SU(3) Spin-Orbit Coupling in Systems of Ultracold Atoms

Motivated by the recent experimental success in realizing synthetic spin-orbit coupling in ultracold atomic systems, we consider N-component atoms coupled to a non-Abelian SU(N) gauge field. More specifically, we focus on the case, referred to here as "SU(3) spin-orbit-coupling," where the internal states of three-component atoms are coupled to their momenta via a matrix structure that involves the Gell-Mann matrices (in contrast to the Pauli matrices in conventional SU(2) spin-orbit-coupled systems). It is shown that the SU(3) spin-orbit-coupling gives rise to qualitatively different phenomena and in particular we find that even a homogeneous SU(3) field on a simple square lattice enables a topologically non-trivial state to exist, while such SU(2) systems always have trivial topology. In deriving this result, we first establish an exact equivalence between the Hofstadter model with a 1/N Abelian flux per plaquette and a homogeneous SU(N) non-Abelian model. The former is known to have a topological spectrum for N>2, which is thus inherited by the latter. It is explicitly verified by an exact calculation for N=3, where we develop and use a new algebraic method to calculate topological indices in the SU(3) case. Finally, we consider a strip geometry and establish the existence of three gapless edge states -- the hallmark feature of such an SU(3) topological insulator.Comment: 4.2 pages, 1 figur

Policy analysis research in higher education: Negotiating dilemmas

Increasingly, qualitative research is funded by agencies - whether government or national agencies or in the private sector that have a direct interest in the research that they are funding. Especially in qualitative research in such situations, methodological issues arise but so too do dilemmas, both in the actual conduct of the study and in the writing and the positioning of ensuing texts (for example, in relation to value neutrality and value commitment, in doing justice to the multiple and conflicting interests of various constituencies and in steering among competing ideologies). Here, in this paper, such dilemmas are brought out in an account of a study conducted in the UK in the 1990s, to review and to evaluate the UK's then quality assurance system

Creating insurance markets for natural disaster risk in lower income countries: the potential role for securitization

This paper considers the potential for securitizing index-based insurance products that transfer weather and natural disaster risks from lower income countries. The paper begins with a brief overview of why markets for natural disaster risks are important in lower income countries and a review of some recent activities using index-based weather insurance. Next, the paper explains how natural disaster risks are handled in higher income countries. These examples along with the example of an innovative index-based livestock insurance pilot project in Mongolia illustrate how layers, or tranches, of natural disaster risk can be financed during the product development phase by creating structures similar to the Special Purpose Vehicles used in catastrophe bond, mortgage bond, and the emerging microfinance bond markets. We refer to these investment alternatives as micro-CAT bonds since the principal amounts would be small relative to the existing CAT bond market.Catastrophe risk, index insurance, weather risks, socially responsible investing, reinsurance, Risk and Uncertainty,

Innovations in Government Responses to Catastrophic Risk Sharing for Agriculture in Developing Countries

Markets for transferring catastrophic risk in agriculture are woefully lacking in developing countries. Even in developed countries, markets for transferring the risk of crop losses caused by natural hazards generally exist only with large government subsidies. However, such subsidies can be expensive, inefficient, and have detrimental implications that make future catastrophes even worse. In developing countries fiscal constraints limit the degree to which governments can subsidize markets for agricultural risk-sharing. Nonetheless, there are specific things governments can do to facilitate the development of these markets. This paper addresses the role of government in agricultural risk-sharing for natural disasters that impact crop yields or livestock mortality.Agricultural and Food Policy, Risk and Uncertainty, D8, H5, Q14, Q18, Q54,

Combining real and virtual Higgs boson mass constraints

Within the framework of the standard model we observe that there is a significant discrepancy between the most precise $Z$ boson decay asymmetry measurement and the limit from direct searches for Higgs boson production. Using methods inspired by the Particle Data Group we explore the possible effect on fits of the Higgs boson mass. In each case the central value and the 95% confidence level upper limit increase significantly relative to the conventional fit. The results suggest caution in drawing conclusions about the Higgs boson mass from the existing data.Comment: 11 pages, Latex. Citations are added and paper is otherwise reconciled with version to be published in Physical Review Letter

Retrodiction of Generalised Measurement Outcomes

If a generalised measurement is performed on a quantum system and we do not know the outcome, are we able to retrodict it with a second measurement? We obtain a necessary and sufficient condition for perfect retrodiction of the outcome of a known generalised measurement, given the final state, for an arbitrary initial state. From this, we deduce that, when the input and output Hilbert spaces have equal (finite) dimension, it is impossible to perfectly retrodict the outcome of any fine-grained measurement (where each POVM element corresponds to a single Kraus operator) for all initial states unless the measurement is unitarily equivalent to a projective measurement. It also enables us to show that every POVM can be realised in such a way that perfect outcome retrodiction is possible for an arbitrary initial state when the number of outcomes does not exceed the output Hilbert space dimension. We then consider the situation where the initial state is not arbitrary, though it may be entangled, and describe the conditions under which unambiguous outcome retrodiction is possible for a fine-grained generalised measurement. We find that this is possible for some state if the Kraus operators are linearly independent. This condition is also necessary when the Kraus operators are non-singular. From this, we deduce that every trace-preserving quantum operation is associated with a generalised measurement whose outcome is unambiguously retrodictable for some initial state, and also that a set of unitary operators can be unambiguously discriminated iff they are linearly independent. We then examine the issue of unambiguous outcome retrodiction without entanglement. This has important connections with the theory of locally linearly dependent and locally linearly independent operators.Comment: To appear in Physical Review

Photon production from the vacuum close to the super-radiant transition: When Casimir meets Kibble-Zurek

The dynamical Casimir effect (DCE) predicts the generation of photons from the vacuum due to the parametric amplification of the quantum fluctuation of an electromagnetic field\cite{casimir1,casimir2}. The verification of such effect is still elusive in optical systems due to the very demanding requirements of its experimental implementation. This typically requires very fast changes of the boundary conditions of the problem, such as the high-frequency driving of the positions of the mirrors of a cavity accommodating the field. Here, we show that an ensemble of two-level atoms collectively coupled to the electromagnetic field of a cavity (thus embodying the quantum Dicke model\cite{dicke}), driven at low frequencies and close to a quantum phase transition, stimulates the production of photons from the vacuum. This paves the way to an effective simulation of the DCE through a mechanism that has recently found an outstanding experimental demonstration\cite{esslinger}. The spectral properties of the emitted radiation reflect the critical nature of the system and allow us to link the detection of DCE to the Kibble-Zurek mechanism for the production of defects when crossing a continuous phase transition\cite{KZ1,KZ2}. We illustrate the features of our proposal by addressing a simple cavity quantum-electrodynamics (cQED) setting of immediate experimental realisation.Comment: 4+1 pages, major changes in the second part of the paper. To appear in Physical Review Letter

Generalized Log-Normal Chain-Ladder

We propose an asymptotic theory for distribution forecasting from the log normal chain-ladder model. The theory overcomes the difficulty of convoluting log normal variables and takes estimation error into account. The results differ from that of the over-dispersed Poisson model and from the chain-ladder based bootstrap. We embed the log normal chain-ladder model in a class of infinitely divisible distributions called the generalized log normal chain-ladder model. The asymptotic theory uses small $\sigma$ asymptotics where the dimension of the reserving triangle is kept fixed while the standard deviation is assumed to decrease. The resulting asymptotic forecast distributions follow t distributions. The theory is supported by simulations and an empirical application

Sampling bias in systems with structural heterogeneity and limited internal diffusion

Complex systems research is becomingly increasingly data-driven, particularly in the social and biological domains. Many of the systems from which sample data are collected feature structural heterogeneity at the mesoscopic scale (i.e. communities) and limited inter-community diffusion. Here we show that the interplay between these two features can yield a significant bias in the global characteristics inferred from the data. We present a general framework to quantify this bias, and derive an explicit corrective factor for a wide class of systems. Applying our analysis to a recent high-profile survey of conflict mortality in Iraq suggests a significant overestimate of deaths