Macdonald Polynomials from Sklyanin Algebras: A Conceptual Basis for the pp-Adics-Quantum Group Connection

We establish a previously conjectured connection between $p$-adics and quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra and its generalizations, the conceptual basis for the Macdonald polynomials, which ``interpolate'' between the zonal spherical functions of related real and $p$\--adic symmetric spaces. The elliptic quantum algebras underlie the $Z_n$\--Baxter models. We show that in the n \air \infty limit, the Jost function for the scattering of {\em first} level excitations in the $Z_n$\--Baxter model coincides with the Harish\--Chandra\--like $c$\--function constructed from the Macdonald polynomials associated to the root system $A_1$. The partition function of the $Z_2$\--Baxter model itself is also expressed in terms of this Macdonald\--Harish\--Chandra\ $c$\--function, albeit in a less simple way. We relate the two parameters $q$ and $t$ of the Macdonald polynomials to the anisotropy and modular parameters of the Baxter model. In particular the $p$\--adic ``regimes'' in the Macdonald polynomials correspond to a discrete sequence of XXZ models. We also discuss the possibility of ``$q$\--deforming'' Euler products.Comment: 25 page

The role of matter density uncertainties in the analysis of future neutrino factory experiments

Matter density uncertainties can affect the measurements of the neutrino oscillation parameters at future neutrino factory experiments, such as the measurements of the mixing parameters $\theta_{13}$ and \deltacp. We compare different matter density uncertainty models and discuss the possibility to include the matter density uncertainties in a complete statistical analysis. Furthermore, we systematically study in which measurements and where in the parameter space matter density uncertainties are most relevant. We illustrate this discussion with examples that show the effects as functions of different magnitudes of the matter density uncertainties. We find that matter density uncertainties are especially relevant for large \stheta \gtrsim 10^{-3}. Within the KamLAND-allowed range, they are most relevant for the precision measurements of \stheta and \deltacp, but less relevant for ``binary'' measurements, such as for the sign of \ldm, the sensitivity to \stheta, or the sensitivity to maximal CP violation. In addition, we demonstrate that knowing the matter density along a specific baseline better than to about 1% precision means that all measurements will become almost independent of the matter density uncertainties.Comment: 21 pages, 7 figures, LaTeX. Final version to be published in Phys. Rev.

Eureka and beyond: mining's impact on African urbanisation

This collection brings separate literatures on mining and urbanisation together at a time when both artisanal and large-scale mining are expanding in many African economies. While much has been written about contestation over land and mineral rights, the impact of mining on settlement, notably its catalytic and fluctuating effects on migration and urban growth, has been largely ignored. African nation-states’ urbanisation trends have shown considerable variation over the past half century. The current surge in ‘new’ mining countries and the slow-down in ‘old’ mining countries are generating some remarkable settlement patterns and welfare outcomes. Presently, the African continent is a laboratory of national mining experiences. This special issue on African mining and urbanisation encompasses a wide cross-section of country case studies: beginning with the historical experiences of mining in Southern Africa (South Africa, Zambia, Zimbabwe), followed by more recent mineralizing trends in comparatively new mineral-producing countries (Tanzania) and an established West African gold producer (Ghana), before turning to the influence of conflict minerals (Angola, the Democratic Republic of Congo and Sierra Leone)

Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz

We construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as ``${\bf T}$-operators'', act in highest weight Virasoro modules. The ${\bf T}$-operators depend on the spectral parameter $\lambda$ and their expansion around $\lambda = \infty$ generates an infinite set of commuting Hamiltonians of the quantum KdV system. The ${\bf T}$-operators can be viewed as the continuous field theory versions of the commuting transfer-matrices of integrable lattice theory. In particular, we show that for the values $c=1-3{{(2n+1)^2}\over {2n+3}} , n=1,2,3,...$of the Virasoro central charge the eigenvalues of the ${\bf T}$-operators satisfy a closed system of functional equations sufficient for determining the spectrum. For the ground-state eigenvalue these functional equations are equivalent to those of massless Thermodynamic Bethe Ansatz for the minimal conformal field theory ${\cal M}_{2,2n+3}$; in general they provide a way to generalize the technique of Thermodynamic Bethe Ansatz to the excited states. We discuss a generalization of our approach to the cases of massive field theories obtained by perturbing these Conformal Field Theories with the operator $\Phi_{1,3}$. The relation of these ${\bf T}$-operators to the boundary states is also briefly described.Comment: 24 page

Non-standard Hamiltonian effects on neutrino oscillations

We investigate non-standard Hamiltonian effects on neutrino oscillations, which are effective additional contributions to the vacuum or matter Hamiltonian. Since these effects can enter in either flavor or mass basis, we develop an understanding of the difference between these bases representing the underlying theoretical model. In particular, the simplest of these effects are classified as ``pure'' flavor or mass effects, where the appearance of such a ``pure'' effect can be quite plausible as a leading non-standard contribution from theoretical models. Compared to earlier studies investigating particular effects, we aim for a top-down classification of a possible ``new physics'' signature at future long-baseline neutrino oscillation precision experiments. We develop a general framework for such effects with two neutrino flavors and discuss the extension to three neutrino flavors, as well as we demonstrate the challenges for a neutrino factory to distinguish the theoretical origin of these effects with a numerical example. We find how the precision measurement of neutrino oscillation parameters can be altered by non-standard effects alone (not including non-standard interactions in the creation and detection processes) and that the non-standard effects on Hamiltonian level can be distinguished from other non-standard effects (such as neutrino decoherence and decay) if we consider specific imprint of the effects on the energy spectra of several different oscillation channels at a neutrino factory.Comment: 30 pages, 6 figures, LaTeX, final version, published in Eur.Phys.J.

Universally Coupled Massive Gravity, II: Densitized Tetrad and Cotetrad Theories

Einstein's equations in a tetrad formulation are derived from a linear theory in flat spacetime with an asymmetric potential using free field gauge invariance, local Lorentz invariance and universal coupling. The gravitational potential can be either covariant or contravariant and of almost any density weight. These results are adapted to produce universally coupled massive variants of Einstein's equations, yielding two one-parameter families of distinct theories with spin 2 and spin 0. The theories derived, upon fixing the local Lorentz gauge freedom, are seen to be a subset of those found by Ogievetsky and Polubarinov some time ago using a spin limitation principle. In view of the stability question for massive gravities, the proven non-necessity of positive energy for stability in applied mathematics in some contexts is recalled. Massive tetrad gravities permit the mass of the spin 0 to be heavier than that of the spin 2, as well as lighter than or equal to it, and so provide phenomenological flexibility that might be of astrophysical or cosmological use.Comment: 2 figures. Forthcoming in General Relativity and Gravitatio

Supercoherent States, Super K\"ahler Geometry and Geometric Quantization

Generalized coherent states provide a means of connecting square integrable representations of a semi-simple Lie group with the symplectic geometry of some of its homogeneous spaces. In the first part of the present work this point of view is extended to the supersymmetric context, through the study of the OSp(2/2) coherent states. These are explicitly constructed starting from the known abstract typical and atypical representations of osp(2/2). Their underlying geometries turn out to be those of supersymplectic OSp(2/2) homogeneous spaces. Moment maps identifying the latter with coadjoint orbits of OSp(2/2) are exhibited via Berezin's symbols. When considered within Rothstein's general paradigm, these results lead to a natural general definition of a super K\"ahler supermanifold, the supergeometry of which is determined in terms of the usual geometry of holomorphic Hermitian vector bundles over K\"ahler manifolds. In particular, the supergeometry of the above orbits is interpreted in terms of the geometry of Einstein-Hermitian vector bundles. In the second part, an extension of the full geometric quantization procedure is applied to the same coadjoint orbits. Thanks to the super K\"ahler character of the latter, this procedure leads to explicit super unitary irreducible representations of OSp(2/2) in super Hilbert spaces of $L^2$ superholomorphic sections of prequantum bundles of the Kostant type. This work lays the foundations of a program aimed at classifying Lie supergroups' coadjoint orbits and their associated irreducible representations, ultimately leading to harmonic superanalysis. For this purpose a set of consistent conventions is exhibited.Comment: 53 pages, AMS-LaTeX (or LaTeX+AMSfonts

Experimental Study of the Shortest Reset Word of Random Automata

In this paper we describe an approach to finding the shortest reset word of a finite synchronizing automaton by using a SAT solver. We use this approach to perform an experimental study of the length of the shortest reset word of a finite synchronizing automaton. The largest automata we considered had 100 states. The results of the experiments allow us to formulate a hypothesis that the length of the shortest reset word of a random finite automaton with $n$ states and 2 input letters with high probability is sublinear with respect to $n$ and can be estimated as $1.95 n^{0.55}.

Event-by-event fluctuations of average transverse momentum in central Pb+Pb collisions at 158 GeV per nucleon

We present first data on event-by-event fluctuations in the average transverse momentum of charged particles produced in Pb+Pb collisions at the CERN SPS. This measurement provides previously unavailable information allowing sensitive tests of microscopic and thermodynamic collision models and to search for fluctuations expected to occur in the vicinity of the predicted QCD phase transition. We find that the observed variance of the event-by-event average transverse momentum is consistent with independent particle production modified by the known two-particle correlations due to quantum statistics and final state interactions and folded with the resolution of the NA49 apparatus. For two specific models of non-statistical fluctuations in transverse momentum limits are derived in terms of fluctuation amplitude. We show that a significant part of the parameter space for a model of isospin fluctuations predicted as a consequence of chiral symmetry restoration in a non-equilibrium scenario is excluded by our measurement.Comment: 6 pages, 2 figures, submitted to Phys. Lett.

Gravitational excitons from extra dimensions

Inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold are investigated under dimensional reduction. In the Einstein conformal frame, small excitations of the scale factors of the internal spaces near minima of an effective potential have a form of massive scalar fields in the external space-time. Parameters of models which ensure minima of the effective potentials are obtained for particular cases and masses of gravitational excitons are estimated.Comment: Revised version --- 12 references added, Introduction enlarged, 20 pages, LaTeX, to appear in Phys.Rev.D56 (15.11.97