Quantum dynamics of a dc-SQUID coupled to an asymmetric Cooper pair transistor

We present a theoretical analysis of the quantum dynamics of a superconducting circuit based on a highly asymmetric Cooper pair transistor (ACPT) in parallel to a dc-SQUID. Starting from the full Hamiltonian we show that the circuit can be modeled as a charge qubit (ACPT) coupled to an anharmonic oscillator (dc-SQUID). Depending on the anharmonicity of the SQUID, the Hamiltonian can be reduced either to one that describes two coupled qubits or to the Jaynes-Cummings Hamiltonian. Here the dc-SQUID can be viewed as a tunable micron-size resonator. The coupling term, which is a combination of a capacitive and a Josephson coupling between the two qubits, can be tuned from the very strong- to the zero-coupling regimes. It describes very precisely the tunable coupling strength measured in this circuit and explains the 'quantronium' as well as the adiabatic quantum transfer read-out.Comment: 20 page

An accurate formula for the period of a simple pendulum oscillating beyond the small-angle regime

A simple approximation formula is derived here for the dependence of the period of a simple pendulum on amplitude that only requires a pocket calculator and furnishes an error of less than 0.25% with respect to the exact period. It is shown that this formula describes the increase of the pendulum period with amplitude better than other simple formulas found in literature. A good agreement with experimental data for a low air-resistance pendulum is also verified and it suggests, together with the current availability/precision of timers and detectors, that the proposed formula is useful for extending the pendulum experiment beyond the usual small-angle oscillations.Comment: 15 pages and 4 figures. to appear in American Journal of Physic

Quantum Gravity Phenomenology, Lorentz Invariance and Discreteness

Contrary to what is often stated, a fundamental spacetime discreteness need not contradict Lorentz invariance. A causal set's discreteness is in fact locally Lorentz invariant, and we recall the reasons why. For illustration, we introduce a phenomenological model of massive particles propagating in a Minkowski spacetime which arises from an underlying causal set. The particles undergo a Lorentz invariant diffusion in phase space, and we speculate on whether this could have any bearing on the origin of high energy cosmic rays.Comment: 13 pages. Replaced version with corrected fundamental solution, missing m's (mass) and c's (speed of light) added and reference on diffusion on the three sphere changed. Note with additional references added and addresses updated, as in published versio

Molecular evolution of the sheep prion protein gene

Transmissible spongiform encephalopathies (TSEs) are infectious, fatal neurodegenerative diseases characterized by aggregates of modified forms of the prion protein (PrP) in the central nervous system. Well known examples include variant Creutzfeldt-Jakob Disease (vCJD) in humans, BSE in cattle, chronic wasting disease in deer and scrapie in sheep and goats. In humans, sheep and deer, disease susceptibility is determined by host genotype at the prion protein gene (PRNP). Here I examine the molecular evolution of PRNP in ruminants and show that variation in sheep appears to have been maintained by balancing selection, a profoundly different process from that seen in other ruminants. Scrapie eradication programs such as those recently implemented in the UK, USA and elsewhere are based on the assumption that PRNP is under positive selection in response to scrapie. If, as these data suggest, that assumption is wrong, eradication programs will disrupt this balancing selection, and may have a negative impact on the fitness or scrapie resistance of national flocks

Evaluation and management implications of uncertainty in a multispecies size-structured model of population and community responses to fishing

1. Implementation of an ecosystem approach to fisheries requires advice on trade-offs among fished species and between fisheries yields and biodiversity or food web properties. However, the lack of explicit representation, analysis and consideration of uncertainty in most multispecies models has limited their application in analyses that could support management advice. 2. We assessed the consequences of parameter uncertainty by developing 78 125 multispecies size-structured fish community models, with all combinations of parameters drawn from ranges that spanned parameter values estimated from data and literature. This unfiltered ensemble was reduced to 188 plausible models, the filtered ensemble (FE), by screening outputs against fish abundance data and ecological principles such as requiring species' persistence. 3. Effects of parameter uncertainty on estimates of single-species management reference points for fishing mortality (FMSY, fishing mortality rate providing MSY, the maximum sustainable yield) and biomass (BMSY, biomass at MSY) were evaluated by calculating probability distributions of estimated reference points with the FE. There was a 50% probability that multispecies FMSY could be estimated to within ±25% of its actual value, and a 50% probability that BMSY could be estimated to within ±40% of its actual value. 4. Signal-to-noise ratio was assessed for four community indicators when mortality rates were reduced from current rates to FMSY. The slope of the community size spectrum showed the greatest signal-to-noise ratio, indicating that it would be the most responsive indicator to the change in fishing mortality F. Further, the power of an ongoing international monitoring survey to detect predicted responses of size spectrum slope was higher than for other size-based metrics. 5. Synthesis and applications: Application of the ensemble model approach allows explicit representation of parameter uncertainty and supports advice and management by (i) providing uncertainty intervals for management reference points, (ii) estimating working values of reference points that achieve a defined reduction in risk of not breaching the true reference point, (iii) estimating the responsiveness of population, community, food web and biodiversity indicators to changes in F, (iv) assessing the performance of indicators and monitoring programmes and (v) identifying priorities for data collection and changes to model structure to reduce uncertainty