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Let $L$ be a monotone Lagrangian torus inside a compact symplectic manifold $X$, with superpotential $W_L$. We show that a geometrically-defined closed-open map induces a decomposition of the quantum cohomology $\operatorname{QH}^*(X)$ into a product, where one factor is the localisation of the Jacobian ring $\operatorname{Jac} W_L$ at the set of isolated critical points of $W_L$. The proof involves describing the summands of the Fukaya category corresponding to this factor -- verifying the expectations of mirror symmetry -- and establishing an automatic generation criterion in the style of Ganatra and Sanda, which may be of independent interest. We apply our results to understanding the structure of quantum cohomology and to constraining the possible superpotentials of monotone tori, Comment: 22 pages, comments welcome!

Photonic crystal cavities (PhCCs) can confine optical fields in ultra-small volumes, enabling efficient light-matter interactions for quantum and non-linear optics, sensing and all-optical signal processing. The inherent nanometric tolerances of micro-fabrication platforms can induce cavity resonant wavelength shifts two-orders of magnitude larger than cavity linewidths, prohibiting fabrication of arrays of nominally identical devices. We address this device variability by fabricating PhCCs as releasable pixels that can be transferred from their native substrate to a receiver where ordered micro-assembly can overcome the inherent fabrication variance. We demonstrate the measurement, binning and transfer of 119 PhCCs in a single session, producing spatially ordered arrays of PhCCs, sorted by resonant wavelength. Furthermore, the rapid in-situ measurement of the devices enables measurements of the PhCCs dynamic response to the print process for the first time, showing plastic and elastic effects in the seconds to hours range.

Let $A \subset \mathbb{Z}^d$ be a finite set. It is known that the sumset $NA$ has predictable size ($\vert NA\vert = P_A(N)$ for some $P_A(X) \in \mathbb{Q}[X]$) and structure (all of the lattice points in some finite cone other than all of the lattice points in a finite collection of exceptional subcones), once $N$ is larger than some threshold. In previous work, joint with Shakan, the first and third named authors established the first effective bounds for both of these thresholds for an arbitrary set $A$. In this article we substantially improve each of these bounds, coming much closer to the corresponding lower bounds known., Comment: 15 pages

In order to assess observational evidence for potential atmospheric biosignatures on exoplanets, it will be essential to test whether spectral fingerprints from multiple gases can be explained by abiotic or biotic-only processes. Here, we develop and apply a coupled 1D atmosphere-ocean-ecosystem model to understand how primitive biospheres, which exploit abiotic sources of H2, CO and O2, could influence the atmospheric composition of rocky terrestrial exoplanets. We apply this to the Earth at 3.8 Ga and to TRAPPIST-1e. We focus on metabolisms that evolved before the evolution of oxygenic photosynthesis, which consume H2 and CO and produce potentially detectable levels of CH4. O2-consuming metabolisms are also considered for TRAPPIST-1e, as abiotic O2 production is predicted on M-dwarf orbiting planets. We show that these biospheres can lead to high levels of surface O2 (approximately 1-5 %) as a result of \ch{CO} consumption, which could allow high O2 scenarios, by removing the main loss mechanisms of atomic oxygen. Increasing stratospheric temperatures, which increases atmospheric OH can reduce the likelihood of such a state forming. O2-consuming metabolisms could also lower O2 levels to around 10 ppm and support a productive biosphere at low reductant inputs. Using predicted transmission spectral features from CH4, CO, O2/O3 and CO2 across the hypothesis space for tectonic reductant input, we show that biotically-produced CH4 may only be detectable at high reductant inputs. CO is also likely to be a dominant feature in transmission spectra for planets orbiting M-dwarfs, which could reduce the confidence in any potential biosignature observations linked to these biospheres., Comment: 29 pages, 19 figures

Optical fields can exert forces of chiral nature on molecules and nanoparticles, which would prove extremely valuable in the separation of enantiomers with pharmaceutical applications, yet it is inherently complex, and the varied frameworks used in the literature further complicate the theoretical understanding. This paper unifies existing approaches used to describe dipolar optical forces and introduces a new symmetry-based `force basis' consisting of twelve vector fields, each weighted by particle-specific coefficients, for a streamlined description of force patterns. The approach is rigorously applied to evanescent waves and dielectric nanofibres, yielding concise analytical expressions for optical forces. Through this, we identify optimal strategies for enantiomer separation, offering invaluable guidance for future experiments., Comment: 18 pages, 5 figures

Given a closed, orientable Lagrangian submanifold $L$ in a symplectic manifold $(X, \omega)$, we show that if $L$ is relatively exact then any Hamiltonian diffeomorphism preserving $L$ setwise must preserve its orientation. In contrast to previous results in this direction, there are no spin hypotheses on $L$. Curiously, the proof uses only mod-2 coefficients in its singular and Floer cohomology rings., Comment: v2 improved exposition, 2 pages, comments welcome; to appear in Advances in Geometry

Given a monotone Lagrangian $L$ in a compact symplectic manifold $X$, we construct a commutative diagram relating the closed-open string map $CO_\lambda : QH^*(X) \to HH^*(\mathcal{F}(X)_\lambda)$ to a variant of the length-zero closed-open map on $L$ incorporating $\mathbf{k}[H_1(L; \mathbb{Z})]$ coefficients, denoted $CO^0_\mathbf{L}$. The former is categorically important but very difficult to compute, whilst the latter is geometrically natural and amenable to calculation. We further show that, after a suitable completion, injectivity of $CO^0_\mathbf{L}$ implies injectivity of $CO_\lambda$. Via Sheridan's version of Abouzaid's generation criterion, this gives a powerful tool for proving split-generation of the Fukaya category. We illustrate this by showing that the real part of a monotone toric manifold (of minimal Chern number at least 2) split-generates the Fukaya category in characteristic 2. We also give a short new proof (modulo foundational assumptions in the non-monotone case) that the Fukaya category of an arbitrary compact toric manifold is split-generated by toric fibres., Comment: 55 pages, 9 figures, comments welcome, v2 typos corrected

The study of an optical beam interacting with material structures is a fundamental of nanophotonics. Computational electromagnetic solvers facilitate the rapid calculation of the scattering from material structures with arbitrary geometry and complexity, but have limited efficiency when employing structured excitation fields. We have developed a post-processing method and package that can efficiently calculate the full three-dimensional electric and magnetic fields for any optical beam incident on a particle or structure with at least one axis of continuous rotational symmetry, called an axisymmetric body (such as a sphere, cylinder, cone, torus or surface). Provided an initial batch of plane wave simulations is computed, this open-source package combines data from computational electromagnetic solvers in a post-processing fashion using the angular spectrum representation to create arbitrarily structured beams, including vector vortex beams. Any and all possible incident beams can be generated from the initial batch of plane wave simulations, without the need for further simulations. This allows for efficiently performing parameter sweeps such as changing the angle of illumination or translating the particle position relative to the beam, all in post-processing, with no need for additional time-consuming simulations. We demonstrate some applications by numerically calculating optical force and torque maps for a spherical plasmonic nanoparticle in a tightly focused Gaussian beam, a plasmonic nanocone in an azimuthally polarised beam and compute the fields of a non-paraxial Laguerre-Gaussian vortex beam reflecting on a multilayered surface. We believe this package, called BEAMS, is a valuable tool for rapidly quantifying electromagnetic systems that are beyond traditional analytical methods., Comment: 25 pages, 4 figures, for associated software package see https://doi.org/10.18742/21975998.v1

The momentum carried by structured light fields exhibits a rich array of surprising features. In this work, we generate transverse orbital angular momentum (TOAM) in the interference field of two parallel and counterpropagating linearly-polarised focused beams, synthesising an array of identical handedness vortices carrying intrinsic TOAM. We explore this structured light field using an optomechanical sensor, consisting of an optically levitated silicon nanorod, whose rotation is a probe of the optical angular momentum, which generates an exceptionally large torque. This simple creation and direct observation of TOAM will have applications in studies of fundamental physics, the optical manipulation of matter and quantum optomechanics.

The heterogeneous integration of lithium niobate photonic waveguide devices onto a silicon nitride waveguide platform via a transfer-printing approach has been demonstrated for the first time. A fabrication process was developed to make free-standing lithium niobate membrane devices compatible with back-end integration onto photonic integrated circuits. Micro-ring resonators in membrane format were lithographically defined by using laser direct writing and plasma dry etching. The lithium niobate micro-ring resonators were then transferred from their host substrate and released onto a silicon nitride waveguide chip. An all-pass ring resonator transmission spectrum was obtained in the 1.5 {\mu}m to 1.6 {\mu}m wavelength range, with a measured loaded Q-factor larger than 32000., Comment: 8 pages, 6 figures

Vector optical vortices exhibit complex polarisation patterns due to the interplay between spin and orbital angular momenta. Here we demonstrate, both analytically and with simulations, that certain polarisation features of optical vortex beams maintain constant transverse spatial dimensions independently of beam divergence due to diffraction. These polarisation features appear in the vicinity of the phase singularity and are associated with the presence of longitudinal electric fields. The predicted effect may prove important in metrology and high resolution imaging applications., Comment: 18 pages, 4 figures; revised text and figures

Given a Lagrangian submanifold $L$ in a symplectic manifold $X$, the homological Lagrangian monodromy group $\mathcal{H}_L$ describes how Hamiltonian diffeomorphisms of $X$ preserving $L$ setwise act on $H_*(L)$. We begin a systematic study of this group when $L$ is a monotone Lagrangian $n$-torus. Among other things, we describe $\mathcal{H}_L$ completely when $L$ is a monotone toric fibre, make significant progress towards classifying the groups than can occur for $n=2$, and make a conjecture for general $n$. Our classification results rely crucially on arithmetic properties of Floer cohomology rings., Comment: v4 Incorporating referee comments. To appear in Quantum Topology. 23 pages, comments welcome

First conceptualised in Olaf Stapledon's 1937 novel 'Star Maker', before being popularised by Freeman Dyson in the 1960s, Dyson Spheres are structures which surround a civilisation's sun to collect all the energy it radiates. Through discussion of the features of such a feat of engineering, the viability, scale and likely design of a Dyson structure is evaluated, before details about each stage of its construction and operation are investigated. It is found that a Dyson Swarm, a large array of individual satellites orbiting another planetary body, is the ideal design for such a structure over the solid sun-surrounding structure which is typically associated with the Dyson Sphere. In our solar system, such a structure based around Mars would be able to account for the Earth's 2019 global power consumption of 18.35 TW within fifty years once its construction has begun, which itself could start by 2040. The swarm of over 5.5 billion satellites would be constructed on the surface of Mars before being launched by electromagnetic accelerators into a Martian orbit. Efficiency of the Dyson Swarm ranges from around 0.74 - 2.77% of the Sun's $3.85\times10^{26}$ W output, with large potential for growth as both current technologies improve and future concepts are brought to reality in the time before and during the swarm's construction. Not only would a Dyson Swarm provide a near infinite, renewable power source for Earth, it would allow for significant expansions in human space exploration and for our civilisation as a whole., Comment: 30 pages, 16 figures

There has been an increasing interest in and growing need for high performance computing (HPC), popularly known as supercomputing, in domains such as textual analytics, business domains analytics, forecasting and natural language processing (NLP), in addition to the relatively mature supercomputing domains of quantum physics and biology. HPC has been widely used in computer science (CS) and other traditionally computation intensive disciplines, but has remained largely siloed away from the vast array of social, behavioral, business and economics disciplines. However, with ubiquitous big data, there is a compelling need to make HPC technologically and economically accessible, easy to use, and operationally democratized. Therefore, this research focuses on making two key contributions, the first is the articulation of strategies based on availability, accessibility and usability for the demystification and democratization of HPC, based on an analytical review of Caliburn, a notable supercomputer at its inception. The second contribution is a set of principles for HPC adoption based on an experiential narrative of HPC usage for textual analytics and NLP of social media data from a first time user perspective. Both, the HPC usage process and the output of the early stage analytics are summarized. This research study synthesizes expert input on HPC democratization strategies, and chronicles the challenges and opportunities from a multidisciplinary perspective, of a case of rapid adoption of supercomputing for textual analytics and NLP. Deductive logic is used to identify strategies which can lead to efficacious engagement, adoption, production and sustained usage for research, teaching, application and innovation by researchers, faculty, professionals and students across a broad range of disciplines.

Optically-induced magnetic resonances in non-magnetic media have unlocked magnetic light-matter interactions and led to new technologies in many research fields. Previous proposals for the levitation of nanoscale particles without structured illumination have worked on the basis of epsilon-near-zero surfaces or anisotropic materials but these carry with them significant fabrication difficulties. We report the optical levitation of a magnetic dipole over a wide range of realistic materials, including bulk metals, thereby relieving these difficulties. The repulsion is independent of surface losses and we propose an experiment to detect this force which consists of a core-shell nanoparticle, exhibiting a magnetic resonance, in close proximity to a gold substrate under plane wave illumination. We anticipate the use of this phenomenon in new nanomechanical devices., Comment: 5 pages, 2 figures