Geochronology (Re–Os and U–Pb) and fluid inclusion studies of molybdenite mineralisation associated with the Shap, Skiddaw and Weardale granites, UK

Late Devonian magmatism in Northern England records key events associated with the Acadian phase of the Caledonian-Appalachian Orogen (C-AO). Zircon U-Pb and molybdenite Re-Os geochronology date emplacement and mineralisation in the Shap (405·2±1·8 Ma), Skiddaw (398·8±0·4 and 392·3±2·8 Ma) and Weardale granites (398·3±1·6 Ma). For the Shap granite, mineralisation and magmatism are contemporaneous, with mineralisation being directly associated with the boiling of CO2-rich magmatic fluids between 300 and 450°C, and 440 and 620 bars. For the Skiddaw granite, the Re-Os age suggests that sulphide mineralisation occurred post-magmatism (398·8±0·4 Ma) and was associated with the boiling (275 and 400°C and at 375-475 bars) of a non-magmatic fluid, enriched in N2, CH4 and S, which is isotopically heavy. In contrast, the co-magmatic molybdenite mineralisation of the Weardale granite formed from non-fluid boiling at 476 to 577°C at 1-1·7 kbars. The new accurate and precise ages indicate that magmatism and Mo-mineralisation occurred during the same period across eastern Avalonia (cf. Ireland). In addition, the ages provide a timing of tectonism of the Acadian phase of the C-AO in northern England. Based on the post-tectonic metamorphic mineral growth associated with the Shap and Skiddaw granite aureoles, Acadian deformation in the northern England continued episodically (before ∼405 Ma) throughout the Emsian (∼398 Ma)

Construction of an instrument for the measurement of educational philosophy

Thesis (M.Ed.)--Boston Universit

Strategies for enhancing quantum entanglement by local photon subtraction

Subtracting photons from a two-mode squeezed state is a well-known method to increase entanglement. We analyse different strategies of local photon subtraction from a two-mode squeezed state in terms of entanglement gain and success probability. We develop a general framework that incorporates imperfections and losses in all stages of the process: before, during, and after subtraction. By combining all three effects into a single efficiency parameter, we provide analytical and numerical results for subtraction strategies using photon-number-resolving and threshold detectors. We compare the entanglement gain afforded by symmetric and asymmetric subtraction scenarios across the two modes. For a given amount of loss, we identify an optimised set of parameters, such as initial squeezing and subtraction beam splitter transmissivity, that maximise the entanglement gain rate. We identify regimes for which asymmetric subtraction of different Fock states on the two modes outperforms symmetric strategies. In the lossless limit, subtracting a single photon from one mode always produces the highest entanglement gain rate. In the lossy case, the optimal strategy depends strongly on the losses on each mode individually, such that there is no general optimal strategy. Rather, taking losses on each mode as the only input parameters, we can identify the optimal subtraction strategy and required beam splitter transmissivities and initial squeezing parameter. Finally, we discuss the implications of our results for the distillation of continuous-variable quantum entanglement.Comment: 13 pages, 11 figures. Updated version for publicatio

Quantum and Classical in Adiabatic Computation

Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in a readily initialised state and then slowly changing its Hamiltonian, one may achieve quantum states that would otherwise be inaccessible. Moreover, a judicious choice of final Hamiltonian whose groundstate encodes the solution to a problem allows adiabatic transport to be used for universal quantum computation. However, the dephasing effects of the environment limit the quantum correlations that an open system can support and degrade the power of such adiabatic computation. We quantify this effect by allowing the system to evolve over a restricted set of quantum states, providing a link between physically inspired classical optimisation algorithms and quantum adiabatic optimisation. This new perspective allows us to develop benchmarks to bound the quantum correlations harnessed by an adiabatic computation. We apply these to the D-Wave Vesuvius machine with revealing - though inconclusive - results

Mean field theory of failed thermalizing avalanches

We show that localization in quasiperiodically modulated, two-dimensional systems is stable to the presence of a finite density of ergodic grains. This contrasts with the case of randomly modulated systems, where such grains seed thermalizing avalanches. These results are obtained within a quantitatively accurate, self-consistent entanglement mean field theory which analytically describes two level systems connected to a central ergodic grain. The theory predicts the distribution of entanglement entropies of each two level system across eigenstates, and the late time values of dynamical observables. In addition to recovering the known phenomenology of avalanches, the theory reproduces exact diagonalization data, and predicts the spatial profile of the thermalized region when the avalanche fails.Comment: 13 pages, 5 figure

A constructive theory of the numerically accessible many-body localized to thermal crossover

The many-body localised (MBL) to thermal crossover observed in exact diagonalisation studies remains poorly understood as the accessible system sizes are too small to be in an asymptotic scaling regime. We develop a model of the crossover in short 1D chains in which the MBL phase is destabilised by the formation of many-body resonances. The model reproduces several properties of the numerically observed crossover, including an apparent correlation length exponent $\nu=1$, exponential growth of the Thouless time with disorder strength, linear drift of the critical disorder strength with system size, scale-free resonances, apparent $1/\omega$ dependence of disorder-averaged spectral functions, and sub-thermal entanglement entropy of small subsystems. In the crossover, resonances induced by a local perturbation are rare at numerically accessible system sizes $L$ which are smaller than a \emph{resonance length} $\lambda$. For $L \gg \sqrt{\lambda}$, resonances typically overlap, and this model does not describe the asymptotic transition. The model further reproduces controversial numerical observations which Refs. [\v{S}untajs et al, 2019] and [Sels & Polkovnikov, 2020] claimed to be inconsistent with MBL. We thus argue that the numerics to date is consistent with a MBL phase in the thermodynamic limit.Comment: 27 pages, 12 figure

Avalanche induced co-existing localised and thermal regions in disordered chains

We investigate the stability of an Anderson localized chain to the inclusion of a single finite interacting thermal seed. This system models the effects of rare low-disorder regions on many-body localized chains. Above a threshold value of the mean localization length, the seed causes runaway thermalization in which a finite fraction of the orbitals are absorbed into a thermal bubble. This `partially avalanched' regime provides a simple example of a delocalized, non-ergodic dynamical phase. We derive the hierarchy of length scales necessary for typical samples to exhibit the avalanche instability, and show that the required seed size diverges at the avalanche threshold. We introduce a new dimensionless statistic that measures the effective size of the thermal bubble, and use it to numerically confirm the predictions of avalanche theory in the Anderson chain at infinite temperature.Comment: 26 pages, 18 figure