. This is used to compute quenched and annealed averages of quantum observables.Comment: 8 pages, 2 figures, references adde