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Multiplicity dependence of inclusive J/ψ production at midrapidity in pp collisions at √s = 13 TeV
(2020)
Measurements of the inclusive J/ψ yield as a function of charged-particle pseudorapidity density dNch/dη in pp collisions at √s = 13 TeV with ALICE at the LHC are reported. The J/ψ meson yield is measured at midrapidity (|y| < 0.9) in the dielectron channel, for events selected based on the charged-particle multiplicity at midrapidity (|η| < 1) and at forward rapidity (−3.7 < η < −1.7 and 2.8 < η < 5.1); both observables are normalized to their corresponding averages in minimum bias events. The increase of the normalized J/ψ yield with normalized dNch/dη is significantly stronger than linear and dependent on the transverse momentum. The data are compared to theoretical predictions, which describe the observed trends well, albeit not always quantitatively.
The inclusive charged particle transverse momentum distribution is measured in proton–proton collisions at s=900 GeV at the LHC using the ALICE detector. The measurement is performed in the central pseudorapidity region (|η|<0.8) over the transverse momentum range 0.15<pT<10 GeV/c. The correlation between transverse momentum and particle multiplicity is also studied. Results are presented for inelastic (INEL) and non-single-diffractive (NSD) events. The average transverse momentum for |η|<0.8 is 〈pT〉INEL=0.483±0.001 (stat.)±0.007 (syst.) GeV/c and 〈pT〉NSD=0.489±0.001 (stat.)±0.007 (syst.) GeV/c, respectively. The data exhibit a slightly larger 〈pT〉 than measurements in wider pseudorapidity intervals. The results are compared to simulations with the Monte Carlo event generators PYTHIA and PHOJET.
In this short note on my talk I want to point out the mathematical difficulties that arise in the study of the relation of Wightman and Euclidean quantum field theory, i.e., the relation between the hierarchies of Wightman and Schwinger functions. The two extreme cases where the reconstructed Wightman functions are either tempered distributions - the well-known Osterwalder-Schrader reconstruction - or modified Fourier hyperfunctions are discussed in some detail. Finally, some perpectives towards a classification of Euclidean reconstruction theorems are outlined and preliminary steps in that direction are presented.
We present a method for the construction of a Krein space completion for spaces of test functions, equipped with an indefinite inner product induced by a kernel which is more singular than a distribution of finite order. This generalizes a regularization method for infrared singularities in quantum field theory, introduced by G. Morchio and F. Strocchi, to the case of singularites of infinite order. We give conditions for the possibility of this procedure in terms of local differential operators and the Gelfand-Shilov test function spaces, as well as an abstract sufficient condition. As a model case we construct a maximally positive definite state space for the Heisenberg algebra in the presence of an infinite infrared singularity. See the corresponding paper: Schmidt, Andreas U.: "Mathematical Problems of Gauge Quantum Field Theory: A Survey of the Schwinger Model" and the presentation "Infinite Infrared Regularization in Krein Spaces"
This extended write-up of a talk gives an introductory survey of mathematical problems of the quantization of gauge systems. Using the Schwinger model as an exactly tractable but nontrivial example which exhibits general features of gauge quantum field theory, I cover the following subjects: The axiomatics of quantum field theory, formulation of quantum field theory in terms of Wightman functions, reconstruction of the state space, the local formulation of gauge theories, indefiniteness of the Wightman functions in general and in the special case of the Schwinger model, the state space of the Schwinger model, special features of the model. New results are contained in the Mathematical Appendix, where I consider in an abstract setting the Pontrjagin space structure of a special class of indefinite inner product spaces - the so called quasi-positive ones. This is motivated by the indefinite inner product space structure appearing in the above context and generalizes results of Morchio and Strocchi [J. Math. Phys. 31 (1990) 1467], and Dubin and Tarski [J. Math. Phys. 7 (1966) 574]. See the corresponding paper: Schmidt, Andreas U.: "Infinite Infrared Regularization and a State Space for the Heisenberg Algebra" and the presentation "Infinite Infrared Regularization in Krein Spaces".
Presentation at the AMS Southeastern Sectional Meeting 14-16 March 2003, and the Workshop Asymptotic Analysis, Stability, and Generalized Functions', 17-19 March 2003, Louisiana State University, Baton Rouge, Louisiana. See the corresponding papers "Mathematical Problems of Gauge Quantum Field Theory: A Survey of the Schwinger Model" and "Infinite Infrared Regularization and a State Space for the Heisenberg Algebra".
Wir führen eine neue Unterklasse der Fourier Hyperfunktionen mit polynomialen Wachstumsbedingungen ein mit dem Ziel, asymptotische Entwicklungen von Hyperfunktionen studieren zu wollen, wie sie für gewisse Distributionenklassen bekannt sind. Wir entwickeln zuerst die Theorie analytischer Funktionale auf Räumen integrabler Funktionen bezüglich Maßen mit Wachstum O(|Re z|^gamma), wobei gamma in R ist, im Unendlichen. Ein an das berühmte Phragmén-Lindelöf-Prinzip erinnerndes, einfaches analytisches Resultat bildet die Basis der Dualitätstheorie dieser Räume zu Funktionen mit festgelegtem Wachstumstyp. Wir studieren diese Dualität analytischer Funktionale mit Wachstumsbedingungen und unbeschränkten Trägern gründlich in einer Dimension unter Verwendung des von den Fourier Hyperfunktionen her bekannten exponentiell abfallenden Cauchy-Hilbert-Kerns. Daraus ergeben sich Analoga zu den Theoremen von Runge und Mittag-Leffler, die die Grundlage für die Garbentheorie der Hyperfunktionen mit polynomialen Wachstumsbedingungen sind, die wir sodann entwickeln. Die für uns wichtigsten neuen Klassen von Fourier Hyperfunktionen sind die von unendlichem Typ, das heißt solche, die wie eine beliebige Potenz wachsen beziehungsweise schneller als jede Potenz abfallen. In n Dimensionen benutzen wir die Fouriertransformation und Dualität um das Verhältnis dieser temperierten beziehungsweise asymptotischen Hyperfunktionen zu bekannten Distributionenräumen zu studieren. Wir leiten Theoreme vom Paley-Wiener-Typ her, die es uns erlauben, unsere Hyperfunktionen in ein Schema zu ordnen, das Wachstumsordnung und Singularität gegenüberstellt. Wir zeigen, daß dieses Schema eine sinvolle Erweiterung des von Gelfand und Shilow zur Charakterisierung von Testfunktionenräumen eingeführten Schemas der Räume S(alpha,beta) um verallgemeinerte Funktionen ist. Schließlich zeigen wir die Nuklearität der temperierten und asymptotischen Hyperfunktionen. Wir zeigen, daß die asymptotischen Hyperfunktionen genau die Klasse bilden, die Moment-asymptotische Entwicklungen erlauben, wie sie von Estrada et al. für Distributionen betrachtet wurden. Estradas Theorie ist damit ein Spezialfall der unsrigen. Für Hyperfunktionen lassen sich aber dank des Konzeptes der standard definierenden Funktionen die Moment-asymptotischen Entwicklungen als klassische asymptotische Entwicklungen von analytischen Funktionen verstehen. Wir zeigen die einfache Beziehung zwischen der Moment-asymptotischen Entwicklung und der Taylorentwicklung der Fouriertransformierten und benutzen dann ein Resultat von Estrada, um die Vollständigkeit unseres Moment-asymptotischen Schemas abzuleiten. Wir geben genaue Bedingungen für die Moment-Folgen von Hyperfunktionen mit kompaktem Träger an, die kürzlich von Kim et al. gefunden wurden. Die asymptotischen Entwicklungen übertragen wir auf den höherdimensionalen Fall, indem wir die von Kaneko und Takiguchi eingeführte Radontransformation für Hyperfunktionen verwenden. Die wohlbekannte Beziehung zwischen Radon- und Fouriertransformation zeigt wiederum das enge Verhältnis von asymptotischer Entwicklung zur Taylorentwicklung der Fouriertransformierten. Wir benutzen Kims Resultate, um die Moment-Folgen von Hyperfunktionen zu charakterisieren, die von Kugeln mit endlichem Radius getragen werden. Schließlich verwenden wir das Träger-Theorem der Radontransformation, um ein Resultat über das Singularitätenspektrum aus Bedingungen an die Radontransformierte abzuleiten.
Presentation at the Università di Pisa, Pisa, Itlay 3 July 2002, the conference on Irreversible Quantum Dynamics', the Abdus Salam ICTP, Trieste, Italy, 29 July - 2 August 2002, and the University of Natal, Pietermaritzburg, South Africa, 14 May 2003. Version of 24 April 2003: examples added; 16 December 2002: revised; 12 Sptember 2002. See the corresponding papers "Zeno Dynamics of von Neumann Algebras", "Zeno Dynamics in Quantum Statistical Mechanics" and "Mathematics of the Quantum Zeno Effect"
The dynamical quantum Zeno effect is studied in the context of von Neumann algebras. It is shown that the Zeno dynamics coincides with the modular dynamics of a localized subalgebra. This relates the modular operator of that subalgebra to the modular operator of the original algebra by a variant of the Kato-Lie-Trotter product formula.
We present an overview of the mathematics underlying the quantum Zeno effect. Classical, functional analytic results are put into perspective and compared with more recent ones. This yields some new insights into mathematical preconditions entailing the Zeno paradox, in particular a simplified proof of Misra's and Sudarshan's theorem. We empahsise the complex-analytic structures associated to the issue of existence of the Zeno dynamics. On grounds of the assembled material, we reason about possible future mathematical developments pertaining to the Zeno paradox and its counterpart, the anti-Zeno paradox, both of which seem to be close to complete characterisations. PACS-Klassifikation: 03.65.Xp, 03.65Db, 05.30.-d, 02.30.T . See the corresponding presentation: Schmidt, Andreas U.: "Zeno Dynamics of von Neumann Algebras" and "Zeno Dynamics in Quantum Statistical Mechanics"
We study the quantum Zeno effect in quantum statistical mechanics within the operator algebraic framework. We formulate a condition for the appearance of the effect in W*-dynamical systems, in terms of the short-time behaviour of the dynamics. Examples of quantum spin systems show that this condition can be effectively applied to quantum statistical mechanical models. Furthermore, we derive an explicit form of the Zeno generator, and use it to construct Gibbs equilibrium states for the Zeno dynamics. As a concrete example, we consider the X-Y model, for which we show that a frequent measurement at a microscopic level, e.g. a single lattice site, can produce a macroscopic effect in changing the global equilibrium. PACS - Klassifikation: 03.65.Xp, 05.30.-d, 02.30. See the corresponding papers: Schmidt, Andreas U.: "Zeno Dynamics of von Neumann Algebras" and "Mathematics of the Quantum Zeno Effect" and the talk "Zeno Dynamics in Quantum Statistical Mechanics" - http://publikationen.ub.uni-frankfurt.de/volltexte/2005/1167/
We reconsider estimates for the heat kernel on weighted graphs recently found by Metzger and Stollmann. In the case that the weights satisfy a positive lower bound as well as a finite upper bound, we obtain a specialized lower estimate and a proper generalization of a previous upper estimate. Reviews: Math. Rev. 1979406, Zbl. Math. 0934.46042
Denisovite is a rare mineral occurring as aggregates of fibres typically 200–500 nm diameter. It was confirmed as a new mineral in 1984, but important facts about its chemical formula, lattice parameters, symmetry and structure have remained incompletely known since then. Recently obtained results from studies using microprobe analysis, X-ray powder diffraction (XRPD), electron crystallography, modelling and Rietveld refinement will be reported. The electron crystallography methods include transmission electron microscopy (TEM), selected-area electron diffraction (SAED), high-angle annular dark-field imaging (HAADF), high-resolution transmission electron microscopy (HRTEM), precession electron diffraction (PED) and electron diffraction tomography (EDT). A structural model of denisovite was developed from HAADF images and later completed on the basis of quasi-kinematic EDT data by ab initio structure solution using direct methods and least-squares refinement. The model was confirmed by Rietveld refinement. The lattice parameters are a = 31.024 (1), b = 19.554 (1) and c = 7.1441 (5) Å, β = 95.99 (3)°, V = 4310.1 (5) Å3 and space group P12/a1. The structure consists of three topologically distinct dreier silicate chains, viz. two xonotlite-like dreier double chains, [Si6O17]10−, and a tubular loop-branched dreier triple chain, [Si12O30]12−. The silicate chains occur between three walls of edge-sharing (Ca,Na) octahedra. The chains of silicate tetrahedra and the octahedra walls extend parallel to the z axis and form a layer parallel to (100). Water molecules and K+ cations are located at the centre of the tubular silicate chain. The latter also occupy positions close to the centres of eight-membered rings in the silicate chains. The silicate chains are geometrically constrained by neighbouring octahedra walls and present an ambiguity with respect to their z position along these walls, with displacements between neighbouring layers being either Δz = c/4 or −c/4. Such behaviour is typical for polytypic sequences and leads to disorder along [100]. In fact, the diffraction pattern does not show any sharp reflections with l odd, but continuous diffuse streaks parallel to a* instead. Only reflections with l even are sharp. The diffuse scattering is caused by (100) nanolamellae separated by stacking faults and twin boundaries. The structure can be described according to the order–disorder (OD) theory as a stacking of layers parallel to (100).