Quantum statistics on graphs

Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph, concentrating on the simplest case of abelian statistics for two particles. In spite of the fact that graphs are locally one-dimensional, anyon statistics emerge in a generalized form. A given graph may support a family of independent anyon phases associated with topologically inequivalent exchange processes. In addition, for sufficiently complex graphs, there appear new discrete-valued phases. Our analysis is simplified by considering combinatorial rather than metric graphs -- equivalently, a many-particle tight-binding model. The results demonstrate that graphs provide an arena in which to study new manifestations of quantum statistics. Possible applications include topological quantum computing, topological insulators, the fractional quantum Hall effect, superconductivity and molecular physics.Comment: 21 pages, 6 figure

The periods of the intermediate polar RX J0153.3+7446

We present the first optical photometry of the counterpart to the candidate intermediate polar RX J0153.3+7446. This reveals an optical pulse period of 2333s +/- 5s. Reanalysis of the previously published ROSAT X-ray data reveals that the true X-ray pulse period is probably 1974s +/- 30s, rather than the 1414 s previously reported. Given that the previously noted orbital period of the system is 3.94 h, we are able to identify the X-ray pulse period with the white dwarf spin period and the optical pulse period with the rotation period of the white dwarf in the binary reference frame, as commonly seen in other intermediate polars. We thus confirm that RX J0153.3+7446 is indeed a typical intermediate polar.Comment: 4 pages, submitted to A&A Letter

The status of harbour seals (Phoca vitulina) in the UK

Surveys in England and the Moray Firth were funded by the UK Natural Environment Research Council (National Capability Grant no. SMRU1001). Surveys in the rest of Scotland were funded by Scottish Natural Heritage and surveys in Northern Ireland were funded by The Department of Trade and Industry, Marine Current Turbines, and the Northern Ireland Department of Agriculture, Environment and Rural Affairs.1. Estimates of population size and trends are essential for effective conservation and management of wildlife populations. For harbour seals (Phoca vitulina), these data are required to fulfil statutory reporting obligations under national and international regulations. 2. Aerial survey counts of harbour seals hauled out during their annual moult were used to estimate population sizes and trends at UK, regional (seal management unit, SMU) and local (Special Area of Conservation, SAC) scales. 3. Results indicate that the current UK harbour seal population is similar to estimates from the late 1990s, but there were significant declines in some subpopulations and increases in others. 4. Fitted trends suggest that the UK harbour seal population can be divided into three geographically coherent groups: South‐east populations (South‐East and North‐East England SMUs) have shown continuous increases punctuated by phocine distemper virus epidemics in 1988 and 2002; north‐east populations (East Scotland, Moray Firth, North Coast and Orkney, and Shetland SMUs) have declined since the late 1990s; north‐west populations (West Scotland, Western Isles, and South‐West Scotland SMUs) have remained stable or increased. Similar geographical population substructure is evident in recent population genetics results. 5. Trends within SACs generally match SMU trends since 2002. Of the nine SACs designated for harbour seals, four declined (in East Scotland, Moray Firth, and North Coast and Orkney SMUs), four remained stable (in Shetland and West Scotland SMUs), and one increased (in South‐East England SMU). 6. Large changes in relative abundance have resulted from differences in regional trends. For example, in 1996–1997 the West Scotland and North Coast and Orkney SMUs each held ~27% of the Great Britain population but now hold ~50% and ~4% respectively; in 1980, the South‐East England SMU population was ~50% that of the Wadden Sea population, but by 2016 it was equivalent to <20% of the Wadden Sea count.PostprintPeer reviewe

Quantum indistinguishability from general representations of SU(2n)

A treatment of the spin-statistics relation in nonrelativistic quantum mechanics due to Berry and Robbins [Proc. R. Soc. Lond. A (1997) 453, 1771-1790] is generalised within a group-theoretical framework. The construction of Berry and Robbins is re-formulated in terms of certain locally flat vector bundles over n-particle configuration space. It is shown how families of such bundles can be constructed from irreducible representations of the group SU(2n). The construction of Berry and Robbins, which leads to a definite connection between spin and statistics (the physically correct connection), is shown to correspond to the completely symmetric representations. The spin-statistics connection is typically broken for general SU(2n) representations, which may admit, for a given value of spin, both bose and fermi statistics, as well as parastatistics. The determination of the allowed values of the spin and statistics reduces to the decomposition of certain zero-weight representations of a (generalised) Weyl group of SU(2n). A formula for this decomposition is obtained using the Littlewood-Richardson theorem for the decomposition of representations of U(m+n) into representations of U(m)*U(n).Comment: 32 pages, added example section 4.

Monitoring long-term changes in UK grey seal pup production

The work was supported by funding from the Natural Environment Research Council to SMRU (grant no. SMRU1001).1.  The population size of many species, particularly those in the aquatic environment, cannot be censused directly. Counts, during the breeding season, of one component of the population (e.g. breeding females) are often used as an index to allow investigation of trends. In species, such as grey seals (Halichoerus grypus), for which births are not tightly synchronous, single counts of pups represent an unknown proportion of the total number of pups born (pup production), and thus of breeding females (i.e. each pup born represents a breeding female). 2.  Grey seals pup at large colonies around the coast of the UK. Information on their populations is required under national and international legislation. 3.  In the UK, pup production has been monitored at some colonies since 1956. Currently, large colonies (~90% of UK pup production) are monitored either using ground (~10%; annually) or aerial surveys (~80%; annually until 2010, and thereafter biennially). 4.  Here, the model used to estimate pup production at aerially surveyed colonies from 1987 to 2010 is described; structured pup counts from multiple surveys are combined with knowledge of life‐history parameters to model birth curves. 5.  The resulting trends in pup production up to 2010 (aerially surveyed colonies) and 2016 (ground surveyed colonies) are examined. 6.  In 2010, over 45,000 pups were estimated to be born in the UK. Pup production appeared to have reached an asymptote in the Inner Hebrides, Outer Hebrides and Orkney, whereas it is still increasing exponentially in the North Sea. Although density‐dependent processes acting at sea are likely to be responsible for these regional trends, we suggest that the substantial variation in trends within regions are likely caused by processes acting at the colony level. Some long‐established colonies, including Special Areas of Conservation, are exhibiting decreasing trends. 7.  Special Areas of Conservation often serve as de facto monitoring sites and are the focus of management efforts. The observed temporal and spatial variability in patterns of colony growth rates highlight the potential risks of using such sites to develop wider management policies.PostprintPeer reviewe

Inelastic collapse of a randomly forced particle

We consider a randomly forced particle moving in a finite region, which rebounds inelastically with coefficient of restitution r on collision with the boundaries. We show that there is a transition at a critical value of r, r_c\equiv e^{-\pi/\sqrt{3}}, above which the dynamics is ergodic but beneath which the particle undergoes inelastic collapse, coming to rest after an infinite number of collisions in a finite time. The value of r_c is argued to be independent of the size of the region or the presence of a viscous damping term in the equation of motion.Comment: 4 pages, REVTEX, 2 EPS figures, uses multicol.sty and epsf.st

Indistinguishable Particles in Quantum Mechanics: An Introduction

In this article, we discuss the identity and indistinguishability of quantum systems and the consequent need to introduce an extra postulate in Quantum Mechanics to correctly describe situations involving indistinguishable particles. This is, for electrons, the Pauli Exclusion Principle, or in general, the Symmetrization Postulate. Then, we introduce fermions and bosons and the distributions respectively describing their statistical behaviour in indistinguishable situations. Following that, we discuss the spin-statistics connection, as well as alternative statistics and experimental evidence for all these results, including the use of bunching and antibunching of particles emerging from a beam splitter as a signature for some bosonic or fermionic states.Comment: To appear in Contemp. Phy

The Effect of Three-Dimensional Freestream Disturbances on the Supersonic Flow Past a Wedge

The interaction between a shock wave (attached to a wedge) and small amplitude, three-dimensional disturbances of a uniform, supersonic, freestream flow are investigated. The paper extends the two-dimensional study of Duck et al, through the use of vector potentials, which render the problem tractable by the same techniques as in the two-dimensional case, in particular by expansion of the solution by means of a Fourier-Bessel series, in appropriately chosen coordinates. Results are presented for specific classes of freestream disturbances, and the study shows conclusively that the shock is stable to all classes of disturbances (i.e. time periodic perturbations to the shock do not grow downstream), provided the flow downstream of the shock is supersonic (loosely corresponding to the weak shock solution). This is shown from our numerical results and also by asymptotic analysis of the Fourier-Bessel series, valid far downstream of the shock

Quantifying the impact of BOReal forest fires on Tropospheric oxidants over the Atlantic using Aircraft and Satellites (BORTAS) experiment: design, execution and science overview

We describe the design and execution of the BORTAS (Quantifying the impact of BOReal forest fires on Tropospheric oxidants over the Atlantic using Aircraft and Satellites) experiment, which has the overarching objective of understanding the chemical aging of air masses that contain the emission products from seasonal boreal wildfires and how these air masses subsequently impact downwind atmospheric composition. The central focus of the experiment was a two-week deployment of the UK BAe-146-301 Atmospheric Research Aircraft (ARA) over eastern Canada, based out of Halifax, Nova Scotia. Atmospheric ground-based and sonde measurements over Canada and the Azores associated with the planned July 2010 deployment of the ARA, which was postponed by 12 months due to UK-based flights related to the dispersal of material emitted by the Eyjafjallajökull volcano, went ahead and constituted phase A of the experiment. Phase B of BORTAS in July 2011 involved the same atmospheric measurements, but included the ARA, special satellite observations and a more comprehensive ground-based measurement suite. The high-frequency aircraft data provided a comprehensive chemical snapshot of pyrogenic plumes from wildfires, corresponding to photochemical (and physical) ages ranging from 45 sr 10 days, largely by virtue of widespread fires over Northwestern Ontario. Airborne measurements reported a large number of emitted gases including semi-volatile species, some of which have not been been previously reported in pyrogenic plumes, with the corresponding emission ratios agreeing with previous work for common gases. Analysis of the NOy data shows evidence of net ozone production in pyrogenic plumes, controlled by aerosol abundance, which increases as a function of photochemical age. The coordinated ground-based and sonde data provided detailed but spatially limited information that put the aircraft data into context of the longer burning season in the boundary layer. Ground-based measurements of particulate matter smaller than 2.5 μm (PM2.5) over Halifax show that forest fires can on an episodic basis represent a substantial contribution to total surface PM2.5