Fermi-Bose Correspondence and Bose-Einstein Condensation in The Two-Dimensional Ideal Gas

The ideal uniform two-dimensional (2D) Fermi and Bose gases are considered both in the thermodynamic limit and the finite case. We derive May's Theorem, viz. the correspondence between the internal energies of the Fermi and Bose gases in the thermodynamic limit. This results in both gases having the same heat capacity. However, as we shall show, the thermodynamic limit is never truly reached in two dimensions and so it is essential to consider finite-size effects. We show in an elementary manner that for the finite 2D Bose gas, a pseudo-Bose-Einstein condensate forms at low temperatures, incompatible with May's Theorem. The two gases now have different heat capacities, dependent on the system size and tending to the same expression in the thermodynamic limit.Comment: 18 pages, 3 figures in EPS format, to be published in Journal of Low Temperature Physic

Unifying Evolutionary and Network Dynamics

Many important real-world networks manifest "small-world" properties such as scale-free degree distributions, small diameters, and clustering. The most common model of growth for these networks is "preferential attachment", where nodes acquire new links with probability proportional to the number of links they already have. We show that preferential attachment is a special case of the process of molecular evolution. We present a new single-parameter model of network growth that unifies varieties of preferential attachment with the quasispecies equation (which models molecular evolution), and also with the Erdos-Renyi random graph model. We suggest some properties of evolutionary models that might be applied to the study of networks. We also derive the form of the degree distribution resulting from our algorithm, and we show through simulations that the process also models aspects of network growth. The unification allows mathematical machinery developed for evolutionary dynamics to be applied in the study of network dynamics, and vice versa.Comment: 11 pages, 12 figures, Accepted for publication in Physical Review

Canonical decompositions of 3-manifolds

We describe a new approach to the canonical decompositions of 3-manifolds along tori and annuli due to Jaco-Shalen and Johannson (with ideas from Waldhausen) - the so-called JSJ-decomposition theorem. This approach gives an accessible proof of the decomposition theorem; in particular it does not use the annulus-torus theorems, and the theory of Seifert fibrations does not need to be developed in advance.Comment: 20 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol1/paper3.abs.htm

Interaction of a circularly polarised gravitational wave with a charged particle in a static magnetic background

Interaction of a charged particle in a static magnetic background, i.e., a Landau system with circularly polarised gravitational wave (GW) is studied quantum mechanically in the long wavelength and low velocity limit. We quantize the classical Hamiltonian following \cite{speli}. The rotating polarization vectors of the circularly polarized GW are employed to form a unique directional triad which served as the coordinate axes. The Schrodinger equations for the system are cast in the form of a set of coupled linear differential equations. This system is solved by iterative technique. We compute the time-evolution of the position and momentum expectation values of the particle. The results show that the resonance behaviour obtained earlier\cite{emgw_classical} by classical treatements of the system has a quantum analogue not only for the linearly polarized GW \cite{emgw_1_lin}, but for circularly polarized GW as well.Comment: 8 pages, Late

Longevity: Trends, uncertainty and the implications for pension systems

This paper presents historical trends in life expectancy in the United Kingdom and other countries and discusses how these trends might evolve over the coming decades. The paper argues that the expected increases in longevity are likely to have significant implications for the structure of pension systems in the future. Individuals, businesses and governments have already responded to these expected increases – for example by working longer, closing defined-benefit pension schemes or introducing parametric reforms to the state pension system – and are likely to change their behaviours further in the future. The issue is complicated by the fact that future longevity trends are uncertain. This makes it more difficult to allocate longevity risk efficiently and fairly across the different economic agents, while making it also more difficult to guarantee the sustainability of the system overall. The paper shows though that innovative solutions to this challenge are being developed, from businesses moving towards hybrid defined-benefit/defined-contribution pension schemes, to governments introducing mechanisms which automatically split the financial burden arising from future increases in life expectancy between state and individual, to businesses taking advantage of new products being developed to transfer any risk to the capital markets. --Pensions,Uncertainty,Financial markets,Longevity,Pension liabilities

Trace of phase-space noncommutativity in the response of a free particle to linearized gravitational waves

Interaction of linearized gravitational waves with a otherwise free particle has been studied quantum mechanically in a noncommutative phase-space to examine whether the particle's response to the gravitational wave gets modified due to spatial and/or momentum noncommutativity. The result shows that momentum noncommutativity introduces a oscillatory noise with a specific frequency determined by the fundamental momentum scale and particle mass. Because of the global nature of the phase-space noncommutativity such noise will have similar characteristics for all detector sites and thus will stand out in a data cross-correlation procedure. If detected, this noise will provide evidence of momentum noncommutativity and also an estimation of the relevant noncommutative parameter.Comment: 9 pages, Latex, Published version, discussions and references adde