High Density Effective Theory Confronts the Fermi Liquid

The high density effective theory recently introduced by Hong and Hsu to describe ultradense relativistic fermionic matter is used to calculate the tree-level forward scattering amplitude between two particles at the Fermi surface. While the direct term correctly reproduces that of the underlying gauge theory, the exchange term has the wrong sign. The physical consequences are discussed in the context of Landau's theoretical description of the Fermi liquid.Comment: 15 pages, 2 figures; conclusion expanded, reference adde

A way to estimate the heavy quark thermalization rate from the lattice

The thermalization rate of a heavy quark is related to its momentum diffusion coefficient. Starting from a Kubo relation and using the framework of the heavy quark effective theory, we argue that in the large-mass limit the momentum diffusion coefficient can be defined through a certain Euclidean correlation function, involving color-electric fields along a Polyakov loop. Furthermore, carrying out a perturbative computation, we demonstrate that the spectral function corresponding to this correlator is relatively flat at small frequencies. Therefore, unlike in the case of several other transport coefficients, for which the narrowness of the transport peak makes analytic continuation from Euclidean lattice data susceptible to severe systematic uncertainties, it appears that the determination of the heavy quark thermalization rate could be relatively well under control.Comment: 17 pages. v2: clarifications and references added, published versio

Symmetry of bound and antibound states in the semiclassical limit

We consider one dimensional scattering and show how the presence of a mild positive barrier separating the interaction region from infinity implies that the bound and antibound states are symmetric modulo exponentially small errors in 1/h. This simple result was inspired by a numerical experiment and we describe the numerical scheme for an efficient computation of resonances in one dimension

Decision problem structuring method for the specification and selection of active fire protection systems

The UK along with the EU has witnessed a recent proliferation of designs for potential active fire suppression systems for the mitigation of fire risks in buildings and equipment; from five in 1986 (BSI, 1986) to eleven in 2011 (BSI, 2011a). However, each technology remains limited to the protection of certain types of application only, rather than offering a solution to guard against all possible hazards. This trend occurs at the same time as a transition from prescriptive to performance based standards and against the backdrop of the current nonprescriptive regulatory frameworks including the Building Regulations (HMSO, 2010), The Regulatory (fire) Reform Order (HMSO, 2005) and associated guidance (Approved Documents, standards, codes of practice and guides). Hazards can be difficult to assess and describe and the inequality or absence of satisfactory methods is notable in many recently published guidance documents. Active fire protection systems are installed to meet legislative requirements (to protect life), and / or when identified as appropriate by a cost-benefit analysis (e.g. to achieve risk reduction for business resilience purposes or to historic assets). There are many guidance documents available to assist users and designers in choosing and specifying appropriate active fire protection. These documents vary in age, relevance, scope, quality, impartiality and suitability. The Fire Protection Association (FPA) and several leading insurers who participate in its risk management work, have identified the requirement for assistance with the decision making process of analysing fire hazards and matching them to appropriate candidate systems, in order to make informed and impartial recommendations. This has led to the undertaking of a four year research project aimed at developing a decision problem structuring method and a software tool (Expert System), for the specification and selection of Active Fire Protection Systems. The research aim is to develop a tool that will assist users in making an informed selection of a system that is likely to best suit their needs and thereby contribute to overall improvements in fire safety and outcomes. This paper presents a summary of the work to date, focusing on the demand for the work, development of the methodology and practical application of the emerging Expert System

On the Lieb-Thirring constants L_gamma,1 for gamma geq 1/2

Let $E_i(H)$ denote the negative eigenvalues of the one-dimensional Schr\"odinger operator $Hu:=-u^{\prime\prime}-Vu,\ V\geq 0,$ on $L_2({\Bbb R})$. We prove the inequality \sum_i|E_i(H)|^\gamma\leq L_{\gamma,1}\int_{\Bbb R} V^{\gamma+1/2}(x)dx, (1) for the "limit" case $\gamma=1/2.$ This will imply improved estimates for the best constants $L_{\gamma,1}$ in (1), as $1/2<\gamma<3/2.Comment: AMS-LATEX, 15 page

Development of a fixed firefighting system selection tool for improved outcomes

The UK along with the European Union has experienced a recent proliferation in design approaches for potential fixed firefighting systems. Such systems are installed to mitigate fire hazards in buildings and equipment. In the UK, for example there were five general design approaches to fixed firefighting systems protection in 1986. This had increased to eleven in 2011. This is against the backdrop of the current non-prescriptive regulatory frameworks including the Building Regulations, the repeal of so-called ‘local acts’, the Regulatory (fire) Reform Order and associated guidance (Approved Documents, standards, codes of practice and guides). In response to this trend, as was intended, the market place is becoming increasingly competitive. However, the capability of each technology remains limited to protection against certain hazards, rather than offering a solution to guard against all possible scenarios. When selecting a fixed firefighting system, fire hazards and interactions can be difficult to assess and describe and the inequality or absence of satisfactory methods is notable in many recently published guidance documents. The absence of good quality guidance for non-expert practitioners (specifiers) and regulatory changes means a good quality source of impartial and expert knowledge is increasingly desirable. The challenge is to amass this knowledge and render it in an accessible format to the non-expert user. This paper reports on progress to-date; understanding the problem, amassing and structuring the knowledge base and developing a suitable knowledge management tool

Trace elements in magnetite from massive iron oxide-apatite deposits indicate a combined formation by igneous and magmatic-hydrothermal processes

Iron oxide-apatite (IOA) deposits are an important source of iron and other elements (e.g., REE, P, U, Ag and Co) vital to modern society. However, their formation, including the namesake Kiruna-type IOA deposit (Sweden), remains controversial. Working hypotheses include a purely magmatic origin involving separation of an Fe-, P-rich, volatile-rich oxide melt from a Si-rich silicate melt, and precipitation of magnetite from an aqueous ore fluid, which is either of magmatic-hydrothermal or non-magmatic surface or metamorphic origin. In this study, we focus on the geochemistry of magnetite from the Cretaceous Kiruna-type Los Colorados IOA deposit (~350. Mt Fe) located in the northern Chilean Iron Belt. Los Colorados has experienced minimal hydrothermal alteration that commonly obscures primary features in IOA deposits. Laser ablation-inductively coupled plasma-mass spectroscopy (LA-ICP-MS) transects and electron probe micro-analyzer (EPMA) wavelength-dispersive X-ray (WDX) spectrometry mapping demonstrate distinct chemical zoning in magnetite grains, wherein cores are enriched in Ti, Al, Mn and Mg. The concentrations of these trace elements in magnetite cores are consistent with igneous magnetite crystallized from a silicate melt, whereas magnetite rims show a pronounced depletion in these elements, consistent with magnetite grown from an Fe-rich magmatic-hydrothermal aqueous fluid. Further, magnetite grains contain polycrystalline inclusions that re-homogenize at magmatic temperatures (>850. °C). Smaller inclusions (500. ppm) concentrations

Schwinger Terms and Cohomology of Pseudodifferential Operators

We study the cohomology of the Schwinger term arising in second quantization of the class of observables belonging to the restricted general linear algebra. We prove that, for all pseudodifferential operators in 3+1 dimensions of this type, the Schwinger term is equivalent to the ``twisted'' Radul cocycle, a modified version of the Radul cocycle arising in non-commutative differential geometry. In the process we also show how the ordinary Radul cocycle for any pair of pseudodifferential operators in any dimension can be written as the phase space integral of the star commutator of their symbols projected to the appropriate asymptotic component.Comment: 19 pages, plain te

Nontrivial eigenvalues of the Liouvillian of an open quantum system

We present methods of finding complex eigenvalues of the Liouvillian of an open quantum system. The goal is to find eigenvalues that cannot be predicted from the eigenvalues of the corresponding Hamiltonian. Our model is a T-type quantum dot with an infinitely long lead. We suggest the existence of the non-trivial eigenvalues of the Liouvillian in two ways: one way is to show that the original problem reduces to the problem of a two-particle Hamiltonian with a two-body interaction and the other way is to show that diagram expansion of the Green's function has correlation between the bra state and the ket state. We also introduce the integral equations equivalent to the original eigenvalue problem.Comment: 5 pages, 2 figures, proceeding

The signed loop approach to the Ising model: foundations and critical point

The signed loop method is a beautiful way to rigorously study the two-dimensional Ising model with no external field. In this paper, we explore the foundations of the method, including details that have so far been neglected or overlooked in the literature. We demonstrate how the method can be applied to the Ising model on the square lattice to derive explicit formal expressions for the free energy density and two-point functions in terms of sums over loops, valid all the way up to the self-dual point. As a corollary, it follows that the self-dual point is critical both for the behaviour of the free energy density, and for the decay of the two-point functions.Comment: 38 pages, 7 figures, with an improved Introduction. The final publication is available at link.springer.co