Generating-function method for fusion rules

This is the second of two articles devoted to an exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper focuses on fusion rules, using the machinery developed for tensor products in the companion article. Although the Kac-Walton algorithm provides a method for constructing a fusion generating function from the corresponding tensor-product generating function, we describe a more powerful approach which starts by first defining the set of fusion elementary couplings from a natural extension of the set of tensor-product elementary couplings. A set of inequalities involving the level are derived from this set using Farkas' lemma. These inequalities, taken in conjunction with the inequalities defining the tensor products, define what we call the fusion basis. Given this basis, the machinery of our previous paper may be applied to construct the fusion generating function. New generating functions for sp(4) and su(4), together with a closed form expression for their threshold levels are presented.Comment: Harvmac (b mode : 47 p) and Pictex; to appear in J. Math. Phy

Equivalent qubit dynamics under classical and quantum noise

We study the dynamics of quantum systems under classical and quantum noise, focusing on decoherence in qubit systems. Classical noise is described by a random process leading to a stochastic temporal evolution of a closed quantum system, whereas quantum noise originates from the coupling of the microscopic quantum system to its macroscopic environment. We derive deterministic master equations describing the average evolution of the quantum system under classical continuous-time Markovian noise and two sets of master equations under quantum noise. Strikingly, these three equations of motion are shown to be equivalent in the case of classical random telegraph noise and proper quantum environments. Hence fully quantum-mechanical models within the Born approximation can be mapped to a quantum system under classical noise. Furthermore, we apply the derived equations together with pulse optimization techniques to achieve high-fidelity one-qubit operations under random telegraph noise, and hence fight decoherence in these systems of great practical interest.Comment: 5 pages, 2 figures; converted to PRA format, added Fig. 2, corrected typo

Effects of Naltrexone on Pain Sensitivity and Mood in Fibromyalgia: No Evidence for Endogenous Opioid Pathophysiology

The pathophysiological mechanisms underlying fibromyalgia are still unknown, although some evidence points to endogenous opioid dysfunction. We examined how endogenous opioid antagonism affects pain and mood for women with and without fibromyalgia. Ten women with fibromyalgia and ten age- and gender-matched, healthy controls each attended two laboratory sessions. Each participant received naltrexone (50mg) at one session, and placebo at the other session, in a randomized and double-blind fashion. Participants were tested for changes in sensitivity to heat, cold, and mechanical pain. Additionally, we collected measures of mood and opioid withdrawal symptoms during the laboratory sessions and at home the night following each session. At baseline, the fibromyalgia group exhibited more somatic complaints, greater sensory sensitivity, more opioid withdrawal somatic symptoms, and lower mechanical and cold pain-tolerance than did the healthy control group. Neither group experienced changes in pain sensitivity due to naltrexone administration. Naltrexone did not differentially affect self-reported withdrawal symptoms, or mood, in the fibromyalgia and control groups. Consistent with prior research, there was no evidence found for abnormal endogenous opioid activity in women with fibromyalgia

Generating-function method for tensor products

This is the first of two articles devoted to a exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit of fusions rules. We start by reviewing Sharp's character method. An alternative approach to the construction of tensor-product generating functions is then presented which overcomes most of the technical difficulties associated with the character method. It is based on the reformulation of the problem of calculating tensor products in terms of the solution of a set of linear and homogeneous Diophantine equations whose elementary solutions represent ``elementary couplings''. Grobner bases provide a tool for generating the complete set of relations between elementary couplings and, most importantly, as an algorithm for specifying a complete, compatible set of ``forbidden couplings''.Comment: Harvmac (b mode : 39 p) and Pictex; this is a substantially reduced version of hep-th/9811113 (with new title); to appear in J. Math. Phy

Managerial decision making under uncertainty: the case of Twenty20 cricket

We consider managerial decision making by examining the impact of decisions taken by cricket captains on Twenty20 International (T20I) match outcomes. In particular, we examine whether pressure from external commentators is associated with suboptimal decision making by captains. Using data from over 300 T20I matches, we find little evidence that either winning the toss or choosing to bat first improves the likelihood of winning. Despite this, we find that captains in T20I cricket are significantly more likely to choose to bat rather than bowl after winning the toss, a finding that is consistent with social pressure constraining captains’ decision making

Molecular mode-coupling theory applied to a liquid of diatomic molecules

We study the molecular mode coupling theory for a liquid of diatomic molecules. The equations for the critical tensorial nonergodicity parameters ${\bf F}_{ll'}^m(q)$ and the critical amplitudes of the $\beta$ - relaxation ${\bf H}_{ll'}^m(q)$ are solved up to a cut off $l_{co}$ = 2 without any further approximations. Here $l,m$ are indices of spherical harmonics. Contrary to previous studies, where additional approximations were applied, we find in agreement with simulations, that all molecular degrees of freedom vitrify at a single temperature $T_c$. The theoretical results for the non ergodicity parameters and the critical amplitudes are compared with those from simulations. The qualitative agreement is good for all molecular degrees of freedom. To study the influence of the cut off on the non ergodicity parameter, we also calculate the non ergodicity parameters for an upper cut off $l_{co}=4$. In addition we also propose a new method for the calculation of the critical nonergodicity parameterComment: 27 pages, 17 figure

Lie group weight multiplicities from conformal field theory

Dominant weight multiplicities of simple Lie groups are expressed in terms of the modular matrices of Wess-Zumino-Witten conformal field theories, and related objects. Symmetries of the modular matrices give rise to new relations among multiplicities. At least for some Lie groups, these new relations are strong enough to completely fix all multiplicities.Comment: 12 pages, Plain TeX, no figure

Berenstein-Zelevinsky triangles, elementary couplings and fusion rules

We present a general scheme for describing su(N)_k fusion rules in terms of elementary couplings, using Berenstein-Zelevinsky triangles. A fusion coupling is characterized by its corresponding tensor product coupling (i.e. its Berenstein-Zelevinsky triangle) and the threshold level at which it first appears. We show that a closed expression for this threshold level is encoded in the Berenstein-Zelevinsky triangle and an explicit method to calculate it is presented. In this way a complete solution of su(4)_k fusion rules is obtained.Comment: 14 page

Planning and Public Health professionals’ experiences of using the planning system to regulate hot food takeaway outlets in England: A qualitative study

Takeaway food outlets offer limited seating and sell hot food to be consumed away from their premises. They typically serve energy-dense, nutrient-poor food. National planning guidelines in England offer the potential for local planning policies to promote healthier food environments through regulation of takeaway food outlets. Around half of English local government areas use this approach, but little is known about the process of adoption. We aimed to explore experiences and perceived success of planning policy adoption. In 2018 we recruited Planning and Public Health professionals from 16 local government areas in England and completed 26 telephone interviews. We analysed data with a thematic analysis approach. Participants felt that planning policy adoption was appropriate and can successfully regulate takeaway food outlets with the intention to improve health. They identified several facilitators and barriers towards adoption. Facilitators included internal co-operation between Planning and Public Health departments, and precedent for planning policy adoption set elsewhere. Barriers included “nanny-state” criticism, and difficulty demonstrating planning policy effectiveness. These could be considered in future guidelines to support widespread planning policy adoption

Test of mode coupling theory for a supercooled liquid of diatomic molecules. II. q-dependent orientational correlators

Using molecular dynamics computer simulations we study the dynamics of a molecular liquid by means of a general class of time-dependent correlators S_{ll'}^m(q,t) which explicitly involve translational (TDOF) and orientational degrees of freedom (ODOF). The system is composed of rigid, linear molecules with Lennard- Jones interactions. The q-dependence of the static correlators S_{ll'}^m(q) strongly depend on l, l' and m. The time dependent correlators are calculated for l=l'. A thorough test of the predictions of mode coupling theory (MCT) is performed for S_{ll}^m(q,t) and its self part S_{ll}^{(s)m}(q,t), for l=1,..,6. We find a clear signature for the existence of a single temperature T_c, at which the dynamics changes significantly. The first scaling law of MCT, which involves the critical correlator G(t), holds for l>=2, but no critical law is observed. Since this is true for the same exponent parameter lambda as obtained for the TDOF, we obtain a consistent description of both, the TDOF and ODOF, with the exception of l=1. This different behavior for l \ne 1 and l=1 can also be seen from the corresponding susceptibilities (chi'')_{ll}^m(q,omega) which exhibit a minimum at about the same frequency omega_{min} for all q and all l \ne 1, in contrast to (chi'')_{11}^m(q,omega) for which omega'_{min} approx 10 omega_{min} . The asymptotic regime, for which the first scaling law holds, shrinks with increasing l. The second scaling law of MCT (time-temperature superposition principle) is reasonably fulfilled for l \ne 1 but not for l=1. Furthermore we show that the q- and (l,m)-dependence of the self part approximately factorizes, i.e. S_{ll}^{(s)m}(q,t) \cong C_l^{(s)}(t) F_s(q,t) for all m.Comment: 11 pages of RevTex, 16 figure