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We determine the energy splitting of the conduction-band valleys in two-dimensional electrons confined in silicon metal oxide semiconductor Hall-bar transistors. These silicon metal oxide semiconductor Hall bars are made by advanced semiconductor manufacturing on 300 mm silicon wafers and support a two-dimensional electron gas of high quality with a maximum mobility of 17.6×10^{3} cm^{2}/Vs and minimum percolation density of 3.45×10^{10} cm^{-2}. Because of the low disorder, we observe beatings in the Shubnikov-de Haas oscillations that arise from the energy splitting of the two low-lying conduction band valleys. From the analysis of the oscillations beating patterns up to T=1.7 K, we estimate a maximum valley splitting of ΔE_{VS}=8.2 meV at a density of 6.8×10^{12} cm^{-2}. Furthermore, the valley splitting increases with density at a rate consistent with theoretical predictions for a near-ideal semiconductor-oxide interface.

Full-scale quantum computers require the integration of millions of quantum bits. The promise of leveraging industrial semiconductor manufacturing to meet this requirement has fueled the pursuit of quantum computing in silicon quantum dots. However, to date, their fabrication has relied on electron-beam lithography and, with few exceptions, on academic style lift-off processes. Although these fabrication techniques offer process flexibility, they suffer from low yield and poor uniformity. An important question is whether the processing conditions developed in the manufacturing fab environment to enable high yield, throughput, and uniformity of transistors are suitable for quantum dot arrays and do not compromise the delicate qubit properties. Here, we demonstrate quantum dots hosted at a 28Si/28SiO2 interface, fabricated in a 300 mm semiconductor manufacturing facility using all-optical lithography and fully industrial processing. As a result, we achieve nanoscale gate patterns with remarkable homogeneity. The quantum dots are well-behaved in the multi-electron regime, with excellent tunnel barrier control, a crucial feature for fault-tolerant two-qubit gates. Single-spin qubit operation using magnetic resonance reveals relaxation times of over 1 s at 1 Tesla and coherence times of over 3 ms, matching the quality of silicon spin qubits reported to date. The feasibility of high-quality qubits made with fully-industrial techniques strongly enhances the prospects of a large-scale quantum computer, Comment: 23 pages, 4 figures, 12 supplementary figures

Quantum computation requires many qubits that can be coherently controlled and coupled to each other

The UK produces an estimated 2 Mt of waste electrical and electronic equipment (WEEE) annually and the management of this waste has become a foremost environmental issue in the UK. Whilst the collection, transportation and treatment of WEEE contributes to climate change due to its considerable energy and material requirements, the effective recovery and reuse or recycling of WEEE can contribute towards a net climate benefit. Here, we present a combined material flow analysis and carbon footprint approach (based on a bespoke calculator tool) for quantifying the flows of WEEE through a national waste management system and evaluating their potential climate impacts. We apply this approach to analyse the WEEE management system for the UK from 2010 to 2030 using prospective scenario analysis and assess the carbon footprint of their management pathways. Reuse was identified as the most favourable end-of-life management option in terms of potential climate impact, followed by recycling, with landfill identified as being the least favourable option. Overall, current end-of-life management practices for WEEE in the UK were found to result in a net positive (i.e. beneficial) climatic effect, although this saving was found to reduce when WEEE recycled as non-obligated WEEE was not included. Overall, we recommend that future national policies should focus on formalising indirect WEEE collection pathways to help increase overall collection rates and, thus, reuse and recycling activities.

Quantum computation requires many qubits that can be coherently controlled and coupled to each other. Qubits that are defined using lithographic techniques are often argued to be promising platforms for scalability, since they can be implemented using semiconductor fabrication technology. However, leading solid-state approaches function only at temperatures below 100 mK, where cooling power is extremely limited, and this severely impacts the perspective for practical quantum computation. Recent works on spins in silicon have shown steps towards a platform that can be operated at higher temperatures by demonstrating long spin lifetimes, gate-based spin readout, and coherent single-spin control, but the crucial two-qubit logic gate has been missing. Here we demonstrate that silicon quantum dots can have sufficient thermal robustness to enable the execution of a universal gate set above one Kelvin. We obtain single-qubit control via electron-spin-resonance (ESR) and readout using Pauli spin blockade. We show individual coherent control of two qubits and measure single-qubit fidelities up to 99.3 %. We demonstrate tunability of the exchange interaction between the two spins from 0.5 up to 18 MHz and use this to execute coherent two-qubit controlled rotations (CROT). The demonstration of `hot' and universal quantum logic in a semiconductor platform paves the way for quantum integrated circuits hosting the quantum hardware and their control circuitry all on the same chip, providing a scalable approach towards practical quantum information.

We show that three conditions associated with “entanglement,”viz., non-locality, non-factorisability and statistical dependence, are equivalent for pure states, and that non-factorisability and statistical dependence are equivalent for mixed states. Discussion then reinforces the generally held view that the key condition for mixed states is nonseparability.

Using a reformulation of conventional results in decoherence theory, a condition is proposed for singling out a distinguished class of histories which includes those which use the “pointer basis” of Zurek.

An account is given of recent advances in mathematical techniques for extending space-times through weak singularities. This gives one more hope of proving a cosmic censorship theorem, and hence of understanding whether the final state of gravitational collapse will indeed be a black hole.

We prove a rigorous existence theorem in the case of one-dimensional Newtonian gravity for a pressureless fluid, in which a caustic separates a single-fluid region from a region with three superimposed fluid flows. This is of interest both for the shell crossing singularities of general relativity and for models of galaxy formation.

Following a survey of the abstract boundary definition of Scott and Szekeres, a rigidity result is proved for the smooth case, showing that the topological structure of the regular part of this boundary in invariantly defined., Comment: 14 pages, 2 figures; to appear in Clas. Quant. Grav

The conditions of elementary flatness, trivial behaviour under parallel propagation of frames, and regularity to various degrees of differentiability, are given precise definitions and related to practical criteria. As an example, their relations are explored in the case of cylindrically symmetrical stationary dust.

Biological interest attaches to systems of coupled electric dipoles with pumping applied to the phonon modes. In certain cases known as Frohlich systems the master equation for pumped phonon models in general is known to admit Bose condensations. It is shown, in contrast, that for the biological systems of interest a Bose condensation does not occur (though this does not rule out a generalized condensation).

Starting from the original formulation of weak cosmic censorship, an account is given of progress so far in resolving the cosmic censorship conjectures, and of hope for the future.

In numerical relativity there would seem to be considerable advantages in combining Cauchy and characteristic methods in different regions of spacetime. Numerical experiments demonstrate, for the model problem of the scalar wave equation in flat space using general null coordinates, that there are no unforseen problems with the interface between the two regions.

A formalism is presented for evaluating error estimates for continuous source reconstruction in the biomagnetic inverse problem (MEG). This is applied to simulated data, demonstrating the application of the method to detecting when the source is localized.

This chapter first reviews strands of work in philosophy, psychology and physics which, taken together, undermine the world-views of both the Cartesian duality of body and soul, and the mechanistic picture of a system governed only by universal deterministic law. Starting from an alternative polarity suggested by recent work in psychology and using established ideas from modern quantum physics, a provisional structure is presented for an alternative world view. The consequences of this for future research are indicated.

A new method is proposed for the non-perturbative quantization of certain nonlinear field theories (group-bundle theories), based on a generalization of the idea of a promeasure from vector spaces to infinite-dimensional Lie groups. The quantum theory is not automatically finite, but there is a natural way of imposing a momentum cut-off, leading to the possibility of renormalization. The method relies on the geometrical structure of the classical theory and so may provide clues for the quantization of gravity.

A general method for obtaining continuous solutions to the biomagnetic inverse problem is outlined and illustrated with a wide range of test cases, in a variety of experimental geometries. Magnetic sources are discussed briefly, but the main emphasis is on ionic flows, both in free space and in a homogeneous conducting sphere. The authors describe a way of obtaining depth information from measurements taken in a single plane and show how instrumental noise affects the quality of the reconstructions. An iterative scheme is introduced, capable of pinpointing a number of localised sources with a minimum of prior assumptions. However, the method is most naturally adapted to distributed sources. A number of inversions of distributed sources demonstrate that the method is powerful, accurate and convenient.

The authors propose a solution to the topological problems inherent in the evolution of a collapsing star from an initially regular state to a final state resembling the Kerr solution with a>m. The simplest scenario involves two fragments receding from each other with high relative velocity. In order to describe the situation, a precise definition is given of the concept of a time machine.

The results of a feasibility study on using a transputer array to obtain a numerical solution of the characteristic initial value problem of general relativity are presented. Codes have been developed for two cases: gravity only, and gravity and matter. The testing of the codes is, so far, very limited, but timing results etc. are presented thus giving an indication of the expected performance.

A new concept analogous to global hyperbolicity is introduced, based on test fields. It is shown that the space-times termed here ``curve integrable'' are globally hyperbolic in this new sense, and a plausibility argument is given suggesting that the result applies to shell crossing singularities. If the assumptions behind this last argument are valid, this provides an alternative route to the assertion that such singularities do not violate cosmic censorship., Comment: This replacement alters the type of solution considered from "weak" to a solution lying in a specified function space. 9 pages, TeX, eps figure included with psfig

You might think of ice cream as a delicious treat to be enjoyed on a sunny summer's day. However, to the ice-cream scientists who recently gathered in Thessaloniki in Greece for the 2nd International Ice Cream Symposium, it is a complex composite material. Ice cream consists of three dispersed phases: ice crystals, which have a mean size of 50 μm, air bubbles with a diameter of about 70 μm, and fat droplets with a size of 1 μm. These phases are held together by what is called the matrix – not a sci-fi film, but a viscous solution of sugars, milk proteins and polysaccharides.

The theorems of Hawking and Penrose show that space-times are likely to contain incomplete geodesics. Such geodesics are said to end at a singularity if it is impossible to continue the space-time and geodesic without violating the usual topological and smoothness conditions on the space-time. In this book the different possible singularities are defined, and the mathematical methods needed to extend the space-time are described in detail. The results obtained (many appearing here for the first time) show that singularities are associated with a lack of smoothness in the Riemann tensor. While the Friedmann singularity is analysed as an example, the emphasis is on general theorems and techniques rather than on the classification of particular exact solutions.

INTRODUCTION Those of us who had the privilege of being Dennis Sciama's students during what Hajicek has described as ‘the Golden Age of General Relativity’ can trace many of the current concerns of the subject back to the ideas which he fostered, either directly or indirectly, within his research group in Cambridge. This was the environment in which major contributions to most of the foundational ideas about singularities: from the controversies about the steady state and big bang theories; through the critique of the early Lifshitz-Khalatnikov arguments which at first suggested that the big bang singularity was not generic, leading to definitions of just what constituted a singularity; to the Hawking-Penrose singularity theorems themselves. The issue of cosmic censorship stemmed naturally from this work, and illustrates well the combination of rigorous mathematics with a firm hold on physical relevance which he established at that time. In this talk I shall try to give an outline of the historical work on cosmic censorship, focussing at the end on my own recent work on shell crossing singularities. I shall not be concerned with what George Ellis, in this meeting, has termed the position of the goal posts — the details of exactly what the target is; rather, I shall be arguing that we should in fact be playing a different game.

In a series of recent books, John Polkinghorne – the high-energy physicist who became an Anglican priest – has put forward a view of the universe that combines insights from both physics and theology. In this latest offering, he wants to mark out the boundaries of science, so that he can clarify the different arguments that are needed when one moves "beyond science", while at the same time maintaining a rational stance.

What's your ambition in life? Is it something big like winning a Nobel prize, climbing Mount Everest or scoring the winning goal in a World Cup final? Or are you content with something more attainable, like winning the prize for the best poster at a conference, gradually climbing the career ladder or scoring a goal for your Sunday-morning football team? I have ambitions of both types, but I never really expected to achieve any of the big ones. It therefore came as a bit of a surprise to me when I recently found that I had.

A new and effective algorithm is derived for reconstructing the non-ohmic (or 'impressed') part of a current distribution in a conducting medium, given a number of external magnetometer readings. The method allows for a weight function expressing any structure in the source that may be known a priori, and does not make the assumptions on the invertability of matrices used in earlier versions. The numerical implementation is outlined, and estimates derived for the errors caused by truncation of series.

Interpretations, or generalizations, of quantum theory that are applicable to cosmology are of interest because they must display and resolve the “paradoxes” directly. The Everett interpretation is reexamined and compared with two alternatives. Its “metaphysical” connotations can be removed, after which it is found to be more acceptable than a theory which incorporates collapse, while retaining some unsatisfactory features.

A singularity reached on a timelike curve in a globally hyperbolic space-time must be a point at which the Riemann tensor becomes infinite (as a curvature or intermediate singularity) or is of typeD and electrovac.

It is shown that the differentiability of a space-time is implied by that of its Riemann tensor, assuming a priori only boundedness of the first derivations of the metric. Consequently all the results on space-time singularities proved in earlier papers by the author hold true in C2− space-times.

A class of space-times without spin-structure is discussed. It is shown that these space-times admit a globally defined structure which is locally equivalent to a spin structure. ‘Generalised spinors’ can be defined, locally indistinguishable from ordinary spinors, which suffice for defining particle fields.

An example is given of a spacetime with an isometry group having spherical orbits but where the spacetime is not the direct product of a typical orbit with an orthogonal 2-space. It is shown that, if a general spacetime is not such a product, then it has a covering space which is.

The method of maximum statistical entropy (to be distinguished from the more usual maximum configurational entropy) is explained for a general inverse problem. Application to the biomagnetic situation then yields a solution which, in the limit as the available information becomes zero, gives the minimum-power current distribution. The method is developed in detail for the case of a uniform sphere.