Entropic Measure of Epistemic Uncertainties in Multibody System Models by Axiomatic Design

Directory of Open Access Journals (Sweden)

Francesco Villecco

2017-06-01

Full Text Available In this paper, the use of the MaxInf Principle in real optimization problems is investigated for engineering applications, where the current design solution is actually an engineering approximation. In industrial manufacturing, multibody system simulations can be used to develop new machines and mechanisms by using virtual prototyping, where an axiomatic design can be employed to analyze the independence of elements and the complexity of connections forming a general mechanical system. In the classic theories of Fisher and Wiener-Shannon, the idea of information is a measure of only probabilistic and repetitive events. However, this idea is broader than the probability alone field. Thus, the Wiener-Shannon’s axioms can be extended to non-probabilistic events and it is possible to introduce a theory of information for non-repetitive events as a measure of the reliability of data for complex mechanical systems. To this end, one can devise engineering solutions consistent with the values of the design constraints analyzing the complexity of the relation matrix and using the idea of information in the metric space. The final solution gives the entropic measure of epistemic uncertainties which can be used in multibody system models, analyzed with an axiomatic design.

A note on completeness of bounded lattices postulated in some axiomatics of the mathematical foundations of quantum theory

International Nuclear Information System (INIS)

Mukherjee, M.K.

1981-01-01

In an axiomatic study of quantum theory Jauch postulated the completeness of the lattice underlying a quantum logic. The theory of Baer semigroup is utilized to specify quite generally the completeness of the lattice. (author)

S-matrix theory of nuclear forces

International Nuclear Information System (INIS)

Vinh Mau, R.

1984-09-01

The use of the S-matrix theory for deriving the nucleon-nucleon interaction is reviewed. Fits to recent NN data are described. Applications to nuclear structure properties and nucleon-nucleus reactions are also discussed, and the results compared with data. 20 references

The early S-matrix theory and its propagation (1942-1952)

International Nuclear Information System (INIS)

Rechenberg, H.

1989-01-01

This paper describes the development of S-matrix theory in the 1940s and 1950s, which described the scattering and emission problems in elementary particle theory. Its chief architect, Werner Heisenberg, worked in Germany all through the Second World War. Communication problems were intense and made discussion of this useful tool very difficult. Werner Heisenberg's collaborative efforts with Hendrik Kramers in Holland and Christian Moeller are noted. The theory had its opponents and their objections are described. As other scientists took up the theory it was used in new ways such as in quantum electrodynamics, and to predict the creation of massive particles by analyzing S-matrix threshold behaviour. Although the theory fell into disfavour in the early 1950s, it was later readopted when ideas such as crossed channels and analytic behaviour in the complex angular-momentum plane needed explanations. (UK)

Causal theory in (2+1)-dimensional Qed

International Nuclear Information System (INIS)

Scharf, G.; Wreszinski, W.F.

1994-01-01

The program of constructing the S-matrix by means of causality in quantum field theory goes back to Stueckelberg and Bogoliubov. Epstein and Glaser proposed an axiomatic construct where ultraviolet divergences do not appear, leading directly to the renormalized perturbation series. They have shown that in the causal theory the UV problem is a consequence of incorrect distribution splitting. This paper studies the causal theory in (2+1)D Qed

Al- Khwarizmi and axiomatic foundation of algebra

International Nuclear Information System (INIS)

Fares, N.

2015-01-01

This paper intends to investigate the axiomatic foundations of algebra, as they were presented in the book of algebra of al-Khwarizmi (9 th century), and as they were developed in many subsequent Arabic works. The paper gives also a description of algebra evolution towards a discipline independent ofgeometry and arithmetic: the two disciplines whosemarriage had led to its birth.By an in depth reading of some details in the text of al Khwarizmi , we concluded that this mathematician intended to lay down the axiomatic foundations of that new discipline. His resort to arithmetical and geometrical means was a way of making his theory more accessible. He used them to justify the axioms: those that were not explicitly introduced per se, and those that were remained implicit. The paper also relies on some unedited writingsof al-Khwarizmi's successors, which could shedlight on the ways they used to consolidate the foundations of algebra and improve its methods. (author)

Adapt! – Agile Project Management Supported by Axiomatic Design

Directory of Open Access Journals (Sweden)

Weber Jakob

2017-01-01

Full Text Available This paper presents a novel approach for the use of Axiomatic Design Theory in combination with agile project management methods like Scrum for an effective, structured and combined product design and development process. Agile project management methods give a guideline how to manage a project, but there is only minor assistance regarding the actual product development process itself. Axiomatic Design can be used to support these methods in this point. In concrete terms, the results of the decomposition process of this theory can be used to formulate and structure the work packages for the agile project managing process. The Independence Axiom of Axiomatic Design Theory has a substantial contribution by ensuring the independence of the work packages which can be assigned to different project team members and can be processed independently by them. The combination of the different methods not only helps to ensure a good design solution but also helps to work more agile within a project team. The here proposed approach is one part of a holistic product design and development process for changeable production units – called Adapt! – and is described within a use case in the automotive sector.

Unitarity or asymptotic completeness equations and analytic structure of the S matrix and Green functions

International Nuclear Information System (INIS)

Iagolnitzer, D.

1983-11-01

Recent axiomatic results on the (non holonomic) analytic structure of the multiparticle S matrix and Green functions are reviewed and related general conjectures are described: (i) formal expansions of Green functions in terms of (holonomic) Feynman-type integrals in which each vertex represents an irreducible kernel, and (ii) ''graph by graph unitarity'' and other discontinuity formulae of the latter. These conjectures are closely linked with unitarity or asymptotic completeness equations, which they yield in a formal sense. In constructive field theory, a direct proof of the first conjecture (together with an independent proof of the second) would thus imply, as a first step, asymptotic completeness in that sense

Statistical theory of nuclear cross section fluctuations with account s-matrix unitarity

International Nuclear Information System (INIS)

Kun, S.Yu.

1985-01-01

Statistical properties of the S-matrix fluctuating part delta S=S- sub(T) in the T/D>>1, N>>1 Ericoson fluctuations mode are investigated. A unitary representation is used for the investigation of statistical properties of the S-matrix. The problem on correlation of fluctuating elements of the S-matrix is discussed. The S-matrix unitary representation allows one to strictly substantiates the assumptions of the Ericson fluctuations theory: a) the real and imaginary parts of the deltaS-matrix have identical dispersions, do not correlate and are distributed according to the normal law; 2) various deltaS-matrix elements do not correlate

Matrix analysis for associated consistency in cooperative game theory

NARCIS (Netherlands)

Xu Genjiu, G.; Driessen, Theo; Sun, H.; Sun, H.

Hamiache axiomatized the Shapley value as the unique solution verifying the inessential game property, continuity and associated consistency. Driessen extended Hamiache’s axiomatization to the enlarged class of efficient, symmetric, and linear values. In this paper, we introduce the notion of row

S matrix theory of the massive Thirring model

International Nuclear Information System (INIS)

Berg, B.

1980-01-01

The S matrix theory of the massive Thirring model, describing the exact quantum scattering of solitons and their boundstates, is reviewed. Treated are: Factorization equations and their solution, boundstates, generalized Jost functions and Levinson's theorem, scattering of boundstates, 'virtual' and anomalous thresholds. (orig.) 891 HSI/orig. 892 MKO

Intuition and the axiomatic method

CERN Document Server

Carson, Emily

2006-01-01

Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant's theory of intuition to be obsolete. But this only represents one side of the story concerning Kant, intuition and twentieth century science. Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. All of Hilbert, Gödel, Poincaré, Weyl and Bohr thought that intuition was an indispensable element in

Axiomatic design in large systems complex products, buildings and manufacturing systems

CERN Document Server

Suh, Nam

2016-01-01

This book provides a synthesis of recent developments in Axiomatic Design theory and its application in large complex systems. Introductory chapters provide concise tutorial materials for graduate students and new practitioners, presenting the fundamentals of Axiomatic Design and relating its key concepts to those of model-based systems engineering. A mathematical exposition of design axioms is also provided. The main body of the book, which represents a concentrated treatment of several applications, is divided into three parts covering work on: complex products; buildings; and manufacturing systems. The book shows how design work in these areas can benefit from the scientific and systematic underpinning provided by Axiomatic Design, and in so doing effectively combines the state of the art in design research with practice. All contributions were written by an international group of leading proponents of Axiomatic Design. The book concludes with a call to action motivating further research into the engineeri...

Compound nucleus in Livsic open-system theory: Factorization of the S matrix

International Nuclear Information System (INIS)

Avishai, Y.

1988-01-01

The compound-nucleus system fits into a mathematical theory of open systems in physics developed by the mathematician M. Livsic [Translations of Mathematical Monographs (American Mathematical Society, Providence, Rhode Island, 1973), Vol. 34]. In this article we review some basic concepts of the above theory and apply it to study the structure of the compound-nucleus S matrix. One of the results is a factorization of the S matrix in the form S(ω) = S +iA/sub k//(tau/sub k/-ω)], where A/sub k/ are known matrices and tau/sub k/ are the complex resonance energies

M(atrix) theory: matrix quantum mechanics as a fundamental theory

International Nuclear Information System (INIS)

Taylor, Washington

2001-01-01

This article reviews the matrix model of M theory. M theory is an 11-dimensional quantum theory of gravity that is believed to underlie all superstring theories. M theory is currently the most plausible candidate for a theory of fundamental physics which reconciles gravity and quantum field theory in a realistic fashion. Evidence for M theory is still only circumstantial -- no complete background-independent formulation of the theory exists as yet. Matrix theory was first developed as a regularized theory of a supersymmetric quantum membrane. More recently, it has appeared in a different guise as the discrete light-cone quantization of M theory in flat space. These two approaches to matrix theory are described in detail and compared. It is shown that matrix theory is a well-defined quantum theory that reduces to a supersymmetric theory of gravity at low energies. Although its fundamental degrees of freedom are essentially pointlike, higher-dimensional fluctuating objects (branes) arise through the non-Abelian structure of the matrix degrees of freedom. The problem of formulating matrix theory in a general space-time background is discussed, and the connections between matrix theory and other related models are reviewed

Axiomatizations of Pareto Equilibria in Multicriteria Games

NARCIS (Netherlands)

Voorneveld, M.; Vermeulen, D.; Borm, P.E.M.

1997-01-01

We focus on axiomatizations of the Pareto equilibrium concept in multicriteria games based on consistency.Axiomatizations of the Nash equilibrium concept by Peleg and Tijs (1996) and Peleg, Potters, and Tijs (1996) have immediate generalizations.The axiomatization of Norde et al.(1996) cannot be

Unconventional Algorithms: Complementarity of Axiomatics and Construction

Directory of Open Access Journals (Sweden)

Gordana Dodig Crnkovic

2012-10-01

Full Text Available In this paper, we analyze axiomatic and constructive issues of unconventional computations from a methodological and philosophical point of view. We explain how the new models of algorithms and unconventional computations change the algorithmic universe, making it open and allowing increased flexibility and expressive power that augment creativity. At the same time, the greater power of new types of algorithms also results in the greater complexity of the algorithmic universe, transforming it into the algorithmic multiverse and demanding new tools for its study. That is why we analyze new powerful tools brought forth by local mathematics, local logics, logical varieties and the axiomatic theory of algorithms, automata and computation. We demonstrate how these new tools allow efficient navigation in the algorithmic multiverse. Further work includes study of natural computation by unconventional algorithms and constructive approaches.

Axiomatic derivation of Feynman rules and related topics

International Nuclear Information System (INIS)

Dorfmeister, G.K.

1992-01-01

Previous results in axiomatic field theory by Steinmann and Epstein-Glaser establish the existence of the retarded and time ordered Green's functions in every order of perturbation. To connect these Green's functions with the ones calculated in canonical field theories via the Feynman rules, one has to consistently build them not just for every order of perturbation but for each specific graph. (open-quotes Consisentlyclose quotes means here that the Green functions associated with two open-quotes smallclose quotes graphs build up to the Green's functions of the open-quotes bigclose quotes graph formed by connecting the two open-quotes smallclose quotes ones). This paper shows that this can indeed be done; that in this sense the Feynman rules of perturbative Lagrangian field theory can be derived from the abstract, but physically very basic, principles of axiomatic field theory. All results hold only for massive field theories. The LSZ formalism, to the best knowledge of the author, has so far not been modified to admit mass zero fields. To make the representation simpler and more transparent, the author restricts the discussion to a single component, scalar Φ 4 interaction which is a part of the Standard Model of Particle Physics. Motivated by its role in particle physics, the author complements the perturbative study of Φ 4 -theory by reviewing the status of non-perturbative solutions to the theory in the final chapter

On the S-matrix of type-0 string theory

International Nuclear Information System (INIS)

DeWolfe, Oliver; Roiban, Radu; Spradlin, Marcus; Volovich, Anastasia; Walcher, Johannes

2003-01-01

The recent discovery of non-perturbatively stable two-dimensional string back-grounds and their dual matrix models allows the study of complete scattering matrices in string theory. In this note we adapt work of Moore, Plesser, and Ramgoolam on the bosonic string to compute the exact S-matrices of 0A and 0B string theory in two dimensions. Unitarity of the 0B theory requires the inclusion of massless soliton sectors carrying RR scalar charge as asymptotic states. We propose a regularization of IR divergences and find transition probabilities that distinguish the otherwise energetically degenerate soliton sectors. Unstable D-branes can decay into distinct soliton sectors. (author)

The semiclassical S-matrix theory of three body Coulomb break-up

International Nuclear Information System (INIS)

Chocian, P.

1999-01-01

Using semiclassical methods we investigate the threshold behaviour for 3-particle break-up of a system with one particle of charge Z and two other particles of charge -q. For the particular case where the ratio of the charges of the third particle to the wing particles is Z/q = 1/4, the Wannier exponent for break-up diverges and it is found that the threshold law changes from a power law to an exponential law of the form exp(-λ/√E) which is in agreement with other results. Wannier's threshold theory is extended analytically to above threshold energies and it is found that the classical law for the divergent case is identical to an analytical result from the quantal hidden crossing theory. Corrections to the threshold behaviour for hydrogen from the above-threshold derivation are compared with those predicted by a calculation from hidden crossing theory. Excellent agreement is found which confirms the success of our classical derivation. The threshold behaviour is tested using semiclassical S-matrix theory above the region of divergence and it is found that for Z/q - of the initial states in S-matrix theory translates to a uniform distribution of outgoing trajectories on the boundary of the reaction zone. Observations of classical trajectories suggest that the radius of the reaction zone (R b ) is dependent on the total energy of the system. R b is determined numerically from ionization trajectories. When the dependence on R b is included in half-collision calculations, cross sections are produced which are in excellent agreement with full-collision S-matrix results for all values of Z > 0.25. (author)

Elementary process theory axiomatic introduction and applications

CERN Document Server

Cabbolet, Marcoen J T F

2011-01-01

Modern physics lacks a unitary theory that applies to all four fundamental interactions. This PhD thesis is a proposal for a single, complete, and coherent scheme of mathematically formulated elementary laws of nature. While the first chapter presents the general background, the second chapter addresses the method by which the main result has been developed. The next three chapters rigorously introduce the Elementary Process Theory, its mathematical foundations, and its applications to physics, cosmology and philosophy of mind. The final two chapters discuss the results and present the conclusions. Summarizing, the Elementary Process Theory is a scheme of seven well-formed closed expressions, written in the mathematical language of set matrix theory – a generalization of Zermelo-Fraenkel set theory. In the physical world, these seven expressions can be interpreted as elementary principles governing the universe at supersmall scale. The author critically confronts the theory with Quantum Mechanics and Genera...

Alternative Axiomatic Characterizations of the Grey Shapley Value

Directory of Open Access Journals (Sweden)

Sirma Zeynep Alparslan Gok

2014-05-01

Full Text Available The Shapley value, one of the most common solution concepts of cooperative game theory is defined and axiomatically characterized in different game-theoretic models. Certainly, the Shapley value can be used in interesting sharing cost/reward problems in the Operations Research area such as connection, routing, scheduling, production and inventory situations. In this paper, we focus on the Shapley value for cooperative games, where the set of players is finite and the coalition values are interval grey numbers. The central question in this paper is how to characterize the grey Shapley value. In this context, we present two alternative axiomatic characterizations. First, we characterize the grey Shapley value using the properties of efficiency, symmetry and strong monotonicity. Second, we characterize the grey Shapley value by using the grey dividends.

The general theory of quantized fields in the 1950s

International Nuclear Information System (INIS)

Wightman, A.S.

1989-01-01

This review describes developments in theoretical particle physics in the 1950s which were important in the race to develop a putative general theory of quantized fields, especially ideas that offered a mathematically rigorous theory. Basic theoretical concepts then available included the Hamiltonian formulation of quantum dynamics, canonical quantization, perturbative renormalization theory and the theory of distributions. Following a description of various important theoretical contributions of this era, the review ends with a summary of the most important contributions of axiomatic field theory to concrete physics applications. (UK)

Quark Physics without Quarks: A Review of Recent Developments in S-Matrix Theory.

Science.gov (United States)

Capra, Fritjof

1979-01-01

Reviews the developments in S-matrix theory over the past five years which have made it possible to derive results characteristic of quark models without any need to postulate the existence of physical quarks. In the new approach, the quark patterns emerge as a consequence of combining the general S-matrix principles with the concept of order.…

Axiomatics of uniform space-time models

International Nuclear Information System (INIS)

Levichev, A.V.

1983-01-01

The mathematical statement of space-time axiomatics of the special theory of relativity is given; it postulates that the space-time M is the binding single boundary Hausedorf local-compact four-dimensional topological space with the given order. The theorem is proved: if the invariant order in the four-dimensional group M is given by the semi-group P, which contingency K contains inner points , then M is commutative. The analogous theorem is correct for the group of two and three dimensionalities

Supergravity duals of matrix string theory

International Nuclear Information System (INIS)

Morales, Jose F.; Samtleben, Henning

2002-01-01

We study holographic duals of type II and heterotic matrix string theories described by warped AdS 3 supergravities. By explicitly solving the linearized equations of motion around near horizon D-string geometries, we determine the spectrum of Kaluza-Klein primaries for type I, II supergravities on warped AdS 3 xS 7 . The results match those coming from the dual two-dimensional gauge theories living on the D-string worldvolumes. We briefly discuss the connections with the N=(8,8), N=(8,0) orbifold superconformal field theories to which type IIB/heterotic matrix strings flow in the infrared. In particular, we associate the dimension (h,h-bar) (32,32) twisted operator which brings the matrix string theories out from the conformal point (R; 8 ) N /S N with the dilaton profile in the supergravity background. The familiar dictionary between masses and 'scaling' dimensions of field and operators are modified by the presence of non-trivial warp factors and running dilatons. These modifications are worked out for the general case of domain wall/QFT correspondences between supergravities on warped AdS d+1 xS q geometries and super Yang-Mills theories with 16 supercharges. (author)

Generalized canonical formalism and the S-matrix of theories with constraints of the general type

International Nuclear Information System (INIS)

Fradkina, T.Ye.

1987-01-01

A canonical quantization method is given for systems with first and second class constraints of arbitrary rank. The effectiveness of the method is demonstrated using sample Yang-Mills and gravitational fields. A correct expression is derived for the S-matrix of theories that are momentum-quadratic within the scope of canonical gauges, including ghost fields. Generalized quantization is performed and the S-matrix is derived in configurational space for theories of relativistic membranes representing a generalization of theories of strings to the case of an extended spatial implementation. It is demonstrated that the theory of membranes in n+l-dimensional space is a system with rank-n constraints

Axiomatizing GSOS with Predicates

Directory of Open Access Journals (Sweden)

Luca Aceto

2011-08-01

Full Text Available In this paper, we introduce an extension of the GSOS rule format with predicates such as termination, convergence and divergence. For this format we generalize the technique proposed by Aceto, Bloom and Vaandrager for the automatic generation of ground-complete axiomatizations of bisimilarity over GSOS systems. Our procedure is implemented in a tool that receives SOS specifications as input and derives the corresponding axiomatizations automatically. This paves the way to checking strong bisimilarity over process terms by means of theorem-proving techniques.

Uncertainty and complementarity in axiomatic quantum mechanics

International Nuclear Information System (INIS)

Lahti, P.J.

1980-01-01

An investigation of the uncertainty principle and the complementarity principle is carried through. The physical content of these principles and their representation in the conventional Hilbert space formulation of quantum mechanics forms a natural starting point. Thereafter is presented more general axiomatic framework for quantum mechanics, namely, a probability function formulation of the theory. Two extra axioms are stated, reflecting the ideas of the uncertainty principle and the complementarity principle, respectively. The quantal features of these axioms are explicated. (author)

Elementary matrix theory

CERN Document Server

Eves, Howard

1980-01-01

The usefulness of matrix theory as a tool in disciplines ranging from quantum mechanics to psychometrics is widely recognized, and courses in matrix theory are increasingly a standard part of the undergraduate curriculum.This outstanding text offers an unusual introduction to matrix theory at the undergraduate level. Unlike most texts dealing with the topic, which tend to remain on an abstract level, Dr. Eves' book employs a concrete elementary approach, avoiding abstraction until the final chapter. This practical method renders the text especially accessible to students of physics, engineeri

Manning and Automation of Naval Surface Combatants: A Functional Allocation Approach Using Axiomatic Design Theory

National Research Council Canada - National Science Library

Szatkowski, John

2000-01-01

... undesirable effect on other functionally unrelated parameters. A methodology based on axiomatic design principles that strives to eliminate the currently accepted iterative nature of concept level ship design is proposed...

Progress in the application of classical S-matrix theory to inelastic collision processes

International Nuclear Information System (INIS)

McCurdy, C.W.; Miller, W.H.

1980-01-01

Methods are described which effectively solve two of the technical difficulties associated with applying classical S-matrix theory to inelastic/reactive scattering. Specifically, it is shown that rather standard numerical methods can be used to solve the ''root search'' problem (i.e., the nonlinear boundary value problem necessary to impose semiclassical quantum conditions at the beginning and the end of the classical trajectories) and also how complex classical trajectories, which are necessary to describe classically forbidden (i.e., tunneling) processes, can be computed in a numerically stable way. Application is made to vibrational relaxation of H 2 by collision with He (within the helicity conserving approximation). The only remaining problem with regard to applying classical S-matrix theory to complex collision processes has to do with the availability of multidimensional uniform asymptotic formulas for interpolating the ''primitive'' semiclassical expressions between their various regions of validity

Formal scattering theory approach to S-matrix relations in supersymmetric quantum mechanics

International Nuclear Information System (INIS)

Amado, R.D.; Cannata, F.; Dedonder, J.P.

1988-01-01

Combining the methods of scattering theory and supersymmetric quantum mechanics we obtain relations between the S matrix and its supersymmetric partner. These relations involve only asymptotic quantities and do not require knowledge of the dynamical details. For example, for coupled channels with no threshold differences the relations involve the asymptotic normalization constant of the bound state removed by supersymmetry

Minimal theory of quantum electrodynamics

International Nuclear Information System (INIS)

Berrondo, M.; Jauregui, R.

1986-01-01

Within the general framework of the Lehmann-Symanzik-Zimmermann axiomatic field theory, we obtain a simple and coherent formulation of quantum electrodynamics. The definitions of the current densities fulfill the one-particle stability condition, and the commutation relations for the interacting fields are obtained rather than being postulated a priori, thus avoiding the inconsistencies which appear in the canonical formalism. This is possible due to the fact that we use the integral form of the equations of motion in order to compute the propagators and the S matrix. The resulting spectral representations automatically fulfill the correct boundary conditions thus fixing the ubiquitous quasilocal operators in a unique fashion

Matrix analysis for associated consistency in cooperative game theory

NARCIS (Netherlands)

Xu, G.; Driessen, Theo; Sun, H.; Sun, H.

Hamiache's recent axiomatization of the well-known Shapley value for TU games states that the Shapley value is the unique solution verifying the following three axioms: the inessential game property, continuity and associated consistency. Driessen extended Hamiache's axiomatization to the enlarged

Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics.

Science.gov (United States)

Corry, Leo

2018-04-28

The sixth of Hilbert's famous 1900 list of 23 problems was a programmatic call for the axiomatization of the physical sciences. It was naturally and organically rooted at the core of Hilbert's conception of what axiomatization is all about. In fact, the axiomatic method which he applied at the turn of the twentieth century in his famous work on the foundations of geometry originated in a preoccupation with foundational questions related with empirical science in general. Indeed, far from a purely formal conception, Hilbert counted geometry among the sciences with strong empirical content, closely related to other branches of physics and deserving a treatment similar to that reserved for the latter. In this treatment, the axiomatization project was meant to play, in his view, a crucial role. Curiously, and contrary to a once-prevalent view, from all the problems in the list, the sixth is the only one that continually engaged Hilbet's efforts over a very long period of time, at least between 1894 and 1932.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Massive IIA string theory and Matrix theory compactification

International Nuclear Information System (INIS)

Lowe, David A.; Nastase, Horatiu; Ramgoolam, Sanjaye

2003-01-01

We propose a Matrix theory approach to Romans' massive Type IIA supergravity. It is obtained by applying the procedure of Matrix theory compactifications to Hull's proposal of the massive Type IIA string theory as M-theory on a twisted torus. The resulting Matrix theory is a super-Yang-Mills theory on large N three-branes with a space-dependent noncommutativity parameter, which is also independently derived by a T-duality approach. We give evidence showing that the energies of a class of physical excitations of the super-Yang-Mills theory show the correct symmetry expected from massive Type IIA string theory in a lightcone quantization

Elementary process theory: a formal axiomatic system with a potential application as a foundational framework for physics supporting gravitational repulsion of matter and antimatter

International Nuclear Information System (INIS)

Cabbolet, M.J.T.F.

2010-01-01

Theories of modern physics predict that antimatter having rest mass will be attracted by the earth's gravitational field, but the actual coupling of antimatter with gravitation has not been established experimentally. The purpose of the present research was to identify laws of physics that would govern the universe if antimatter having rest mass would be repulsed by the earth's gravitational field. As a result, a formalized axiomatic system was developed together with interpretation rules for the terms of the language: the intention is that every theorem of the system yields a true statement about physical reality. Seven non-logical axioms of this axiomatic system form the elementary process theory (EPT): this is then a scheme of elementary principles describing the dynamics of individual processes taking place at supersmall scale. It is demonstrated how gravitational repulsion functions in the universe of the EPT, and some observed particles and processes have been formalized in the framework of the EPT. Incompatibility of quantum mechanics (QM) and General Relativity (GR) with the EPT is proven mathematically; to demonstrate applicability to real world problems to which neither QM nor GR applies, the EPT has been applied to a theory of the Planck era of the universe. The main conclusions are that a completely formalized framework for physics has been developed supporting the existence of gravitational repulsion and that the present results give rise to a potentially progressive research program. (Abstract Copyright [2010], Wiley Periodicals, Inc.)

Dynamics of Strong Interactions and the S-Matrix

Energy Technology Data Exchange (ETDEWEB)

Omnes, R. [Laboratoire de Physique Theorique et Hautes Energies, Universite de Paris, Orsay (France)

1969-08-15

The physical principles underlying the S-matrix theory of strong interactions are reviewed. In particular, the problem of whether these principles are sufficient to completely determine the S-matrix, i.e. to yield a dynamical theory of strong interactions, is discussed. (author)

Axiomatic conformal field theory

International Nuclear Information System (INIS)

Gaberdiel, M.R.; Goddard, P.

2000-01-01

A new rigourous approach to conformal field theory is presented. The basic objects are families of complex-valued amplitudes, which define a meromorphic conformal field theory (or chiral algebra) and which lead naturally to the definition of topological vector spaces, between which vertex operators act as continuous operators. In fact, in order to develop the theory, Moebius invariance rather than full conformal invariance is required but it is shown that every Moebius theory can be extended to a conformal theory by the construction of a Virasoro field. In this approach, a representation of a conformal field theory is naturally defined in terms of a family of amplitudes with appropriate analytic properties. It is shown that these amplitudes can also be derived from a suitable collection of states in the meromorphic theory. Zhu's algebra then appears naturally as the algebra of conditions which states defining highest weight representations must satisfy. The relationship of the representations of Zhu's algebra to the classification of highest weight representations is explained. (orig.)

Complete Axiomatization for the Bisimilarity Distance on Markov Chains

DEFF Research Database (Denmark)

Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim Guldstrand

2016-01-01

In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS...

Some Consequences of an Analysis of the Kelvin-Clausius Entropy Formulation Based on Traditional Axiomatics

Science.gov (United States)

Jesudason, Christopher G.

2003-09-01

Recently, there have appeared interesting correctives or challenges [Entropy 1999, 1, 111-147] to the Second law formulations, especially in the interpretation of the Clausius equivalent transformations, closely related in area to extensions of the Clausius principle to irreversible processes [Chem. Phys. Lett. 1988, 143(1), 65-70]. Since the traditional formulations are central to science, a brief analysis of some of these newer theories along traditional lines is attempted, based on well-attested axioms which have formed the basis of equilibrium thermodynamics. It is deduced that the Clausius analysis leading to the law of increasing entropy does not follow from the given axioms but it can be proved that for irreversible transitions, the total entropy change of the system and thermal reservoirs (the "Universe") is not negative, even for the case when the reservoirs are not at the same temperature as the system during heat transfer. On the basis of two new simple theorems and three corollaries derived for the correlation between irreversible and reversible pathways and the traditional axiomatics, it is shown that a sequence of reversible states can never be used to describe a corresponding sequence of irreversible states for at least closed systems, thereby restricting the principle of local equilibrium. It is further shown that some of the newer irreversible entropy forms given exhibit some paradoxical properties relative to the standard axiomatics. It is deduced that any reconciliation between the traditional approach and novel theories lie in creating a well defined set of axioms to which all theoretical developments should attempt to be based on unless proven not be useful, in which case there should be consensus in removing such axioms from theory. Clausius' theory of equivalent transformations do not contradict the traditional understanding of heat- work efficiency. It is concluded that the intuitively derived assumptions over the last two centuries seem to

Axiomatic Design of Space Life Support Systems

Science.gov (United States)

Jones, Harry W.

2017-01-01

Systems engineering is an organized way to design and develop systems, but the initial system design concepts are usually seen as the products of unexplained but highly creative intuition. Axiomatic design is a mathematical approach to produce and compare system architectures. The two axioms are:- Maintain the independence of the functional requirements.- Minimize the information content (or complexity) of the design. The first axiom generates good system design structures and the second axiom ranks them. The closed system human life support architecture now implemented in the International Space Station has been essentially unchanged for fifty years. In contrast, brief missions such as Apollo and Shuttle have used open loop life support. As mission length increases, greater system closure and increased recycling become more cost-effective.Closure can be gradually increased, first recycling humidity condensate, then hygiene wastewater, urine, carbon dioxide, and water recovery brine. A long term space station or planetary base could implement nearly full closure, including food production. Dynamic systems theory supports the axioms by showing that fewer requirements, fewer subsystems, and fewer interconnections all increase system stability. If systems are too complex and interconnected, reliability is reduced and operations and maintenance become more difficult. Using axiomatic design shows how the mission duration and other requirements determine the best life support system design including the degree of closure.

Covariantized matrix theory for D-particles

Energy Technology Data Exchange (ETDEWEB)

Yoneya, Tamiaki [Institute of Physics, The University of Tokyo,3-8-1 Komaba, Meguro-ku, Tokyo 153-8902 (Japan); School of Graduate Studies, The Open University of Japan,2-11 Wakaba, Mihama-ku, Chiba 261-8586 (Japan)

2016-06-09

We reformulate the Matrix theory of D-particles in a manifestly Lorentz-covariant fashion in the sense of 11 dimesnional flat Minkowski space-time, from the viewpoint of the so-called DLCQ interpretation of the light-front Matrix theory. The theory is characterized by various symmetry properties including higher gauge symmetries, which contain the usual SU(N) symmetry as a special case and are extended from the structure naturally appearing in association with a discretized version of Nambu’s 3-bracket. The theory is scale invariant, and the emergence of the 11 dimensional gravitational length, or M-theory scale, is interpreted as a consequence of a breaking of the scaling symmetry through a super-selection rule. In the light-front gauge with the DLCQ compactification of 11 dimensions, the theory reduces to the usual light-front formulation. In the time-like gauge with the ordinary M-theory spatial compactification, it reduces to a non-Abelian Born-Infeld-like theory, which in the limit of large N becomes equivalent with the original BFSS theory.

A philosophical assessment of decision theory

DEFF Research Database (Denmark)

Jensen, Karsten Klint

2012-01-01

modern axiomatic decision theory is an instance of fundamental measurement theory. This is then followed by a thorough introduction to Savage’s version of modern axiomatic decision theory. Turning to the interpretation of the theory, the maxim “maximize expected utility,” which stems from classical...... assignments. In the modern approach, the action guidance is to conform to the axioms. Analyzing decision theory as a theory of good, the maxim “maximize expected goodness” repeats the misunderstanding. Moreover, it implies risk neutrality about good and a cardinal measure of good, and both are problematic......The significance of decision theory consists of giving an account of rational decision making under circumstances of uncertainty. This question is important both from the point of view of what is in our personal interest and from the point of view of what is ethically right. But decision theory...

Aspects of U-duality in matrix theory

International Nuclear Information System (INIS)

Blau, M.; O'Loughlin, M.

1997-12-01

We explore various aspects of implementing the full M-theory U-duality group E d+1 , and thus Lorentz invariance, in the finite N matrix theory (DLCQ of M-theory) describing toroidal IIA-compactifications on d-tori: (1) We generalize the analysis of Elitzur et al. (hep-th/9707217) from E d to E d+1 and identify the highest weight states unifying the momentum and flux E d -multiplets into one E d+1 -orbit, (2) We identify the new symmetries, in particular the Weyl group symmetry associated to the (d+1)'th node of the E d+1 Dynkin diagram, with Nahm-duality-like symmetries (N-duality) exchanging the rank N of the matrix theory gauge group with other (electric, magnetic, ...) quantum numbers. (3) We describe the action of N-duality on BPS bound states, thus making testable predictions for the Lorentz invariance of matrix theory. (4) We discuss the problems that arise in the matrix theory limit for BPS states with no top-dimensional branes, i.e. configurations with N = 0. (5) We show that N-duality maps the matrix theory SYM picture to the matrix string picture and argue that, for d even, the latter should be thought of as an M-theory membrane description (which appears to be well defined even for d > 5). (6) We find a compact and unified expression for a U-duality invariant of E d+1 for all d and show that in d = 5,6 it reduces to the black hole entropy cubic E 6 - and quartic E 7 -invariants respectively. (7) Finally, we describe some of the solitonic states in d = 6,7 and give an example (a 'rolled-up' Taub-NUT 6-brane) of a configuration exhibiting the unusual 1/g 3 s -behaviour. (author)

M(atrix) theory on an orbifold and twisted membrane

International Nuclear Information System (INIS)

Kim, N.

1997-01-01

M(atrix) theory on an orbifold and classical two-branes therein are studied with particular emphasis on heterotic M(atrix) theory on S 1 / Z 2 relevant to strongly coupled heterotic and dual type IA string theories. By analyzing the orbifold condition on Chan-Paton factors, we show that three choices of gauge group are possible for heterotic M(atrix) theory: SO(2N), SO(2N+1) or USp(2N). By examining the area-preserving diffeomorphism that underlies the M(atrix) theory, we find that each choice of gauge group restricts the possible topologies of two-branes. The result suggests that only the choice of SO(2N) or SO(2N+1) allows open two-branes, and hence, is relevant to heterotic M(atrix) theory. We show that the requirement of both local vacuum energy cancellation and of world-sheet anomaly cancellation of the resulting heterotic string identifies supersymmetric twisted sector spectra with sixteen fundamental representation spinors from each of the two fixed points. Twisted open and closed two-brane configurations are obtained in the large N limit. (orig.)

Geographic envelope of the Moon and the identification of Moon landscapes with the use of the axiomatic method

Directory of Open Access Journals (Sweden)

Kyryliuk Serhii

2017-09-01

Full Text Available Three consequent concepts that build up the algorithm of the identification of modern landscapes on the Moon surface are suggested. They are anaglyphonosphere axiomatic and landscape concepts obtained with the use of the axiomatic method. The first concept depicts the geographic envelope of the Moon as an anaglyphonosphere layer (relief that is a continuum (total environment. The latter becomes the research subject for both a geomorphologist and a landscape researcher. Continuity, dynamics, range (amplitude, and erosion potential determine anaglyphonosphere. Axiomatic concept means constructing the sole scheme (mathematically determined of the search for the elementary surface units using the geometric interpretation of surface patterns of the Moon and its landscape interpretation. The landscape concept is based on the classical principles of the landscape theory and the axiomatic principles of the previous concept. The synthesis of concepts is implemented in the models of Moon landscapes of four scales: zero, linear, two- and three-dimensional. The paper offers the last two models of Davy Catena. Proposed concepts with appropriate correction can be used in parallel studies of the natural environment: geological, geomorphological, climatic, etc. The advantages of the axiomatic method consist in the objective approach to the division of the surface into specific units (the landscapes in our case. The proposed method of identifying and displaying the landscape complexes on the lunar surface can be a significant complement for the study and mapping of terrestrial planets, satellites of planet-giants, etc.

The S-Matrix coupling dependence for a, d and e affine Toda field theory

International Nuclear Information System (INIS)

Braden, H.W.; Sasaki, R.

1990-09-01

Affine Toda field theories are solvable 1+1 dimensional quantum field theories closely related to integrable deformations of conformal field theory. The S-Matrix elements for an affine Toda field theory are known to depend on the coupling constant β through one universal function B(β) which cannot be determined by unitarity, crossing and the bootstrap. From the requirement of nonexistence of extra poles in the physical region its form is conjectured to be B(β) = (2π) -1 ·β 2 /((1+β 2 )/4π). We show that the above conjecture is correct up to one loop order (i.e., β 4 ) of perturbation for simply laced, i.e., a, d and e affine Toda field theories using a general argument which exhibits much of the richness of these theories. (author)

Rigorous results of low-energy models of the analytic S-matrix theory

International Nuclear Information System (INIS)

Meshcheryakov, V.A.

1974-01-01

Results of analytic S-matrix theory, mainly dealing with the static limit of dispersion relations, are applied to pion-nucleon scattering in the low-energy region. Various approaches to solving equations of the chew-Low type are discussed. It is concluded that interesting results are obtained by reducing the equations to a system of nonlinear difference equations; the crucial element of this approach being the study of functions on the whole Riemann surface. Boundary and crossing symmetry conditions are studied. (HFdV)

Introduction to symmetry and supersymmetry in quantum field theory

International Nuclear Information System (INIS)

Lopuszanski, J.

1988-01-01

This is a set of lecture notes given by the author at the Universities of Gottingen and Wroclaw. The text presents the axiomatic approach to field theory and studies in depth the concepts of symmetry and supersymmetry and their associated generators, currents and charges. It is intended as a one- semester course for graduate students in the field of mathematical physics and high energy physics. Contents: Introduction; Example of a Classical and Quantum Scalar Free Field Theory; Scene and Subject of the Drama. Axiom 1 and 2; Subject of the Drama; Principle of Relativity. Causality. Axiom 3, 4 and 5; Irreducibility of the Field Algebra and Scattering Theory. Axiom 6. Axiom O; Preliminaries about Physical Symmetries; Currents and Charges; Global Symmetries and Supersymmetries of the S - Matrix; Representations of the Super-Lie Algebra; The Case of Massless Particles; Fermionic Charges; Concluding Remarks

Chern-Simons matrix models, two-dimensional Yang-Mills theory and the Sutherland model

International Nuclear Information System (INIS)

Szabo, Richard J; Tierz, Miguel

2010-01-01

We derive some new relationships between matrix models of Chern-Simons gauge theory and of two-dimensional Yang-Mills theory. We show that q-integration of the Stieltjes-Wigert matrix model is the discrete matrix model that describes q-deformed Yang-Mills theory on S 2 . We demonstrate that the semiclassical limit of the Chern-Simons matrix model is equivalent to the Gross-Witten model in the weak-coupling phase. We study the strong-coupling limit of the unitary Chern-Simons matrix model and show that it too induces the Gross-Witten model, but as a first-order deformation of Dyson's circular ensemble. We show that the Sutherland model is intimately related to Chern-Simons gauge theory on S 3 , and hence to q-deformed Yang-Mills theory on S 2 . In particular, the ground-state wavefunction of the Sutherland model in its classical equilibrium configuration describes the Chern-Simons free energy. The correspondence is extended to Wilson line observables and to arbitrary simply laced gauge groups.

Symmetries and Interactions in Matrix String Theory

NARCIS (Netherlands)

Hacquebord, F.H.

1999-01-01

This PhD-thesis reviews matrix string theory and recent developments therein. The emphasis is put on symmetries, interactions and scattering processes in the matrix model. We start with an introduction to matrix string theory and a review of the orbifold model that flows out of matrix string theory

Hilbertian quantum theory as the theory of complementarity

International Nuclear Information System (INIS)

Lahti, P.J.

1983-01-01

It is demonstrated that the notion of complementary physical quantities assumes the possibility of performing ideal first-kind measurements of such quantities. This then leads to an axiomatic reconstruction of the Hilbertian quantum theory based on the complementarity principle and on its connection with the measurement theoretical idealization known as the projection postulate. As the notion of complementary physical quantities does not presuppose the notion of probability, the given axiomatic reconstruction reveals complementarity as an essential reason for the irreducibly probabilistic nature of the quantum theory. (author)

Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory

International Nuclear Information System (INIS)

Lee, Bum-Hoon; Ro, Daeho; Yang, Hyun Seok

2017-01-01

We study localization of five-dimensional supersymmetric U(1) gauge theory on S 3 ×ℝ θ 2 where ℝ θ 2 is a noncommutative (NC) plane. The theory can be isomorphically mapped to three-dimensional supersymmetric U(N→∞) gauge theory on S 3 using the matrix representation on a separable Hilbert space on which NC fields linearly act. Therefore the NC space ℝ θ 2 allows for a flexible path to derive matrix models via localization from a higher-dimensional supersymmetric NC U(1) gauge theory. The result shows a rich duality between NC U(1) gauge theories and large N matrix models in various dimensions.

Measurement Theory and the Foundations of Utilitarianism

OpenAIRE

John a. Weymark

2004-01-01

Harsanyi used expected utility theory to provide two axiomatizations of weighted utilitarian rules. Sen (and later, Weymark) has argued that Harsanyi has not, in fact, axiomatized utilitarianism because he has misapplied expected utility theory. Specifically, Sen and Weymark have argued that von Neumann-Morgenstern expected utility theory is an ordinal theory and, therefore, any increasing transform of a von Neumann-Morgenstern utility function is a satisfactory representation of a preference...

Matrix String Theory

CERN Document Server

Dijkgraaf, R; Verlinde, Herman L

1997-01-01

Via compactification on a circle, the matrix model of M-theory proposed by Banks et al suggests a concrete identification between the large N limit of two-dimensional N=8 supersymmetric Yang-Mills theory and type IIA string theory. In this paper we collect evidence that supports this identification. We explicitly identify the perturbative string states and their interactions, and describe the appearance of D-particle and D-membrane states.

A Finite Axiomatization of G-Dependence

OpenAIRE

Paolini, Gianluca

2015-01-01

We show that a form of dependence known as G-dependence (originally introduced by Grelling) admits a very natural finite axiomatization, as well as Armstrong relations. We also give an explicit translation between functional dependence and G-dependence.

Baryoniums - the S-matrix approach

International Nuclear Information System (INIS)

Roy, D.P.

1979-08-01

In this series of lectures the question of how the baryoniums are related to charmoniums and strangoniums is discussed and it is pointed out that in the S-matrix framework, they all follow from the same pair of hypotheses, duality and no exotics. Invoking no underlying quark structure, except that inherent in the assumption of no exotics, it is shown that there are no mesons outside the singlet and octet representation of SU(3) and no baryons outside the singlet, octet and decaplet. In other words all mesons occur within the quantum number of a q-antiq system and all baryons within those of qqq. This seems to be an experimental fact, which has no natural explanation within the S-matrix framework except that it is the minimal non-zero solution to the duality constraints. The approach in the past has been to take it as an experimental input and build up a phenomenological S-matrix framework. Lately it has been realised that the answer may come from the colour dynamics of quarks. If true this would provide an important link between the fundamental but invisible field theory of quarks and gluons and the phenomenological but visible S-matrix theory overlying it. The subject is discussed under the headings; strangonium and charmonium, baryonium, spectroscopy, baryonium resonances, FESR constraint, baryonium exchange, phenomenological estimate of ω - baryonium mixing at t = 0, and models of ω - baryonium mixing. (UK)

Axiomatic unsharp quantum theory (From Mackey to Ludwig and Piron)

Science.gov (United States)

Cattaneo, Gianpiero; Laudisa, Federico

1994-05-01

On the basis of Mackey's axiomatic approach to quantum physics or, equivalently, of a “state-event-probability” (SEVP) structure, using a quite standard “fuzzification” procedure, a set of unsharp events (or “effects”) is constructed and the corresponding “state-effect-probability” (SEFP) structure is introduced. The introduction of some suitable axioms gives rise to a partially ordered structure of quantum Brouwer-Zadeh (BZ) poset; i.e., a poset endowed with two nonusual orthocomplementation mappings, a fuzzy-like orthocomplementation, and an intuitionistic-like orthocomplementation, whose set of sharp elements is an orthomodular complete lattice. As customary, by these orthocomplementations the two modal-like necessity and possibility operators are introduced, and it is shown that Ludwig's and Jauch-Piron's approaches to quantum physics are “interpreted” in complete SEFP. As a marginal result, a standard procedure to construct a lot of unsharp realizations starting from any sharp realization of a fixed observable is given, and the relationship among sharp and corresponding unsharp realizations is studied.

R matrix: its relation to Titchmarsh-Weyl theory and its complex rotated analogue

International Nuclear Information System (INIS)

Elander, N.; Krylstedt, P.; Braendas, E.; Engdahl, E.

1986-01-01

The R matrix theory in its simplest form is discussed and analyzed in terms of the classical Titchmarsh-Weyl's theory for a singular second order differential equation. It is observed that the R matrix described as an abstract R operator is contained in the framework of Weyls classical extension to an infinite interval of finite Sturm-Liuoville theory. As a result they find that the exterior complex rotation method can be synthesized with the R matrix theory to obtain a method for deriving the S matrix poles out in the complex energy or momentum planes

Lectures on matrix field theory

CERN Document Server

Ydri, Badis

2017-01-01

These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries. The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last chapter offers a general introduction to non-commutative gauge theories, while two appendices round out the text. Primarily written as a self-study guide for postgraduate students – with the aim of pedagogically introducing them to key analytical and numerical tools, as well as useful physical models in applications – these lecture notes will also benefit experienced researchers by providing a reference guide to the fundamentals of non-commutative field theory with an emphasis on matrix models and fuzzy geometries.

A matrix S for all simple current extensions

International Nuclear Information System (INIS)

Fuchs, J.; Schellekens, A.N.; Schweigert, C.

1996-01-01

A formula is presented for the modular transformation matrix S for any simple current extension of the chiral algebra of a conformal field theory. This provides in particular an algorithm for resolving arbitrary simple current fixed points, in such a way that the matrix S we obtain is unitary and symmetric and furnishes a modular group representation. The formalism works in principle for any conformal field theory. A crucial ingredient is a set of matrices S ab J , where J is a simple current and a and b are fixed points of J. We expect that these input matrices realize the modular group for the torus one-point functions of the simple currents. In the case of WZW-models these matrices can be identified with the S-matrices of the orbit Lie algebras that were introduced recently. As a special case of our conjecture we obtain the modular matrix S for WZW-theories based on group manifolds that are not simply connected, as well as for most coset models. (orig.)

The revenge of the S-matrix

CERN Multimedia

CERN. Geneva

2016-01-01

In this talk I will describe recent work aiming to reinvigorate the 50 year old S-matrix program, which aims to constrain scattering of massive particles non-perturbatively. I will begin by considering quantum fields in anti-de Sitter space and show that one can extract information about the S-matrix by considering correlators in conformally invariant theories. The latter can be studied with "bootstrap" techniques, which allow us to constrain the S-matrix. In particular, in 1+1D one obtains bounds which are saturated by known integrable models. I will also show that it is also possible to directly constrain the S-matrix, without using the CFT crutch, by using crossing symmetry and unitarity. This alternative method is simpler and gives results in agreement with the previous approach. Both techniques are generalizable to higher dimensions.

Could a Weak Coupling Massless SU(5) Theory Underly the Standard Model S-Matrix

Science.gov (United States)

White, Alan R.

2011-04-01

The unitary Critical Pomeron connects to a unique massless left-handed SU(5) theory that, remarkably, might provide an unconventional underlying unification for the Standard Model. Multi-regge theory suggests the existence of a bound-state high-energy S-Matrix that replicates Standard Model states and interactions via massless fermion anomaly dynamics. Configurations of anomalous wee gauge boson reggeons play a vacuum-like role. All particles, including neutrinos, are bound-states with dynamical masses (there is no Higgs field) that are formed (in part) by anomaly poles. The contributing zero-momentum chirality transitions break the SU(5) symmetry to vector SU(3)⊗U(1) in the S-Matrix. The high-energy interactions are vector reggeon exchanges accompanied by wee boson sums (odd-signature for the strong interaction and even-signature for the electroweak interaction) that strongly enhance couplings. The very small SU(5) coupling, αQUD ≲ 1/120, should be reflected in small (Majorana) neutrino masses. A color sextet quark sector, still to be discovered, produces both Dark Matter and Electroweak Symmetry Breaking. Anomaly color factors imply this sector could be produced at the LHC with large cross-sections, and would be definitively identified in double pomeron processes.

Geometry and experience: Einstein's 1921 paper and Hilbert's axiomatic system

International Nuclear Information System (INIS)

De Gandt, Francois

2006-01-01

In his 1921 paper Geometrie und Erfahrung, Einstein decribes the new epistemological status of geometry, divorced from any intuitive or a priori content. He calls that 'axiomatics', following Hilbert's theoretical developments on axiomatic systems, which started with the stimulus given by a talk by Hermann Wiener in 1891 and progressed until the Foundations of geometry in 1899. Difficult questions arise: how is a theoretical system related to an intuitive empirical content?

Single determinantal reaction theory as a Schroedinger analog: the time-dependent S-matrix Hartree-Fock method

International Nuclear Information System (INIS)

Griffin, J.J.; Lichtner, P.C.; Dworzecka, M.; Kan, K.K.

1979-01-01

It is suggested that the TDHF method be viewed, not as an approximation to but as a model of the exact Schroedinger system; that is, as a gedanken many-body experiment whose analysis with digital computers provides data worthy in itself of theoretical study. From such a viewpoint attention is focused on the structural analogies of the TDHF system with the exact theory rather than upon its quantitative equivalence, and the TDHF many-body system is studied as a challenge of its own which, although much simpler than the realistic problem, may still offer complexity enough to educate theorists in the present state of knowledge. In this spirit, the TDHF description of continuum reactions can be restructured from an initial-value problem into a form analogous to the S-matrix version of the Schroedinger theory. The resulting TD-S-HF theory involves only self-consistent single determinantal solutions of the TDHF equations and invokes time averaging to obtain a consistent interpretation of the TDHF analogs of quantities which are constant in the exact theory, such as the S-matrix and the asymptotic reaction channel characteristics. Periodic solutions then play the role of stationary eigenstates in the construction of suitable asymptotic reaction channels. If these periodic channel states occur only at discrete energies, then the resulting channels are mutually orthogonal (on the time average) and the theory exhibits a structure fully analogous to the exact theory. In certain special cases where the periodic solutions are known to occur as an energy continuum, the requirement that the periodicity of the channel solutions be gauge invariant provides a natural requantization condition which (suggestively) turns out to be identical with the Bohr-Sommerfeld quantization rule. 11 references

The black hole S-Matrix from quantum mechanics

International Nuclear Information System (INIS)

Betzios, Panagiotis; Gaddam, Nava; Papadoulaki, Olga

2016-01-01

We revisit the old black hole S-Matrix construction and its new partial wave expansion of ’t Hooft. Inspired by old ideas from non-critical string theory & c=1 Matrix Quantum Mechanics, we reformulate the scattering in terms of a quantum mechanical model — of waves scattering off inverted harmonic oscillator potentials — that exactly reproduces the unitary black hole S-Matrix for all spherical harmonics; each partial wave corresponds to an inverted harmonic oscillator with ground state energy that is shifted relative to the s-wave oscillator. Identifying a connection to 2d string theory allows us to show that there is an exponential degeneracy in how a given total initial energy may be distributed among many partial waves of the 4d black hole.

The black hole S-Matrix from quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Betzios, Panagiotis; Gaddam, Nava; Papadoulaki, Olga [Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena,Utrecht University, Princetonplein 5, Utrecht, 3508 TD The (Netherlands)

2016-11-22

We revisit the old black hole S-Matrix construction and its new partial wave expansion of ’t Hooft. Inspired by old ideas from non-critical string theory & c=1 Matrix Quantum Mechanics, we reformulate the scattering in terms of a quantum mechanical model — of waves scattering off inverted harmonic oscillator potentials — that exactly reproduces the unitary black hole S-Matrix for all spherical harmonics; each partial wave corresponds to an inverted harmonic oscillator with ground state energy that is shifted relative to the s-wave oscillator. Identifying a connection to 2d string theory allows us to show that there is an exponential degeneracy in how a given total initial energy may be distributed among many partial waves of the 4d black hole.

Particles as S-matrix poles: hadron democracy

International Nuclear Information System (INIS)

Chew, G.F.

1989-01-01

The connection between two theoretical ideas of the 1950s is traced in this article, namely that hadrons are nonfundamental, ''composite'' particles and that all physically observable particles correspond to singularities of an analytic scattering matrix. The S matrix theory developed by Werner Heisenberg in the early forties now incorporated the concepts of unitarity, invariance, analyticity and causality. The meson-exchange force meant that poles must be present in nucleon-nuclear and pion-nucleon scattering as predicted by dispersion relations. Experimental work in accessible regions determined pole residues. Pole residue became associated with force strength and pole position with particle mass. In 1959, the author discovered the so-called ''bootstrap'' theory the rho meson as a force generates a rho particle. By the end of the 1950s it was clear that all hadrons had equal status, each being bound states of other hadrons, sustained by hadron exchange forces and that hadrons are self-generated by an S-matrix bootstrap mechanism that determines all their properties. (UK)

Uncertainty and Complementarity in Axiomatic Quantum Mechanics

Science.gov (United States)

Lahti, Pekka J.

1980-11-01

In this work an investigation of the uncertainty principle and the complementarity principle is carried through. A study of the physical content of these principles and their representation in the conventional Hilbert space formulation of quantum mechanics forms a natural starting point for this analysis. Thereafter is presented more general axiomatic framework for quantum mechanics, namely, a probability function formulation of the theory. In this general framework two extra axioms are stated, reflecting the ideas of the uncertainty principle and the complementarity principle, respectively. The quantal features of these axioms are explicated. The sufficiency of the state system guarantees that the observables satisfying the uncertainty principle are unbounded and noncompatible. The complementarity principle implies a non-Boolean proposition structure for the theory. Moreover, nonconstant complementary observables are always noncompatible. The uncertainty principle and the complementarity principle, as formulated in this work, are mutually independent. Some order is thus brought into the confused discussion about the interrelations of these two important principles. A comparison of the present formulations of the uncertainty principle and the complementarity principle with the Jauch formulation of the superposition principle is also given. The mutual independence of the three fundamental principles of the quantum theory is hereby revealed.

On the axiomatization of some classes of discrete universal integrals

Czech Academy of Sciences Publication Activity Database

Klement, E.P.; Mesiar, Radko

2012-01-01

Roč. 28, č. 1 (2012), s. 13-18 ISSN 0950-7051 R&D Projects: GA ČR GAP402/11/0378 Institutional research plan: CEZ:AV0Z10750506 Keywords : Comonotone modularity * Copula * Universal integral Subject RIV: BA - General Mathematics Impact factor: 4.104, year: 2012 http://library.utia.cas.cz/separaty/2012/E/mesiar-on the axiomatization of some classes of discrete universal integrals. pdf

Reduced density matrix functional theory via a wave function based approach

Energy Technology Data Exchange (ETDEWEB)

Schade, Robert; Bloechl, Peter [Institute for Theoretical Physics, Clausthal University of Technology, Clausthal (Germany); Pruschke, Thomas [Institute for Theoretical Physics, University of Goettingen, Goettingen (Germany)

2016-07-01

We propose a new method for the calculation of the electronic and atomic structure of correlated electron systems based on reduced density matrix functional theory (rDMFT). The density-matrix functional is evaluated on the fly using Levy's constrained search formalism. The present implementation rests on a local approximation of the interaction reminiscent to that of dynamical mean field theory (DMFT). We focus here on additional approximations to the exact density-matrix functional in the local approximation and evaluate their performance.

Staggered chiral random matrix theory

International Nuclear Information System (INIS)

Osborn, James C.

2011-01-01

We present a random matrix theory for the staggered lattice QCD Dirac operator. The staggered random matrix theory is equivalent to the zero-momentum limit of the staggered chiral Lagrangian and includes all taste breaking terms at their leading order. This is an extension of previous work which only included some of the taste breaking terms. We will also present some results for the taste breaking contributions to the partition function and the Dirac eigenvalues.

An Axiomatic Representation of System Dynamics

CERN Document Server

Baianu, I

2004-01-01

An axiomatic representation of system dynamics is introduced in terms of categories, functors, organismal supercategories, limits and colimits of diagrams. Specific examples are considered in Complex Systems Biology, such as ribosome biogenesis and Hormonal Control in human subjects. "Fuzzy" Relational Structures are also proposed for flexible representations of biological system dynamics and organization.

From outcomes to acts : a non-standard axiomatization of the expected utility principle

NARCIS (Netherlands)

Peterson, M.B.

2004-01-01

This paper presents an axiomatization of the principle of maximizing expected utility that does not rely on the independence axiom or sure-thing principle. Perhaps more importantly the new axiomatization is based on an ex ante approach, instead of the standard ex post approach. An ex post approach

Enumeration of RNA complexes via random matrix theory

DEFF Research Database (Denmark)

Andersen, Jørgen E; Chekhov, Leonid O.; Penner, Robert C

2013-01-01

molecules and hydrogen bonds in a given complex. The free energies of this matrix model are computed using the so-called topological recursion, which is a powerful new formalism arising from random matrix theory. These numbers of RNA complexes also have profound meaning in mathematics: they provide......In the present article, we review a derivation of the numbers of RNA complexes of an arbitrary topology. These numbers are encoded in the free energy of the Hermitian matrix model with potential V(x)=x(2)/2 - stx/(1 - tx), where s and t are respective generating parameters for the number of RNA...

Random matrix theory in nuclear structure: past, present and future

International Nuclear Information System (INIS)

Kota, V.K.B.

2012-01-01

Random matrix theory (RMT) introduced by Wigner in 50's to describe statistical properties of slow-neutron resonances in heavy nuclei such as 232 Th, was developed further in the 60's by Dyson, Mehta, Porter and others and in the 70's by French, Pandey, Bohigas and others. Going beyond this, the demonstration that level fluctuations of quantum analogues of classically chaotic few-degrees-of-freedom systems follow random matrix theory (integrable systems follow Poisson as shown by Berry) in 1984 by Bohigas and others on one hand and the recognition from 1995 onwards that two-body random matrix ensembles derived from shell model have wide ranging applications on the other, defined new directions in RMT applications in nuclear physics. Growth points in RMT in nuclear physics are: (i) analysis of nuclear data looking for order-chaos transitions and symmetry (Time-reversal, Parity, Isospin) breaking; (ii) analysis of shell model driven embedded (or two-body) random matrix ensembles giving statistical properties generated by random interactions in the presence of a mean-field; (iii) statistical nuclear spectroscopy generated by embedded ensembles for level densities, occupancies, GT strengths, transition strength sums and so on; (iv) the new paradigm of regular structures generated by random interactions as brought out by studies using various nuclear models; (v) random matrix theory for nuclear reactions with particular reference to open quantum systems; (vi) RMT results from nuclear physics to atomic physics, mesoscopic physics and quantum information science. Topics (i)-(vi) emphasizing recent results are discussed. (author)

The black hole S-Matrix from quantum mechanics

NARCIS (Netherlands)

Betzios, Panagiotis; Gaddam, Nava; Papadoulaki, Olga

2016-01-01

We revisit the old black hole S-Matrix construction and its new partial wave expansion of 't Hooft. Inspired by old ideas from non-critical string theory \\& $c=1$ Matrix Quantum Mechanics, we reformulate the scattering in terms of a quantum mechanical model\\textemdash of waves scattering off

A Qualitative Linear Utility Theory for Spohn's Theory of Epistemic Beliefs

OpenAIRE

Giang, Phan H.; Shenoy, Prakash P.

2013-01-01

In this paper, we formulate a qualitative "linear" utility theory for lotteries in which uncertainty is expressed qualitatively using a Spohnian disbelief function. We argue that a rational decision maker facing an uncertain decision problem in which the uncertainty is expressed qualitatively should behave so as to maximize "qualitative expected utility." Our axiomatization of the qualitative utility is similar to the axiomatization developed by von Neumann and Morgenstern for probabilistic l...

Combinatorial matrix theory

CERN Document Server

Mitjana, Margarida

2018-01-01

This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in Barcelona. These notes correspond to five series of lectures. The first series is dedicated to the study of several matrix classes defined combinatorially, and was delivered by Richard A. Brualdi. The second one, given by Pauline van den Driessche, is concerned with the study of spectral properties of matrices with a given sign pattern. Dragan Stevanović delivered the third one, devoted to describing the spectral radius of a graph as a tool to provide bounds of parameters related with properties of a graph. The fourth lecture was delivered by Stephen Kirkland and is dedicated to the applications of the Group Inverse of the Laplacian matrix. The last one, given by Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.

Hilbert's sixth problem: between the foundations of geometry and the axiomatization of physics

Science.gov (United States)

Corry, Leo

2018-04-01

The sixth of Hilbert's famous 1900 list of 23 problems was a programmatic call for the axiomatization of the physical sciences. It was naturally and organically rooted at the core of Hilbert's conception of what axiomatization is all about. In fact, the axiomatic method which he applied at the turn of the twentieth century in his famous work on the foundations of geometry originated in a preoccupation with foundational questions related with empirical science in general. Indeed, far from a purely formal conception, Hilbert counted geometry among the sciences with strong empirical content, closely related to other branches of physics and deserving a treatment similar to that reserved for the latter. In this treatment, the axiomatization project was meant to play, in his view, a crucial role. Curiously, and contrary to a once-prevalent view, from all the problems in the list, the sixth is the only one that continually engaged Hilbet's efforts over a very long period of time, at least between 1894 and 1932. This article is part of the theme issue `Hilbert's sixth problem'.

From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems.

Science.gov (United States)

Lozada Aguilar, Miguel Ángel; Khrennikov, Andrei; Oleschko, Klaudia

2018-04-28

As was recently shown by the authors, quantum probability theory can be used for the modelling of the process of decision-making (e.g. probabilistic risk analysis) for macroscopic geophysical structures such as hydrocarbon reservoirs. This approach can be considered as a geophysical realization of Hilbert's programme on axiomatization of statistical models in physics (the famous sixth Hilbert problem). In this conceptual paper , we continue development of this approach to decision-making under uncertainty which is generated by complexity, variability, heterogeneity, anisotropy, as well as the restrictions to accessibility of subsurface structures. The belief state of a geological expert about the potential of exploring a hydrocarbon reservoir is continuously updated by outputs of measurements, and selection of mathematical models and scales of numerical simulation. These outputs can be treated as signals from the information environment E The dynamics of the belief state can be modelled with the aid of the theory of open quantum systems: a quantum state (representing uncertainty in beliefs) is dynamically modified through coupling with E ; stabilization to a steady state determines a decision strategy. In this paper, the process of decision-making about hydrocarbon reservoirs (e.g. 'explore or not?'; 'open new well or not?'; 'contaminated by water or not?'; 'double or triple porosity medium?') is modelled by using the Gorini-Kossakowski-Sudarshan-Lindblad equation. In our model, this equation describes the evolution of experts' predictions about a geophysical structure. We proceed with the information approach to quantum theory and the subjective interpretation of quantum probabilities (due to quantum Bayesianism).This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Evaluation and optimization of General Atomics' GT-MHR reactor cavity cooling system using an axiomatic design approach

International Nuclear Information System (INIS)

Thielman, Jeff; Ge, Ping; Wu, Qiao; Parme, Laurence

2005-01-01

The development of the Generation IV (Gen-IV) nuclear reactors has presented social, technical, and economical challenges to nuclear engineering design and research. To develop a robust, reliable nuclear reactor system with minimal environmental impact and cost, modularity has been gradually accepted as a key concept in designing high-quality nuclear reactor systems. While the establishment and reliability of a nuclear power plant is largely facilitated by the installment of standardized base units, the realization of modularity at the sub-system/sub-unit level in a base unit is still highly heuristic, and lacks consistent, quantifiable measures. In this work, an axiomatic design approach is developed to evaluate and optimize the reactor cavity cooling system (RCCS) of General Atomics' Gas Turbine-Modular Helium Reactor (GT-MHR) nuclear reactor, for the purpose of constructing a quantitative tool that is applicable to Gen-IV systems. According to Suh's axiomatic design theory, modularity is consistently represented by functional independence through the design process. Both qualitative and quantitative measures are developed here to evaluate the modularity of the current RCCS design. Optimization techniques are also used to improve the modularity at both conceptual and parametric level. The preliminary results of this study have demonstrated that the axiomatic design approach has great potential in enhancing modular design, and generating more robust, safer, and less expensive nuclear reactor sub-units

An axiomatic characterization of the Hirsch-index

NARCIS (Netherlands)

Woeginger, G.J.

2008-01-01

The Hirsch-index is a well-known index for measuring and comparing the output of scientific researchers. The main contribution of this article is an axiomatic characterization of the Hirsch-index in terms of three natural axioms. Furthermore, two other scientific impact indices (called the w-index

S-matrices for perturbations of certain conformal field theories

International Nuclear Information System (INIS)

Freund, P.G.O.; Klassen, T.R.; Melzer, E.; Chicago Univ., IL

1989-01-01

We present a family of factorizable S-matrix theories in 1+1 dimensions with an arbitrary number N of particles of distinct masses, and find the conservation laws of these theories. An analysis of the conservation laws of the family of nonunitary CFTs with central charge c=c 2,2N+3 =-2N(6N+5)/(2N+3) perturbed by the φ (1,3) operator, leads us to conjecture the identification of these perturbed CFTs with the S-matrix theories we found. The case N=1 was treated by Cardy and Mussardo. We also present the S-matrix of an E 7 -related unitary model. (orig.)

The amplitude of quantum field theory

International Nuclear Information System (INIS)

Medvedev, B.V.; Pavlov, V.P.; Polivanov, M.K.; Sukhanov, A.D.

1989-01-01

General properties of the transition amplitude in axiomatic quantum field theory are discussed. Bogolyubov's axiomatic method is chosen as the variant of the theory. The axioms of this method are analyzed. In particular, the significance of the off-shell extension and of the various forms of the causality condition are examined. A complete proof is given of the existence of a single analytic function whose boundary values are the amplitudes of all channels of a process with given particle number

Random matrix theory

CERN Document Server

Deift, Percy

2009-01-01

This book features a unified derivation of the mathematical theory of the three classical types of invariant random matrix ensembles-orthogonal, unitary, and symplectic. The authors follow the approach of Tracy and Widom, but the exposition here contains a substantial amount of additional material, in particular, facts from functional analysis and the theory of Pfaffians. The main result in the book is a proof of universality for orthogonal and symplectic ensembles corresponding to generalized Gaussian type weights following the authors' prior work. New, quantitative error estimates are derive

Asymptotic Bethe ansatz S-matrix and Landau-Lifshitz-type effective 2d actions

International Nuclear Information System (INIS)

Roiban, R; Tirziu, A; Tseytlin, A A

2006-01-01

Motivated by the desire to relate Bethe ansatz equations for anomalous dimensions found on the gauge-theory side of the AdS/CFT correspondence to superstring theory on AdS 5 x S 5 we explore a connection between the asymptotic S-matrix that enters the Bethe ansatz and an effective two-dimensional quantum field theory. The latter generalizes the standard 'non-relativistic' Landau-Lifshitz (LL) model describing low-energy modes of ferromagnetic Heisenberg spin chain and should be related to a limit of superstring effective action. We find the exact form of the quartic interaction terms in the generalized LL-type action whose quantum S-matrix matches the low-energy limit of the asymptotic S-matrix of the spin chain of Beisert, Dippel and Staudacher (BDS). This generalizes to all orders in the 't Hooft coupling λ an earlier computation of Klose and Zarembo of the S-matrix of the standard LL model. We also consider a generalization to the case when the spin-chain S-matrix contains an extra 'string' phase and determine the exact form of the LL 4-vertex corresponding to the low-energy limit of the ansatz of Arutyunov, Frolov and Staudacher (AFS). We explain the relation between the resulting 'non-relativistic' non-local action and the second-derivative string sigma model. We comment on modifications introduced by strong-coupling corrections to the AFS phase. We mostly discuss the SU(2) sector but also present generalizations to the SL(2) and SU(1|1) sectors, confirming universality of the dressing phase contribution by matching the low-energy limit of the AFS-type spin-chain S-matrix with tree-level string-theory S-matrix

Low-cost Antenna Positioning System Designed with Axiomatic Design

Directory of Open Access Journals (Sweden)

Timothy Foley Joseph

2017-01-01

Full Text Available The Engineering Optimization and Modeling Center at Reykjavik University has been carrying out research on antenna CAD, including the simulation-driven design of novel antenna topologies. However, simulation is not enough to validate a design: a custom RF anechoic chamber has been built to quantify antenna performance, particularly in terms of field properties such as radiation patterns. Such experiments require careful positioning of the antenna in the chamber accurately in 3-axis with a short development time, challenging material constraints, and minimal funding. Axiomatic Design Theory principles were applied to develop an automated 3-axis positioner system for a reference antenna and the antenna to be calibrated. Each axis can be individually controlled with a repeatability of 1 degree. This 3000 USD device can be fabricated using easily available components and rapid prototyping tools.

On low rank classical groups in string theory, gauge theory and matrix models

International Nuclear Information System (INIS)

Intriligator, Ken; Kraus, Per; Ryzhov, Anton V.; Shigemori, Masaki; Vafa, Cumrun

2004-01-01

We consider N=1 supersymmetric U(N), SO(N), and Sp(N) gauge theories, with two-index tensor matter and added tree-level superpotential, for general breaking patterns of the gauge group. By considering the string theory realization and geometric transitions, we clarify when glueball superfields should be included and extremized, or rather set to zero; this issue arises for unbroken group factors of low rank. The string theory results, which are equivalent to those of the matrix model, refer to a particular UV completion of the gauge theory, which could differ from conventional gauge theory results by residual instanton effects. Often, however, these effects exhibit miraculous cancellations, and the string theory or matrix model results end up agreeing with standard gauge theory. In particular, these string theory considerations explain and remove some apparent discrepancies between gauge theories and matrix models in the literature

Axiomatic Characterizations of IVF Rough Approximation Operators

Directory of Open Access Journals (Sweden)

Guangji Yu

2014-01-01

Full Text Available This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.

The R-matrix theory

International Nuclear Information System (INIS)

Descouvemont, P; Baye, D

2010-01-01

The different facets of the R-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: (i) The 'calculable' R-matrix method is a calculational tool to derive scattering properties from the Schroedinger equation in a large variety of physical problems. It was developed rather independently in atomic and nuclear physics with too little mutual influence. (ii) The 'phenomenological' R-matrix method is a technique to parametrize various types of cross sections. It was mainly (or uniquely) used in nuclear physics. Both directions are explained by starting from the simple problem of scattering by a potential. They are illustrated by simple examples in nuclear and atomic physics. In addition to elastic scattering, the R-matrix formalism is applied to inelastic and radiative-capture reactions. We also present more recent and more ambitious applications of the theory in nuclear physics.

The R-matrix of the Uq(d4(3)) algebra and g2(1) affine Toda field theory

International Nuclear Information System (INIS)

Takacs, G.

1997-01-01

The R-matrix of the U q (d 4 (3) ) algebra is constructed in the 8-dimensional fundamental representation. Using this result, an exact S-matrix is conjectured for the imaginary coupled g 2 (1) affine Toda field theory, the structure of which is found to be very similar to the previously investigated S-matrix of d 4 (3) Toda theory. It is shown that this S-matrix is consistent with the results for the case of real coupling using the breather-particle correspondence. For q a root of unity it is argued that the theory can be restricted to yield Φ(11 vertical stroke 12) perturbations of WA 2 minimal models. (orig.)

The equational theory of prebisimilarity over basic CCS with divergence

NARCIS (Netherlands)

Aceto, L.; Capobianco, S.; Ingólfsdóttir, A.; Luttik, B.

2008-01-01

This paper studies the equational theory of prebisimilarity, a bisimulation-based preorder introduced by Hennessy and Milner in the early 1980s, over basic CCS with the divergent process O. It is well known that prebisimilarity affords a finite ground-complete axiomatization over this language; this

Chern-Simons couplings for dielectric F-strings in matrix string theory

International Nuclear Information System (INIS)

Brecher, Dominic; Janssen, Bert; Lozano, Yolanda

2002-01-01

We compute the non-abelian couplings in the Chern-Simons action for a set of coinciding fundamental strings in both the type IIA and type IIB Matrix string theories. Starting from Matrix theory in a weakly curved background, we construct the linear couplings of closed string fields to type IIA Matrix strings. Further dualities give a type IIB Matrix string theory and a type IIA theory of Matrix strings with winding. (Abstract Copyright[2002], Wiley Periodicals, Inc.)

A survey of matrix theory and matrix inequalities

CERN Document Server

Marcus, Marvin

2010-01-01

Written for advanced undergraduate students, this highly regarded book presents an enormous amount of information in a concise and accessible format. Beginning with the assumption that the reader has never seen a matrix before, the authors go on to provide a survey of a substantial part of the field, including many areas of modern research interest.Part One of the book covers not only the standard ideas of matrix theory, but ones, as the authors state, ""that reflect our own prejudices,"" among them Kronecker products, compound and induced matrices, quadratic relations, permanents, incidence

Nash was a first to axiomatize expected utility

NARCIS (Netherlands)

H. Bleichrodt (Han); C. Li (Chen); I. Moscati (Ivan); P.P. Wakker (Peter)

2016-01-01

textabstractNash is famous for many inventions, but it is less known that he, simultaneously with Marschak, also was the first to axiomatize expected utility for risk. In particular, these authors were the first to state the independence condition, a condition that should have been but was not

Statistical Origin of Black Hole Entropy in Matrix Theory

International Nuclear Information System (INIS)

Lowe, D.A.

1998-01-01

The statistical entropy of black holes in matrix theory is considered. Assuming matrix theory is the discretized light-cone quantization of a theory with eleven-dimensional Lorentz invariance, we map the counting problem onto the original Gibbons-Hawking calculations of the thermodynamic entropy. copyright 1998 The American Physical Society

Matrix approach to the Shapley value and dual similar associated consistency

NARCIS (Netherlands)

Xu, G.; Driessen, Theo

Replacing associated consistency in Hamiache's axiom system by dual similar associated consistency, we axiomatize the Shapley value as the unique value verifying the inessential game property, continuity and dual similar associated consistency. Continuing the matrix analysis for Hamiache's

Enumeration of RNA complexes via random matrix theory.

Science.gov (United States)

Andersen, Jørgen E; Chekhov, Leonid O; Penner, Robert C; Reidys, Christian M; Sułkowski, Piotr

2013-04-01

In the present article, we review a derivation of the numbers of RNA complexes of an arbitrary topology. These numbers are encoded in the free energy of the Hermitian matrix model with potential V(x)=x2/2-stx/(1-tx), where s and t are respective generating parameters for the number of RNA molecules and hydrogen bonds in a given complex. The free energies of this matrix model are computed using the so-called topological recursion, which is a powerful new formalism arising from random matrix theory. These numbers of RNA complexes also have profound meaning in mathematics: they provide the number of chord diagrams of fixed genus with specified numbers of backbones and chords as well as the number of cells in Riemann's moduli spaces for bordered surfaces of fixed topological type.

Matrix effective theories of the fractional quantum Hall effect

International Nuclear Information System (INIS)

Cappelli, Andrea; Rodriguez, Ivan D

2009-01-01

The present understanding of nonperturbative ground states in the fractional quantum Hall effect is based on effective theories of the Jain 'composite fermion' excitations. We review the approach based on matrix variables, i.e. D0 branes, originally introduced by Susskind and Polychronakos. We show that the Maxwell-Chern-Simons matrix gauge theory provides a matrix generalization of the quantum Hall effect, where the composite-fermion construction naturally follows from gauge invariance. The matrix ground states obtained by suitable projections of higher Landau levels are found to be in one-to-one correspondence with the Laughlin and Jain hierarchical states. The matrix theory possesses a physical limit for commuting matrices that could be reachable while staying in the same phase.

Matrix models as non-commutative field theories on R3

International Nuclear Information System (INIS)

Livine, Etera R

2009-01-01

In the context of spin foam models for quantum gravity, group field theories are a useful tool allowing on the one hand a non-perturbative formulation of the partition function and on the other hand admitting an interpretation as generalized matrix models. Focusing on 2d group field theories, we review their explicit relation to matrix models and show their link to a class of non-commutative field theories invariant under a quantum-deformed 3d Poincare symmetry. This provides a simple relation between matrix models and non-commutative geometry. Moreover, we review the derivation of effective 2d group field theories with non-trivial propagators from Boulatov's group field theory for 3d quantum gravity. Besides the fact that this gives a simple and direct derivation of non-commutative field theories for the matter dynamics coupled to (3d) quantum gravity, these effective field theories can be expressed as multi-matrix models with a non-trivial coupling between matrices of different sizes. It should be interesting to analyze this new class of theories, both from the point of view of matrix models as integrable systems and for the study of non-commutative field theories.

The gravitational S-matrix

CERN Document Server

Giddings, Steven B

2010-01-01

We investigate the hypothesized existence of an S-matrix for gravity, and some of its expected general properties. We first discuss basic questions regarding existence of such a matrix, including those of infrared divergences and description of asymptotic states. Distinct scattering behavior occurs in the Born, eikonal, and strong gravity regimes, and we describe aspects of both the partial wave and momentum space amplitudes, and their analytic properties, from these regimes. Classically the strong gravity region would be dominated by formation of black holes, and we assume its unitary quantum dynamics is described by corresponding resonances. Masslessness limits some powerful methods and results that apply to massive theories, though a continuation path implying crossing symmetry plausibly still exists. Physical properties of gravity suggest nonpolynomial amplitudes, although crossing and causality constrain (with modest assumptions) this nonpolynomial behavior, particularly requiring a polynomial bound in c...

Quasi-degenerate perturbation theory using matrix product states

International Nuclear Information System (INIS)

Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali

2016-01-01

In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner’s 2n + 1 rule. Further, our formulation satisfies Granovsky’s requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost

Quasi-degenerate perturbation theory using matrix product states

Energy Technology Data Exchange (ETDEWEB)

Sharma, Sandeep, E-mail: sanshar@gmail.com; Jeanmairet, Guillaume [Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart (Germany); Alavi, Ali, E-mail: a.alavi@fkf.mpg.de [Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart (Germany); Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW (United Kingdom)

2016-01-21

In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner’s 2n + 1 rule. Further, our formulation satisfies Granovsky’s requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.

Endogenous Prospect Theory

OpenAIRE

Schmidt, Ulrich; Zank, Horst

2010-01-01

In previous models of (cumulative) prospect theory reference-dependence of preferences is imposed beforehand and the location of the reference point is exogenously determined. This paper provides an axiomatization of a new specification of cumulative prospect theory, termed endogenous prospect theory, where reference-dependence is derived from preference conditions and a unique reference point arises endogenously.

Random Matrix Theory and Econophysics

Science.gov (United States)

Rosenow, Bernd

2000-03-01

Random Matrix Theory (RMT) [1] is used in many branches of physics as a ``zero information hypothesis''. It describes generic behavior of different classes of systems, while deviations from its universal predictions allow to identify system specific properties. We use methods of RMT to analyze the cross-correlation matrix C of stock price changes [2] of the largest 1000 US companies. In addition to its scientific interest, the study of correlations between the returns of different stocks is also of practical relevance in quantifying the risk of a given stock portfolio. We find [3,4] that the statistics of most of the eigenvalues of the spectrum of C agree with the predictions of RMT, while there are deviations for some of the largest eigenvalues. We interpret these deviations as a system specific property, e.g. containing genuine information about correlations in the stock market. We demonstrate that C shares universal properties with the Gaussian orthogonal ensemble of random matrices. Furthermore, we analyze the eigenvectors of C through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum - a situation reminiscent of localization theory results. This work was done in collaboration with V. Plerou, P. Gopikrishnan, T. Guhr, L.A.N. Amaral, and H.E Stanley and is related to recent work of Laloux et al.. 1. T. Guhr, A. Müller Groeling, and H.A. Weidenmüller, ``Random Matrix Theories in Quantum Physics: Common Concepts'', Phys. Rep. 299, 190 (1998). 2. See, e.g. R.N. Mantegna and H.E. Stanley, Econophysics: Correlations and Complexity in Finance (Cambridge University Press, Cambridge, England, 1999). 3. V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, and H.E. Stanley, ``Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series'', Phys. Rev. Lett. 83, 1471 (1999). 4. V. Plerou, P. Gopikrishnan, T. Guhr, B. Rosenow, L.A.N. Amaral, and H.E. Stanley, ``Random Matrix Theory

Notes on branes in matrix theory

International Nuclear Information System (INIS)

Keski-Vakkuri, E.; Kraus, P.

1998-01-01

We study the effective actions of various brane configurations in matrix theory. Starting from the 0+1-dimensional quantum mechanics, we replace coordinate matrices by covariant derivatives in the large N limit, thereby obtaining effective field theories on the brane world-volumes. Even for non-compact branes, these effective theories are of Yang-Mills type, with constant background magnetic fields. In the case of a D2-brane, we show explicitly how the effective action equals the large magnetic field limit of the Born-Infeld action, and thus derive from matrix theory the action used by Polchinski and Pouliot to compute M-momentum transfer between membranes. We also consider the effect of compactifying transverse directions. Finally, we analyze a scattering process involving a recently proposed background representing a classically stable D6+D0 brane configuration. We compute the potential between this configuration and a D0-brane, and show that the result agrees with supergravity. (orig.)

Matrix Mathematics Theory, Facts, and Formulas (Second Edition)

CERN Document Server

Bernstein, Dennis S

2011-01-01

When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices. Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminat

Matrix algebra theory, computations and applications in statistics

CERN Document Server

Gentle, James E

2017-01-01

This textbook for graduate and advanced undergraduate students presents the theory of matrix algebra for statistical applications, explores various types of matrices encountered in statistics, and covers numerical linear algebra. Matrix algebra is one of the most important areas of mathematics in data science and in statistical theory, and the second edition of this very popular textbook provides essential updates and comprehensive coverage on critical topics in mathematics in data science and in statistical theory. Part I offers a self-contained description of relevant aspects of the theory of matrix algebra for applications in statistics. It begins with fundamental concepts of vectors and vector spaces; covers basic algebraic properties of matrices and analytic properties of vectors and matrices in multivariate calculus; and concludes with a discussion on operations on matrices in solutions of linear systems and in eigenanalysis. Part II considers various types of matrices encountered in statistics, such as...

Recent progress in the application of R-matrix Floquet theory

International Nuclear Information System (INIS)

Hart van der, H.W.

2006-01-01

-electron repulsion reducing the He binding energy. Investigations of He at this photon energy thus give new fundamental insight into the nature of electron-electron repulsion. The description of the collective response of atomic electrons becomes increasingly more difficult with increasing number of atomic electrons. However, R-matrix theory was designed to cope with these difficulties. For example, inner-shell processes involving the absorption of a single photon have been studied extensively using R-matrix theory. We demonstrate that this capability carries over to R-matrix Floquet theory by investigating the multiphoton emission of an inner-shell 1s electron from Li - was chosen, since only a relatively small number of Li target states are necessary to describe the triply excited states of Li - in the calculations.

Paired comparisons analysis: an axiomatic approach to ranking methods

NARCIS (Netherlands)

Gonzalez-Diaz, J.; Hendrickx, Ruud; Lohmann, E.R.M.A.

2014-01-01

In this paper we present an axiomatic analysis of several ranking methods for general tournaments. We find that the ranking method obtained by applying maximum likelihood to the (Zermelo-)Bradley-Terry model, the most common method in statistics and psychology, is one of the ranking methods that

A generalized DEMATEL theory with a shrinkage coefficient for an indirect relation matrix

Directory of Open Access Journals (Sweden)

Liu Hsiang-Chuan

2017-01-01

Full Text Available In this paper, a novel decision-making trial and evaluation laboratory (DEMATEL theory with a shrinkage coefficient of indirect relation matrix is proposed, and a useful validity index, called Liu’s validity index, is also proposed for evaluating the performance of any DEMATEL model. If the shrinkage coefficient of an indirect relation matrix is equal to 1, then this new theory is identical to the traditional theory; in other words, it is a generalization of the traditional theory. Furthermore, the indirect relation is always considerably greater than the direct one in traditional DEMATEL theory, which is unreasonable and unfair because it overemphasizes the influence of the indirect relation. We prove in this paper that if the shrinkage coefficient is equal to 0.5, then the indirect relation is less than its direct relation. Because the shrinkage coefficient belongs to [0.5, 1], according to Liu’s validity index, we can find a more appropriate shrinkage coefficient to obtain a more efficient DEMATEL method. Some crucial properties of this new theory are discussed, and a simple example is provided to illustrate the advantages of the proposed theory.

Mechanical design of an electronic control unit using axiomatic principles

Directory of Open Access Journals (Sweden)

Cazacu Vlad

2017-01-01

Full Text Available If the engine of the car can be considered as the heart, then the E.C.U’s represents the brain of the car. Electronic control units (E.C.U’s are electronic devices which control the way different components of a car (engine, windows, airbags, etc. react in some situations (overheating, button pressed by a passenger, crash, etc.. Axiomatic design is a set of principles that theorizes the act of conceiving a new project. Based on two axiom this method comes into designers help, giving them the option to reach in a short period of time a fully functional and compliant product without supporting the design of the product on chance, past experiences or “try and fail” principle.

Two-matrix models and c =1 string theory

International Nuclear Information System (INIS)

Bonora, L.; Xiong Chuansheng

1994-05-01

We show that the most general two-matrix model with bilinear coupling underlies c = 1 string theory. More precisely we prove that W 1+∞ constraints, a subset of the correlation functions and the integrable hierarchy characterizing such two-matrix model, correspond exactly to the W 1+∞ constraints, to the discrete tachyon correlation functions and the integrable hierarchy of the c = 1 string theory. (orig.)

Matrix model as a mirror of Chern-Simons theory

International Nuclear Information System (INIS)

Aganagic, Mina; Klemm, Albrecht; Marino, Marcos; Vafa, Cumrun

2004-01-01

Using mirror symmetry, we show that Chern-Simons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more conventional canonical quantization of Chern-Simons theory. Moreover, large N dualities in this context lead to computation of all genus A-model topological amplitudes on toric Calabi-Yau manifolds in terms of matrix integrals. In the context of type IIA superstring compactifications on these Calabi-Yau manifolds with wrapped D6 branes (which are dual to M-theory on G2 manifolds) this leads to engineering and solving F-terms for N=1 supersymmetric gauge theories with superpotentials involving certain multi-trace operators. (author)

Axiomatic Ontology Learning Approaches for English Translation of the Meaning of Quranic Texts

Directory of Open Access Journals (Sweden)

Saad Saidah

2017-01-01

Full Text Available Ontology learning (OL is the computational task of generating a knowledge base in the form of an ontology, given an unstructured corpus in natural language (NL. While most works in the field of ontology learning have been primarily based on a statistical approach to extract lightweight OL, very few attempts have been made to extract axiomatic OL (called heavyweight OL from NL text documents. Axiomatic OL supports more precise formal logic-based reasoning when compared to lightweight OL. Lexico-syntactic pattern matching and statisticsal one cannot lead to very accurate learning, mostly because of several linguistic nuances in the NL. Axiomatic OL is an alternative methodology that has not been explored much, where a deep linguistics analysis in computational linguistics is used to generate formal axioms and definitions instead of simply inducing a taxonomy. The ontology that is created not only stores the information about the application domain in explicit knowledge, but also can deduce the implicit knowledge from this ontology. This research will explore the English translation of the meaning of Quranic texts.

Causality and dispersion relations and the role of the S-matrix in the ongoing research

Energy Technology Data Exchange (ETDEWEB)

Schroer, Bert, E-mail: schroer@cbpf.b [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Freie Univ. , Berlin (Germany). Inst. fur Theoretische Physik

2011-07-01

The adaptation of the Kramers-Kronig dispersion relations to the causal localization structure of QFT led to an important project in particle physics, the only one with a successful closure. The same cannot be said about the subsequent attempts to formulate particle physics as a pure S-matrix project. The feasibility of a pure S-matrix approach are critically analyzed and their seri- ous shortcomings are highlighted. Whereas the conceptual/mathematical demands of renormalized perturbation theory are modest and misunderstandings could easily be corrected, the correct understanding about the origin of the crossing property demands the use of the mathematical theory of modular localization and its relation to the thermal KMS condition. These concepts which combine localization, vacuum polarization and thermal properties under the roof of modular theory will be explained and their use in a new constructive (nonperturbative) approach to QFT will be indicated. The S-matrix still plays a predominant role, but different from Heisenberg's and Mandelstam's proposals the new project is not a pure S-matrix approach. (author)

Hamiltonian formalism, quantization and S matrix for supergravity. [S matrix, canonical constraints

Energy Technology Data Exchange (ETDEWEB)

Fradkin, E S; Vasiliev, M A [AN SSSR, Moscow. Fizicheskij Inst.

1977-12-05

The canonical formalism for supergravity is constructed. The algebra of canonical constraints is found. The correct expression for the S matrix is obtained. Usual 'covariant methods' lead to an incorrect S matrix in supergravity since a new four-particle interaction of ghostfields survives in the Lagrangian expression of the S matrix.

A random-matrix theory of the number sense.

Science.gov (United States)

Hannagan, T; Nieder, A; Viswanathan, P; Dehaene, S

2017-02-19

Number sense, a spontaneous ability to process approximate numbers, has been documented in human adults, infants and newborns, and many other animals. Species as distant as monkeys and crows exhibit very similar neurons tuned to specific numerosities. How number sense can emerge in the absence of learning or fine tuning is currently unknown. We introduce a random-matrix theory of self-organized neural states where numbers are coded by vectors of activation across multiple units, and where the vector codes for successive integers are obtained through multiplication by a fixed but random matrix. This cortical implementation of the 'von Mises' algorithm explains many otherwise disconnected observations ranging from neural tuning curves in monkeys to looking times in neonates and cortical numerotopy in adults. The theory clarifies the origin of Weber-Fechner's Law and yields a novel and empirically validated prediction of multi-peak number neurons. Random matrices constitute a novel mechanism for the emergence of brain states coding for quantity.This article is part of a discussion meeting issue 'The origins of numerical abilities'. © 2017 The Author(s).

Reduced-density-matrix theory and algebraic structures

International Nuclear Information System (INIS)

Kryachko, E.S.

1978-01-01

A survey of recent work on algebraic structures and reduced-density-matrix theory is presented. The approach leads to a method of classifying reduced density matrices and generalizes the notion of open and closed shells in many-body theory. 6 references

Tetrahedron equations and the relativistic S-matrix of straight-strings in 2+1-dimensions

International Nuclear Information System (INIS)

Zamolodchikov, A.B.

1981-01-01

The quantum S-matrix theory of straight-strings (infinite one-dimensioanl objects like straight domain walls) in 2 + 1-dimensions is considered. The S-matrix is supposed to be purely elastic and factorized. The tetrahedron equations (which are the factorization conditions) are investigated for the special two-colour model. The relativistic three-string S-matrix, which apparently satisfies this tetrahedron equation, is proposed. (orig.)

An Ar threesome: Matrix models, 2d conformal field theories, and 4dN=2 gauge theories

International Nuclear Information System (INIS)

Schiappa, Ricardo; Wyllard, Niclas

2010-01-01

We explore the connections between three classes of theories: A r quiver matrix models, d=2 conformal A r Toda field theories, and d=4N=2 supersymmetric conformal A r quiver gauge theories. In particular, we analyze the quiver matrix models recently introduced by Dijkgraaf and Vafa (unpublished) and make detailed comparisons with the corresponding quantities in the Toda field theories and the N=2 quiver gauge theories. We also make a speculative proposal for how the matrix models should be modified in order for them to reproduce the instanton partition functions in quiver gauge theories in five dimensions.

arXiv The S-matrix Bootstrap II: Two Dimensional Amplitudes

CERN Document Server

Paulos, Miguel F.; Toledo, Jonathan; van Rees, Balt C.; Vieira, Pedro

2017-11-22

We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 1 + 1 dimensions due to crossing symmetry and unitarity. In this way we establish rigorous bounds on the cubic couplings of a given theory with a fixed mass spectrum. In special cases we identify interesting integrable theories saturating these bounds. Our analytic bounds match precisely with numerical bounds obtained in a companion paper where we consider massive QFT in an AdS box and study boundary correlators using the technology of the conformal bootstrap.

An Axiomatic, Unified Representation of Biosystems and Quantum Dynamics

CERN Document Server

Baianu, I

2004-01-01

An axiomatic representation of system dynamics is introduced in terms of categories, functors, organismal supercategories, limits and colimits of diagrams. Specific examples are considered in Complex Systems Biology, such as ribosome biogenesis and Hormonal Control in human subjects. "Fuzzy" Relational Structures are also proposed for flexible representations of biological system dynamics and organization.

Asymptotic states and the definition of the S-matrix in quantum gravity

International Nuclear Information System (INIS)

Wiesendanger, C

2013-01-01

Viewing gravitational energy–momentum p G μ as equal by observation, but different in essence from inertial energy–momentum p I μ naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner Minkowski space M 4 . The generalized asymptotic free scalar, Dirac and gauge fields in that theory are canonically quantized, the Fock spaces of stationary states are constructed and the gravitational limit—mapping the gravitational energy–momentum onto the inertial energy–momentum to account for their observed equality—is introduced. Next the S-matrix in quantum gravity is defined as the gravitational limit of the transition amplitudes of asymptotic in- to out-states in the gauge theory of volume-preserving diffeomorphisms. The so-defined S-matrix relates in- and out-states of observable particles carrying gravitational equal to inertial energy–momentum. Finally, generalized Lehmann–Symanzik–Zimmermann reduction formulae for scalar, Dirac and gauge fields are established which allow us to express S-matrix elements as the gravitational limit of truncated Fourier-transformed vacuum expectation values of time-ordered products of field operators of the interacting theory. Together with the generating functional of the latter established in Wiesendanger (2011 arXiv:1103.1012) any transition amplitude can in principle be computed consistently to any order in perturbative quantum gravity. (paper)

Introduction to algebraic quantum field theory

International Nuclear Information System (INIS)

Horuzhy, S.S.

1990-01-01

This volume presents a systematic introduction to the algebraic approach to quantum field theory. The structure of the contents corresponds to the way the subject has advanced. It is shown how the algebraic approach has developed from the purely axiomatic theory of observables via superselection rules into the dynamical formalism of fields and observables. Chapter one discusses axioms and their consequences -many of which are now classical theorems- and deals, in general, with the axiomatic theory of local observable algebras. The absence of field concepts makes this theory incomplete and, in chapter two, superselection rules are shown to be the key to the reconstruction of fields from observables. Chapter three deals with the algebras of Wightman fields, first unbounded operator algebras, then Von Neumann field algebras (with a special section on wedge region algebras) and finally local algebras of free and generalised free fields. (author). 447 refs.; 4 figs

Big bang and big crunch in matrix string theory

OpenAIRE

Bedford, J; Papageorgakis, C; Rodríguez-Gómez, D; Ward, J

2007-01-01

Following the holographic description of linear dilaton null Cosmologies with a Big Bang in terms of Matrix String Theory put forward by Craps, Sethi and Verlinde, we propose an extended background describing a Universe including both Big Bang and Big Crunch singularities. This belongs to a class of exact string backgrounds and is perturbative in the string coupling far away from the singularities, both of which can be resolved using Matrix String Theory. We provide a simple theory capable of...

Causality and dispersion relations and the role of the S-matrix in the ongoing research

International Nuclear Information System (INIS)

Schroer, Bert; Freie Univ. , Berlin

2011-01-01

The adaptation of the Kramers-Kronig dispersion relations to the causal localization structure of QFT led to an important project in particle physics, the only one with a successful closure. The same cannot be said about the subsequent attempts to formulate particle physics as a pure S-matrix project. The feasibility of a pure S-matrix approach are critically analyzed and their seri- ous shortcomings are highlighted. Whereas the conceptual/mathematical demands of renormalized perturbation theory are modest and misunderstandings could easily be corrected, the correct understanding about the origin of the crossing property demands the use of the mathematical theory of modular localization and its relation to the thermal KMS condition. These concepts which combine localization, vacuum polarization and thermal properties under the roof of modular theory will be explained and their use in a new constructive (nonperturbative) approach to QFT will be indicated. The S-matrix still plays a predominant role, but different from Heisenberg's and Mandelstam's proposals the new project is not a pure S-matrix approach. (author)

Design of Safety Injection Tanks Using Axiomatic Design and TRIZ

International Nuclear Information System (INIS)

Heo, Gyunyoung; Jeong, Yong Hoon

2008-01-01

Design can be categorized into two steps: 'synthesis' and 'analysis'. While synthesis is the process of decision-making on design parameters, analysis is the process of optimizing the parameters selected. It is known from experience that the mistakes made in the synthesis process are hardly corrected in the analysis process. 'Systematic synthesis' is, therefore, easy to overlook but an important topic. 'Systematic' is interpreted as 'minimizing' uncertainty and subjectivity. This paper will introduce the design product achieved by using Axiomatic Design (AD) and TRIZ (Theory of Inventive Problem Solving romanized acronym for Russian), which is a new design of Safety Injection Tank (SIT). In designing a large-capacity SIT which should play an important role in mitigating the large break loss of coolant accidents, there are three issues: 1) the excessively large plenum for pressurized nitrogen gas; 2) the difficulties maintaining the high initial injection flow rate; and 3) the non-condensable nitrogen gas in the coolant. This study proposes a conceptual idea for SITs that are pressurized by the chemical reaction of solid propellants. The AD theory and the principles of TRIZ enable new approach in problem-solving for those three issues in an innovative way. The paper made an effort to clarify the systematic synthesis process to reach the final design solution. (authors)

Planar plane-wave matrix theory at the four loop order: integrability without BMN scaling

International Nuclear Information System (INIS)

Fischbacher, Thomas; Klose, Thomas; Plefka, Jan

2005-01-01

We study SU(N) plane-wave matrix theory up to fourth perturbative order in its large N planar limit. The effective hamiltonian in the closed su(2) subsector of the model is explicitly computed through a specially tailored computer program to perform large scale distributed symbolic algebra and generation of planar graphs. The number of graphs here was in the deep billions. The outcome of our computation establishes the four-loop integrability of the planar plane-wave matrix model. To elucidate the integrable structure we apply the recent technology of the perturbative asymptotic Bethe ansatz to our model. The resulting S-matrix turns out to be structurally similar but nevertheless distinct to the so far considered long-range spin-chain S-matrices of Inozemtsev, Beisert-Dippel-Staudacher and Arutyunov-Frolov-Staudacher in the AdS/CFT context. In particular our result displays a breakdown of BMN scaling at the four-loop order. That is, while there exists an appropriate identification of the matrix theory mass parameter with the coupling constant of the N=4 superconformal Yang-Mills theory which yields an eighth order lattice derivative for well separated impurities (naively implying BMN scaling) the detailed impurity contact interactions ruin this scaling property at the four-loop order. Moreover we study the issue of 'wrapping' interactions, which show up for the first time at this loop-order through a Konishi descendant length four operator. (author)

The Automatic Integration of Folksonomies with Taxonomies Using Non-axiomatic Logic

Science.gov (United States)

Geldart, Joe; Cummins, Stephen

Cooperative tagging systems such as folksonomies are powerful tools when used to annotate information resources. The inherent power of folksonomies is in their ability to allow casual users to easily contribute ad hoc, yet meaningful, resource metadata without any specialist training. Older folksonomies have begun to degrade due to the lack of internal structure and from the use of many low quality tags. This chapter describes a remedy for some of the problems associated with folksonomies. We introduce a method of automatic integration and inference of the relationships between tags and resources in a folksonomy using non-axiomatic logic. We test this method on the CiteULike corpus of tags by comparing precision and recall between it and standard keyword search. Our results show that non-axiomatic reasoning is a promising technique for integrating tagging systems with more structured knowledge representations.

Time Breath of Psychological Theories

DEFF Research Database (Denmark)

Tateo, Luca; Valsiner, Jaan

2015-01-01

Psychology as a self-aspiring, ambitious, developmental science faces the crucial limit of time—both theoretically and practically. The issue of time in constructing psychology’s theories is a major unresolved metatheoretical task. This raises several questions about generalization of knowledge...... of time—or fail to do that? How can they generalize with respect to time? The different conceptions of time often remain implicit, while shaping the concepts used in understanding psychological processes. Any preconception about time in human development will foster the generalizability of theory, as well......: which is the time length of breath of psychological theories? Which is the temporal dimension of psychological processes? In this article we discuss the role of different axiomatic assumptions about time in the construction of psychological theories. How could different theories include a concept...

Big bang and big crunch in matrix string theory

International Nuclear Information System (INIS)

Bedford, J.; Ward, J.; Papageorgakis, C.; Rodriguez-Gomez, D.

2007-01-01

Following the holographic description of linear dilaton null cosmologies with a big bang in terms of matrix string theory put forward by Craps, Sethi, and Verlinde, we propose an extended background describing a universe including both big bang and big crunch singularities. This belongs to a class of exact string backgrounds and is perturbative in the string coupling far away from the singularities, both of which can be resolved using matrix string theory. We provide a simple theory capable of describing the complete evolution of this closed universe

A two-loop test of M(atrix) theory

International Nuclear Information System (INIS)

Becker, K.

1997-01-01

We consider the scattering of two Dirichlet zero-branes in M(atrix) theory. Using the formulation of M(atrix) theory in terms of ten-dimensional super Yang-Mills theory dimensionally reduced to (0+1) dimensions, we obtain the effective (velocity-dependent) potential describing these particles. At one loop we obtain the well-known result for the leading order of the effective potential V eff ∝v 4 /r 7 , where v and r are the relative velocity and distance between the two zero-branes, respectively. A calculation of the effective potential at two loops shows that no renormalizations of the v 4 term of the effective potential occur at this order. (orig.)

A matrix model from string field theory

Directory of Open Access Journals (Sweden)

Syoji Zeze

2016-09-01

Full Text Available We demonstrate that a Hermitian matrix model can be derived from level truncated open string field theory with Chan-Paton factors. The Hermitian matrix is coupled with a scalar and U(N vectors which are responsible for the D-brane at the tachyon vacuum. Effective potential for the scalar is evaluated both for finite and large N. Increase of potential height is observed in both cases. The large $N$ matrix integral is identified with a system of N ZZ branes and a ghost FZZT brane.

From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems

Science.gov (United States)

Lozada Aguilar, Miguel Ángel; Khrennikov, Andrei; Oleschko, Klaudia

2018-04-01

As was recently shown by the authors, quantum probability theory can be used for the modelling of the process of decision-making (e.g. probabilistic risk analysis) for macroscopic geophysical structures such as hydrocarbon reservoirs. This approach can be considered as a geophysical realization of Hilbert's programme on axiomatization of statistical models in physics (the famous sixth Hilbert problem). In this conceptual paper, we continue development of this approach to decision-making under uncertainty which is generated by complexity, variability, heterogeneity, anisotropy, as well as the restrictions to accessibility of subsurface structures. The belief state of a geological expert about the potential of exploring a hydrocarbon reservoir is continuously updated by outputs of measurements, and selection of mathematical models and scales of numerical simulation. These outputs can be treated as signals from the information environment E. The dynamics of the belief state can be modelled with the aid of the theory of open quantum systems: a quantum state (representing uncertainty in beliefs) is dynamically modified through coupling with E; stabilization to a steady state determines a decision strategy. In this paper, the process of decision-making about hydrocarbon reservoirs (e.g. `explore or not?'; `open new well or not?'; `contaminated by water or not?'; `double or triple porosity medium?') is modelled by using the Gorini-Kossakowski-Sudarshan-Lindblad equation. In our model, this equation describes the evolution of experts' predictions about a geophysical structure. We proceed with the information approach to quantum theory and the subjective interpretation of quantum probabilities (due to quantum Bayesianism). This article is part of the theme issue `Hilbert's sixth problem'.

Design of a nuclear fuel rod support grid using axiomatic design

International Nuclear Information System (INIS)

Song, Kee Nam; Yoon, Kyung Ho; Kang, Byung Soo; Park, Gyung Jin; Choi, Sung Kyoo

2002-01-01

Recently, much attention is imposed on the design of the fuel assemblies in the Pressurized Light Water Reactor (PWR). Spacer grid is one of the main structural components in a fuel assembly. It supports fuel rods, guides cooling water, and maintains a coolable geometry from the external impact loads. In this research, a new shape of the spacer grid is designed by the axiomatic approach. The Independence axiom is utilized for the design. For conceptual design, functional requirements (FRs) are defined and corresponding design parameters (DPs) are found to satisfy FRs in sequence. Overall configuration and shapes are determined in this process. Detail design is carried out based on the result of the axiomatic design. For the detail design, the system performances are evaluated by using linear and nonlinear finite element analysis. The dimensions are determined by optimization. Some commercial codes are utilized for the analysis and design

S-matrix for the theories that admit closure of the algebra with the aid of auxiliary fields. Auxiliary fields in supergravity. [Word identities

Energy Technology Data Exchange (ETDEWEB)

Fradkin, E S; Vasiliev, M A [AN SSSR, Moscow. Fizicheskij Inst.

1978-08-19

A minimal set of auxiliary fields (scalarpseudoscalar and pseudovector) providing the closed algebra in supergravity is constructed. A compact scheme for the generating functional with closed gauge algebra is proposed. The S-matrix and the Ward identities for arbitrary theory that admits the closing of the algebra by introducing auxiliary fields is obtained.

Axiomatic Design of a Framework for the Comprehensive Optimization of Patient Flows in Hospitals

Directory of Open Access Journals (Sweden)

Gabriele Arcidiacono

2017-01-01

Full Text Available Lean Management and Six Sigma are nowadays applied not only to the manufacturing industry but also to service industry and public administration. The manifold variables affecting the Health Care system minimize the effect of a narrow Lean intervention. Therefore, this paper aims to discuss a comprehensive, system-based approach to achieve a factual holistic optimization of patient flows. This paper debates the efficacy of Lean principles applied to the optimization of patient flows and related activities, structures, and resources, developing a theoretical framework based on the principles of the Axiomatic Design. The demand for patient-oriented and efficient health services leads to use these methodologies to improve hospital processes. In the framework, patients with similar characteristics are clustered in families to achieve homogeneous flows through the value stream. An optimization checklist is outlined as the result of the mapping between Functional Requirements and Design Parameters, with the right sequence of the steps to optimize the patient flow according to the principles of Axiomatic Design. The Axiomatic Design-based top-down implementation of Health Care evidence, according to Lean principles, results in a holistic optimization of hospital patient flows, by reducing the complexity of the system.

Computational physics an introduction to Monte Carlo simulations of matrix field theory

CERN Document Server

Ydri, Badis

2017-01-01

This book is divided into two parts. In the first part we give an elementary introduction to computational physics consisting of 21 simulations which originated from a formal course of lectures and laboratory simulations delivered since 2010 to physics students at Annaba University. The second part is much more advanced and deals with the problem of how to set up working Monte Carlo simulations of matrix field theories which involve finite dimensional matrix regularizations of noncommutative and fuzzy field theories, fuzzy spaces and matrix geometry. The study of matrix field theory in its own right has also become very important to the proper understanding of all noncommutative, fuzzy and matrix phenomena. The second part, which consists of 9 simulations, was delivered informally to doctoral students who are working on various problems in matrix field theory. Sample codes as well as sample key solutions are also provided for convenience and completness. An appendix containing an executive arabic summary of t...

Game theory, social choice and ethics

CERN Document Server

1979-01-01

There are problems to whose solution I would attach an infinitely greater import­ ancf! than to those of mathematics, for example touching ethics, or our relation to God, or conceming our destiny and our future; but their solution lies wholly beyond us and completely outside the province 0 f science. J. F. C. Gauss For a1l his prescience in matters physical and mathematieal, the great Gauss apparently did not foresee one development peculiar to OUT own time. The development I have in mind is the use of mathematical reasoning - in partieu­ lar the axiomatic method - to explicate alternative concepts of rationality and morality. The present bipartite collection of essays (Vol. 11, Nos. 2 and 3 of this journal) is entitled 'Game Theory, Social Choiee, and Ethics'. The eight papers represent state-of-the-art research in formal moral theory. Their intended aim is to demonstrate how the methods of game theory, decision theory, and axiomatic social choice theory can help to illuminate ethical questions central not...

Phase Structure Of Fuzzy Field Theories And Multi trace Matrix Models

International Nuclear Information System (INIS)

Tekel, J.

2015-01-01

We review the interplay of fuzzy field theories and matrix models, with an emphasis on the phase structure of fuzzy scalar field theories. We give a self-contained introduction to these topics and give the details concerning the saddle point approach for the usual single trace and multi trace matrix models. We then review the attempts to explain the phase structure of the fuzzy field theory using a corresponding random matrix ensemble, showing the strength and weaknesses of this approach. We conclude with a list of challenges one needs to overcome and the most interesting open problems one can try to solve. (author)

The logical foundations of scientific theories languages, structures, and models

CERN Document Server

Krause, Decio

2016-01-01

This book addresses the logical aspects of the foundations of scientific theories. Even though the relevance of formal methods in the study of scientific theories is now widely recognized and regaining prominence, the issues covered here are still not generally discussed in philosophy of science. The authors focus mainly on the role played by the underlying formal apparatuses employed in the construction of the models of scientific theories, relating the discussion with the so-called semantic approach to scientific theories. The book describes the role played by this metamathematical framework in three main aspects: considerations of formal languages employed to axiomatize scientific theories, the role of the axiomatic method itself, and the way set-theoretical structures, which play the role of the models of theories, are developed. The authors also discuss the differences and philosophical relevance of the two basic ways of aximoatizing a scientific theory, namely Patrick Suppes’ set theoretical predicate...

Design of Safety Injection Tanks Using Axiomatic Design and TRIZ

Energy Technology Data Exchange (ETDEWEB)

Heo, Gyunyoung [Kyung Hee University, 1 Seocheon-dong, Giheung-gu, Yongin-si, Gyeonggi-do, 446-701 (Korea, Republic of); Jeong, Yong Hoon [Korea Advanced Institute of Science and Technology, 373-1 Guseong-dong, Yuseong-gu, Daejeon, 305-701 (Korea, Republic of)

2008-07-01

Design can be categorized into two steps: 'synthesis' and 'analysis'. While synthesis is the process of decision-making on design parameters, analysis is the process of optimizing the parameters selected. It is known from experience that the mistakes made in the synthesis process are hardly corrected in the analysis process. 'Systematic synthesis' is, therefore, easy to overlook but an important topic. 'Systematic' is interpreted as 'minimizing' uncertainty and subjectivity. This paper will introduce the design product achieved by using Axiomatic Design (AD) and TRIZ (Theory of Inventive Problem Solving romanized acronym for Russian), which is a new design of Safety Injection Tank (SIT). In designing a large-capacity SIT which should play an important role in mitigating the large break loss of coolant accidents, there are three issues: 1) the excessively large plenum for pressurized nitrogen gas; 2) the difficulties maintaining the high initial injection flow rate; and 3) the non-condensable nitrogen gas in the coolant. This study proposes a conceptual idea for SITs that are pressurized by the chemical reaction of solid propellants. The AD theory and the principles of TRIZ enable new approach in problem-solving for those three issues in an innovative way. The paper made an effort to clarify the systematic synthesis process to reach the final design solution. (authors)

Low-temperature random matrix theory at the soft edge

International Nuclear Information System (INIS)

Edelman, Alan; Persson, Per-Olof; Sutton, Brian D.

2014-01-01

“Low temperature” random matrix theory is the study of random eigenvalues as energy is removed. In standard notation, β is identified with inverse temperature, and low temperatures are achieved through the limit β → ∞. In this paper, we derive statistics for low-temperature random matrices at the “soft edge,” which describes the extreme eigenvalues for many random matrix distributions. Specifically, new asymptotics are found for the expected value and standard deviation of the general-β Tracy-Widom distribution. The new techniques utilize beta ensembles, stochastic differential operators, and Riccati diffusions. The asymptotics fit known high-temperature statistics curiously well and contribute to the larger program of general-β random matrix theory

Social patterns revealed through random matrix theory

Science.gov (United States)

Sarkar, Camellia; Jalan, Sarika

2014-11-01

Despite the tremendous advancements in the field of network theory, very few studies have taken weights in the interactions into consideration that emerge naturally in all real-world systems. Using random matrix analysis of a weighted social network, we demonstrate the profound impact of weights in interactions on emerging structural properties. The analysis reveals that randomness existing in particular time frame affects the decisions of individuals rendering them more freedom of choice in situations of financial security. While the structural organization of networks remains the same throughout all datasets, random matrix theory provides insight into the interaction pattern of individuals of the society in situations of crisis. It has also been contemplated that individual accountability in terms of weighted interactions remains as a key to success unless segregation of tasks comes into play.

On single-time reduction in quantum field theory

International Nuclear Information System (INIS)

Arkhipov, A.A.

1984-01-01

It is shown, how the causality and spectrality properties in qUantum field theory may help one to carry out a single-time reduction of the Bethe-Salpeter wave fUnction. The single-time reduction technique is not based on any concrete model of the quantum field theory. Axiomatic formulations underline the quantum field theory

Axiomatic Design of a Framework for the Comprehensive Optimization of Patient Flows in Hospitals

Science.gov (United States)

Arcidiacono, Gabriele; Matt, Dominik T.; Rauch, Erwin

2017-01-01

Lean Management and Six Sigma are nowadays applied not only to the manufacturing industry but also to service industry and public administration. The manifold variables affecting the Health Care system minimize the effect of a narrow Lean intervention. Therefore, this paper aims to discuss a comprehensive, system-based approach to achieve a factual holistic optimization of patient flows. This paper debates the efficacy of Lean principles applied to the optimization of patient flows and related activities, structures, and resources, developing a theoretical framework based on the principles of the Axiomatic Design. The demand for patient-oriented and efficient health services leads to use these methodologies to improve hospital processes. In the framework, patients with similar characteristics are clustered in families to achieve homogeneous flows through the value stream. An optimization checklist is outlined as the result of the mapping between Functional Requirements and Design Parameters, with the right sequence of the steps to optimize the patient flow according to the principles of Axiomatic Design. The Axiomatic Design-based top-down implementation of Health Care evidence, according to Lean principles, results in a holistic optimization of hospital patient flows, by reducing the complexity of the system. © 2017 Gabriele Arcidiacono et al.

Commutative monads as a theory of distributions

DEFF Research Database (Denmark)

Kock, Anders

2012-01-01

It is shown how the theory of commutative monads provides an axiomatic framework for several aspects of distribution theory in a broad sense, including probability distributions, physical extensive quantities, and Schwartz distributions of compact support. Among the particular aspects considered...... here are the notions of convolution, density, expectation, and conditional probability....

Essay on a general theory of nervous system functions

Energy Technology Data Exchange (ETDEWEB)

Schweizer, H J

1985-01-01

The axiomatic theory unites the aspects of neurophysiology, psychology and system-theory. The formulation of the structural-nucleus of the theory relies on basic insights from biology, neurophysiology and system-theory. The structural-nucleus allows the reconstruction of the essential properties of nervous system functions, organisation and development. The theory also contributes to the discussion of stochastic automata and artificial intelligence.

Atoms in molecules, an axiomatic approach. I. Maximum transferability

Science.gov (United States)

Ayers, Paul W.

2000-12-01

Central to chemistry is the concept of transferability: the idea that atoms and functional groups retain certain characteristic properties in a wide variety of environments. Providing a completely satisfactory mathematical basis for the concept of atoms in molecules, however, has proved difficult. The present article pursues an axiomatic basis for the concept of an atom within a molecule, with particular emphasis devoted to the definition of transferability and the atomic description of Hirshfeld.

Supersymmetry in random matrix theory

International Nuclear Information System (INIS)

Kieburg, Mario

2010-01-01

I study the applications of supersymmetry in random matrix theory. I generalize the supersymmetry method and develop three new approaches to calculate eigenvalue correlation functions. These correlation functions are averages over ratios of characteristic polynomials. In the first part of this thesis, I derive a relation between integrals over anti-commuting variables (Grassmann variables) and differential operators with respect to commuting variables. With this relation I rederive Cauchy- like integral theorems. As a new application I trace the supermatrix Bessel function back to a product of two ordinary matrix Bessel functions. In the second part, I apply the generalized Hubbard-Stratonovich transformation to arbitrary rotation invariant ensembles of real symmetric and Hermitian self-dual matrices. This extends the approach for unitarily rotation invariant matrix ensembles. For the k-point correlation functions I derive supersymmetric integral expressions in a unifying way. I prove the equivalence between the generalized Hubbard-Stratonovich transformation and the superbosonization formula. Moreover, I develop an alternative mapping from ordinary space to superspace. After comparing the results of this approach with the other two supersymmetry methods, I obtain explicit functional expressions for the probability densities in superspace. If the probability density of the matrix ensemble factorizes, then the generating functions exhibit determinantal and Pfaffian structures. For some matrix ensembles this was already shown with help of other approaches. I show that these structures appear by a purely algebraic manipulation. In this new approach I use structures naturally appearing in superspace. I derive determinantal and Pfaffian structures for three types of integrals without actually mapping onto superspace. These three types of integrals are quite general and, thus, they are applicable to a broad class of matrix ensembles. (orig.)

Supersymmetry in random matrix theory

Energy Technology Data Exchange (ETDEWEB)

Kieburg, Mario

2010-05-04

I study the applications of supersymmetry in random matrix theory. I generalize the supersymmetry method and develop three new approaches to calculate eigenvalue correlation functions. These correlation functions are averages over ratios of characteristic polynomials. In the first part of this thesis, I derive a relation between integrals over anti-commuting variables (Grassmann variables) and differential operators with respect to commuting variables. With this relation I rederive Cauchy- like integral theorems. As a new application I trace the supermatrix Bessel function back to a product of two ordinary matrix Bessel functions. In the second part, I apply the generalized Hubbard-Stratonovich transformation to arbitrary rotation invariant ensembles of real symmetric and Hermitian self-dual matrices. This extends the approach for unitarily rotation invariant matrix ensembles. For the k-point correlation functions I derive supersymmetric integral expressions in a unifying way. I prove the equivalence between the generalized Hubbard-Stratonovich transformation and the superbosonization formula. Moreover, I develop an alternative mapping from ordinary space to superspace. After comparing the results of this approach with the other two supersymmetry methods, I obtain explicit functional expressions for the probability densities in superspace. If the probability density of the matrix ensemble factorizes, then the generating functions exhibit determinantal and Pfaffian structures. For some matrix ensembles this was already shown with help of other approaches. I show that these structures appear by a purely algebraic manipulation. In this new approach I use structures naturally appearing in superspace. I derive determinantal and Pfaffian structures for three types of integrals without actually mapping onto superspace. These three types of integrals are quite general and, thus, they are applicable to a broad class of matrix ensembles. (orig.)

Axiomatizations of Banzhaf Permisson Values for Games with a Hierarchical Permission Structure.

NARCIS (Netherlands)

van den Brink, J.R.

2010-01-01

In games with a permission structure it is assumed that players in a cooperative transferable utility game are hierarchically ordered in the sense that there are players that need permission from other players before they are allowed to cooperate. We provide axiomatic characterizations of Banzhaf

Art-matrix theory and cognitive distance: Farago, Preziosi, and Gell on art and enchantment

Directory of Open Access Journals (Sweden)

Jakub Stejskal

2015-12-01

Full Text Available Theories that treat art objects primarily as agents embedded in a causal nexus of agent–patient relationships, as opposed to studying them as expressions or symbols encoding meanings, tend to identify art’s agency with its power to enchant recipients. I focus on two such approaches, the art-matrix theory of Claire Farago and Donald Preziosi and the art-nexus theory of Alfred Gell. Their authors stress the potential of art to make its enchanting power the topic of our experience with it, that is, to disenchant its own enchantment. This raises the following question: If artworks are to be understood as agents enchanting their recipients, how can they become forces of disenchantment? I argue that the shift in perspective from perceiving art objects as indices of agency within a matrix/nexus to approaching them as possible means of gaining cognitive distance is inadequately addressed by both theories; this is due to features inherent to their respective theoretical outlooks.

Random matrix theories and chaotic dynamics

International Nuclear Information System (INIS)

Bohigas, O.

1991-01-01

A review of some of the main ideas, assumptions and results of the Wigner-Dyson type random matrix theories (RMT) which are relevant in the general context of 'Chaos and Quantum Physics' is presented. RMT are providing interesting and unexpected clues to connect classical dynamics with quantum phenomena. It is this aspect which will be emphasised and, concerning the main body of RMT, the author will restrict himself to a minimum. However, emphasis will be put on some generalizations of the 'canonical' random matrix ensembles that increase their flexibility, rendering the incorporation of relevant physical constraints possible. (R.P.) 112 refs., 35 figs., 5 tabs

Matrix models and stochastic growth in Donaldson-Thomas theory

Energy Technology Data Exchange (ETDEWEB)

Szabo, Richard J. [Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS, United Kingdom and Maxwell Institute for Mathematical Sciences, Edinburgh (United Kingdom); Tierz, Miguel [Grupo de Fisica Matematica, Complexo Interdisciplinar da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, PT-1649-003 Lisboa (Portugal); Departamento de Analisis Matematico, Facultad de Ciencias Matematicas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain)

2012-10-15

We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kaehler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.

Matrix models and stochastic growth in Donaldson-Thomas theory

International Nuclear Information System (INIS)

Szabo, Richard J.; Tierz, Miguel

2012-01-01

We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kähler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.

Exploitation as the Unequal Exchange of Labour : An Axiomatic Approach

OpenAIRE

Yoshihara, Naoki; Veneziani, Roberto

2009-01-01

In subsistence economies with general convex technology and rational optimising agents, a new, axiomatic approach is developed, which allows an explicit analysis of the core positive and normative intuitions behind the concept of exploitation. Three main new axioms, called Labour Exploitation in Subsistence Economies , Relational Exploitation , and Feasibility of Non-Exploitation , are presented and it is proved that they uniquely characterise a definition of exploitation conceptually related...

Dynamic Order Algebras as an Axiomatization of Modal and Tense Logics

Science.gov (United States)

Chajda, Ivan; Paseka, Jan

2015-12-01

The aim of the paper is to introduce and describe tense operators in every propositional logic which is axiomatized by means of an algebra whose underlying structure is a bounded poset or even a lattice. We introduce the operators G, H, P and F without regard what propositional connectives the logic includes. For this we use the axiomatization of universal quantifiers as a starting point and we modify these axioms for our reasons. At first, we show that the operators can be recognized as modal operators and we study the pairs ( P, G) as the so-called dynamic order pairs. Further, we get constructions of these operators in the corresponding algebra provided a time frame is given. Moreover, we solve the problem of finding a time frame in the case when the tense operators are given. In particular, any tense algebra is representable in its Dedekind-MacNeille completion. Our approach is fully general, we do not relay on the logic under consideration and hence it is applicable in all the up to now known cases.

Matrix quantum mechanics on S1/Z2

Directory of Open Access Journals (Sweden)

P. Betzios

2018-03-01

Full Text Available We study Matrix Quantum Mechanics on the Euclidean time orbifold S1/Z2. Upon Wick rotation to Lorentzian time and taking the double-scaling limit this theory provides a toy model for a big-bang/big crunch universe in two dimensional non-critical string theory where the orbifold fixed points become cosmological singularities. We derive the MQM partition function both in the canonical and grand canonical ensemble in two different formulations and demonstrate agreement between them. We pinpoint the contribution of twisted states in both of these formulations either in terms of bi-local operators acting at the end-points of time or branch-cuts on the complex plane. We calculate, in the matrix model, the contribution of the twisted states to the torus level partition function explicitly and show that it precisely matches the world-sheet result, providing a non-trivial test of the proposed duality. Finally we discuss some interesting features of the partition function and the possibility of realising it as a τ-function of an integrable hierarchy.

Matrix quantum mechanics on S1 /Z2

Science.gov (United States)

Betzios, P.; Gürsoy, U.; Papadoulaki, O.

2018-03-01

We study Matrix Quantum Mechanics on the Euclidean time orbifold S1 /Z2. Upon Wick rotation to Lorentzian time and taking the double-scaling limit this theory provides a toy model for a big-bang/big crunch universe in two dimensional non-critical string theory where the orbifold fixed points become cosmological singularities. We derive the MQM partition function both in the canonical and grand canonical ensemble in two different formulations and demonstrate agreement between them. We pinpoint the contribution of twisted states in both of these formulations either in terms of bi-local operators acting at the end-points of time or branch-cuts on the complex plane. We calculate, in the matrix model, the contribution of the twisted states to the torus level partition function explicitly and show that it precisely matches the world-sheet result, providing a non-trivial test of the proposed duality. Finally we discuss some interesting features of the partition function and the possibility of realising it as a τ-function of an integrable hierarchy.

Combinatorial set theory with a gentle introduction to forcing

CERN Document Server

Halbeisen, Lorenz J

2017-01-01

This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Th...

A New Foundation of Physical Theories

CERN Document Server

Ludwig, Günther

2006-01-01

Written in the tradition of G. Ludwig’s groundbreaking works, this book aims to clarify and formulate more precisely the fundamental ideas of physical theories. By introducing a basic descriptive language of simple form, in which it is possible to formulate recorded facts, ambiguities of physical theories are avoided as much as possible. In this approach the field of physics that should be described by a theory is determined by basic concepts only, i.e. concepts that can be explained without a theory. In this context the authors introduce a new concept of idealization and review the process of discovering new concepts. They believe that, when the theories are formulated within an axiomatic basis, solutions can be found to many difficult problems such as the interpretation of physical theories, the relations between theories as well as the introduction of physical concepts. The book addresses both physicists and philosophers of science and should encourage the reader to contribute to the understanding of the...

Towards an axiomatic model of fundamental interactions at Planck scale

OpenAIRE

Kiselev, Arthemy V.

2014-01-01

By exploring possible physical sense of notions, structures, and logic in a class of noncommutative geometries, we try to unify the four fundamental interactions within an axiomatic quantum picture. We identify the objects and algebraic operations which could properly encode the formation and structure of sub-atomic particles, antimatter, annihilation, CP-symmetry violation, mass endowment mechanism, three lepton-neutrino matchings, spin, helicity and chirality, electric charge and electromag...

Pseudo-Hermitian random matrix theory

International Nuclear Information System (INIS)

Srivastava, S.C.L.; Jain, S.R.

2013-01-01

Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present applications to problems in statistical mechanics where new results have become possible. We have found it important to mention the precise directions where advances could be made if further results become available. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Universality in chaos: Lyapunov spectrum and random matrix theory.

Science.gov (United States)

Hanada, Masanori; Shimada, Hidehiko; Tezuka, Masaki

2018-02-01

We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by random matrix theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of a stringy black hole and the mass-deformed models. The massless limit, which has a dual string theory interpretation, is special in that the universal behavior can be seen already at t=0, while in other cases it sets in at late time. The same pattern is demonstrated also in the product of random matrices.

Universality in chaos: Lyapunov spectrum and random matrix theory

Science.gov (United States)

Hanada, Masanori; Shimada, Hidehiko; Tezuka, Masaki

2018-02-01

We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by random matrix theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of a stringy black hole and the mass-deformed models. The massless limit, which has a dual string theory interpretation, is special in that the universal behavior can be seen already at t =0 , while in other cases it sets in at late time. The same pattern is demonstrated also in the product of random matrices.

A J matrix engine for density functional theory calculations

International Nuclear Information System (INIS)

White, C.A.; Head-Gordon, M.

1996-01-01

We introduce a new method for the formation of the J matrix (Coulomb interaction matrix) within a basis of Cartesian Gaussian functions, as needed in density functional theory and Hartree endash Fock calculations. By summing the density matrix into the underlying Gaussian integral formulas, we have developed a J matrix open-quote open-quote engine close-quote close-quote which forms the exact J matrix without explicitly forming the full set of two electron integral intermediates. Several precomputable quantities have been identified, substantially reducing the number of floating point operations and memory accesses needed in a J matrix calculation. Initial timings indicate a speedup of greater than four times for the (pp parallel pp) class of integrals with speedups increasing to over ten times for (ff parallel ff) integrals. copyright 1996 American Institute of Physics

Fuzzy Entropy： Axiomatic Definition and Neural Networks Model

Institute of Scientific and Technical Information of China (English)

QINGMing; CAOYue; HUANGTian-min

2004-01-01

The measure of uncertainty is adopted as a measure of information. The measures of fuzziness are known as fuzzy information measures. The measure of a quantity of fuzzy information gained from a fuzzy set or fuzzy system is known as fuzzy entropy. Fuzzy entropy has been focused and studied by many researchers in various fields. In this paper, firstly, the axiomatic definition of fuzzy entropy is discussed. Then, neural networks model of fuzzy entropy is proposed, based on the computing capability of neural networks. In the end, two examples are discussed to show the efficiency of the model.

Transition matrices and orbitals from reduced density matrix theory

Energy Technology Data Exchange (ETDEWEB)

Etienne, Thibaud [Université de Lorraine – Nancy, Théorie-Modélisation-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy (France); CNRS, Théorie-Modélisation-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy (France); Unité de Chimie Physique Théorique et Structurale, Université de Namur, Rue de Bruxelles 61, 5000 Namur (Belgium)

2015-06-28

In this contribution, we report two different methodologies for characterizing the electronic structure reorganization occurring when a chromophore undergoes an electronic transition. For the first method, we start by setting the theoretical background necessary to the reinterpretation through simple tensor analysis of (i) the transition density matrix and (ii) the natural transition orbitals in the scope of reduced density matrix theory. This novel interpretation is made more clear thanks to a short compendium of the one-particle reduced density matrix theory in a Fock space. The formalism is further applied to two different classes of excited states calculation methods, both requiring a single-determinant reference, that express an excited state as a hole-particle mono-excited configurations expansion, to which particle-hole correlation is coupled (time-dependent Hartree-Fock/time-dependent density functional theory) or not (configuration interaction single/Tamm-Dancoff approximation). For the second methodology presented in this paper, we introduce a novel and complementary concept related to electronic transitions with the canonical transition density matrix and the canonical transition orbitals. Their expression actually reflects the electronic cloud polarisation in the orbital space with a decomposition based on the actual contribution of one-particle excitations from occupied canonical orbitals to virtual ones. This approach validates our novel interpretation of the transition density matrix elements in terms of the Euclidean norm of elementary transition vectors in a linear tensor space. A proper use of these new concepts leads to the conclusion that despite the different principles underlying their construction, they provide two equivalent excited states topological analyses. This connexion is evidenced through simple illustrations of (in)organic dyes electronic transitions analysis.

Maslow's Implied Matrix: A Clarification of the Need Hierarchy Theory.

Science.gov (United States)

Marsh, Edward

1978-01-01

Maslow's need hierarchy theory is restated by means of a matrix arrangement of the constructs within the theory. After consideration of the consequences of this restatement, some significant research is discussed and directions for future research suggested. (Author)

Analysis of metal-matrix composite structures. I - Micromechanics constitutive theory. II - Laminate analyses

Science.gov (United States)

Arenburg, R. T.; Reddy, J. N.

1991-01-01

The micromechanical constitutive theory is used to examine the nonlinear behavior of continuous-fiber-reinforced metal-matrix composite structures. Effective lamina constitutive relations based on the Abouli micromechanics theory are presented. The inelastic matrix behavior is modeled by the unified viscoplasticity theory of Bodner and Partom. The laminate constitutive relations are incorporated into a first-order deformation plate theory. The resulting boundary value problem is solved by utilizing the finite element method. Attention is also given to computational aspects of the numerical solution, including the temporal integration of the inelastic strains and the spatial integration of bending moments. Numerical results the nonlinear response of metal matrix composites subjected to extensional and bending loads are presented.

A book of set theory

CERN Document Server

Pinter, Charles C

2014-01-01

Suitable for upper-level undergraduates, this accessible approach to set theory poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. Starting with a repetition of the familiar arguments of elementary set theory, the level of abstract thinking gradually rises for a progressive increase in complexity.A historical introduction presents a brief account of the growth of set theory, with special emphasis on problems that led to the development of the various systems of axiomatic set theory. Subsequent chapters explore classes and

Haag-Ruelle scattering theory as a scattering theory in different spaces of states

International Nuclear Information System (INIS)

Koshmanenko, V.D.

1979-01-01

The aim of the paper is the extraction of the abstract content from the Haag-Ruelle theory, i.e. to find out the total mathematical scheme of the theory without the account of physical axiomatics. It is shown that the Haag-Ruelle scattering theory may be naturally included into the scheme of the abstract theory of scattering with the pair of spaces, the wave operators being determined by the method of bilinear functionals. A number of trivial features of the scattering operator is found in the abstract theory. The concrete prospects of the application of the data obtained are outlined in the problem of the scattering of the field quantum theory

Axiomatic field theory and quantum electrodynamics: the massive case

International Nuclear Information System (INIS)

Steinmann, O.

1975-01-01

Massive quantum electrodynamics of the electron is formulated as an LSZ theory of the electromagnetic field F(μν) and the electron-positron fields PSI. The interaction is introduced with the help of mathematically well defined subsidiary conditions. These are: 1) gauge invariance of the first kind, assumed to be generated by a conserved current j(μ); 2) the homogeneous Maxwell equations and a massive version of the inhomogeneous Maxwell equations; 3) a minimality condition concerning the high momentum behaviour of the theory. The inhomogeneous Maxwell equation is a linear differential equation connecting Fsub(μν) with the current Jsub(μ). No Lagrangian, no non-linear field equations, and no explicit expression of Jsub(μ) in terms of PSI, anti-PSI are needed. It is shown in perturbation theory that the proposed conditions fix the physically relevant (i.e. observable) quantities of the theory uniquely

Some open problems in random matrix theory and the theory of integrable systems

OpenAIRE

Deift, Percy

2007-01-01

We describe a list of open problems in random matrix theory and integrable systems which was presented at the conference ``Integrable Systems, Random Matrices, and Applications'' at the Courant Institute in May 2006.

Massive quiver matrix models for massive charged particles in AdS

Energy Technology Data Exchange (ETDEWEB)

Asplund, Curtis T.; Denef, Frederik [Department of Physics, Columbia University,538 West 120th Street, New York, New York 10027 (United States); Dzienkowski, Eric [Department of Physics, Broida Hall, University of California Santa Barbara,Santa Barbara, California 93106 (United States)

2016-01-11

We present a new class of N=4 supersymmetric quiver matrix models and argue that it describes the stringy low-energy dynamics of internally wrapped D-branes in four-dimensional anti-de Sitter (AdS) flux compactifications. The Lagrangians of these models differ from previously studied quiver matrix models by the presence of mass terms, associated with the AdS gravitational potential, as well as additional terms dictated by supersymmetry. These give rise to dynamical phenomena typically associated with the presence of fluxes, such as fuzzy membranes, internal cyclotron motion and the appearance of confining strings. We also show how these models can be obtained by dimensional reduction of four-dimensional supersymmetric quiver gauge theories on a three-sphere.

Algebraic number theory

CERN Document Server

Weiss, Edwin

1998-01-01

Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate's thesis).Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract te

Matrix theory

CERN Document Server

Franklin, Joel N

2003-01-01

Mathematically rigorous introduction covers vector and matrix norms, the condition-number of a matrix, positive and irreducible matrices, much more. Only elementary algebra and calculus required. Includes problem-solving exercises. 1968 edition.

Perturbative S-matrix for massive scalar fields in global de Sitter space

International Nuclear Information System (INIS)

Marolf, Donald; Srednicki, Mark; Morrison, Ian A

2013-01-01

We construct a perturbative S-matrix for interacting massive scalar fields in global de Sitter space. Our S-matrix is formulated in terms of asymptotic particle states in the far past and future, taking appropriate care for light fields whose wavefunctions decay only very slowly near the de Sitter conformal boundaries. An alternative formulation expresses this S-matrix in terms of residues of poles in analytically-continued Euclidean correlators (computed in perturbation theory), making it clear that the standard Minkowski-space result is obtained in the flat-space limit. Our S-matrix transforms properly under CPT, is invariant under the de Sitter isometries and perturbative field redefinitions, and is unitary. This unitarity implies a de Sitter version of the optical theorem. We explicitly verify these properties to second order in the coupling for a general cubic interaction, including both tree- and loop-level contributions. Contrary to other statements in the literature, we find that a particle of any positive mass may decay at tree level to any number of particles, each of arbitrary positive masses. In particular, even very light fields (in the complementary series of de Sitter representations) are not protected from tree-level decays. (paper)

Rigorous lower bounds on the imaginary parts of the scattering amplitudes and the positions of their zeros

CERN Document Server

Uchiyama, T

1974-01-01

Rigorous lower bounds are derived from axiomatic field theory, by invoking analyticity and unitarity of the S-matrix. The bounds are expressed in terms of the total cross section and the slope parameter, and are found to be compatible with CERN experimental pp scattering data. It is also shown that the calculated lower-bound values imply non-existence of zeros for -t

A Hub Matrix Theory and Applications to Wireless Communications

Directory of Open Access Journals (Sweden)

Kung HT

2007-01-01

Full Text Available This paper considers communications and network systems whose properties are characterized by the gaps of the leading eigenvalues of for a matrix . It is shown that a sufficient and necessary condition for a large eigen-gap is that is a "hub" matrix in the sense that it has dominant columns. Some applications of this hub theory in multiple-input and multiple-output (MIMO wireless systems are presented.

Λ < 0 quantum gravity in 2 + 1 dimensions: I. Quantum states and stringy S-matrix

International Nuclear Information System (INIS)

Krasnov, Kirill

2002-01-01

We consider the theory of pure gravity in 2 + 1 dimensions, with negative cosmological constant. The theory contains simple matter in the form of point particles; the latter are classically described as lines of conical singularities. We propose a formalism in which quantum amplitudes for the process involving black holes and point particles are obtained as conformal field theory (CFT) correlation functions on Riemann surfaces X. Point particles are described by the CFT vertex operators; black holes (asymptotic regions) are in correspondence with boundaries of X. We consider two examples: the amplitude for emission of a particle by the BTZ black hole and the amplitude of black-hole creation by two point particles. We then define an inner product between quantum states. The value of this inner product can be interpreted as the amplitude for one set of point particles to go into another set producing black holes. The full particle S-matrix is then given by the sum of all such amplitudes. This S-matrix is that of a non-critical string theory, with the worldsheet CFT being essentially the Liouville theory. Λ < 0 quantum gravity in 2 + 1 dimensions is thus a string theory

Matrix theory from generalized inverses to Jordan form

CERN Document Server

Piziak, Robert

2007-01-01

Each chapter ends with a list of references for further reading. Undoubtedly, these will be useful for anyone who wishes to pursue the topics deeper. … the book has many MATLAB examples and problems presented at appropriate places. … the book will become a widely used classroom text for a second course on linear algebra. It can be used profitably by graduate and advanced level undergraduate students. It can also serve as an intermediate course for more advanced texts in matrix theory. This is a lucidly written book by two authors who have made many contributions to linear and multilinear algebra.-K.C. Sivakumar, IMAGE, No. 47, Fall 2011Always mathematically constructive, this book helps readers delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.-L'enseignement Mathématique, January-June 2007, Vol. 53, No. 1-2.

A generalization of random matrix theory and its application to statistical physics.

Science.gov (United States)

Wang, Duan; Zhang, Xin; Horvatic, Davor; Podobnik, Boris; Eugene Stanley, H

2017-02-01

To study the statistical structure of crosscorrelations in empirical data, we generalize random matrix theory and propose a new method of cross-correlation analysis, known as autoregressive random matrix theory (ARRMT). ARRMT takes into account the influence of auto-correlations in the study of cross-correlations in multiple time series. We first analytically and numerically determine how auto-correlations affect the eigenvalue distribution of the correlation matrix. Then we introduce ARRMT with a detailed procedure of how to implement the method. Finally, we illustrate the method using two examples taken from inflation rates for air pressure data for 95 US cities.

Matrix product states for lattice field theories

Energy Technology Data Exchange (ETDEWEB)

Banuls, M.C.; Cirac, J.I. [Max-Planck-Institut fuer Quantenoptik (MPQ), Garching (Germany); Cichy, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Saito, H. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Tsukuba Univ., Ibaraki (Japan). Graduate School of Pure and Applied Sciences

2013-10-15

The term Tensor Network States (TNS) refers to a number of families of states that represent different ansaetze for the efficient description of the state of a quantum many-body system. Matrix Product States (MPS) are one particular case of TNS, and have become the most precise tool for the numerical study of one dimensional quantum many-body systems, as the basis of the Density Matrix Renormalization Group method. Lattice Gauge Theories (LGT), in their Hamiltonian version, offer a challenging scenario for these techniques. While the dimensions and sizes of the systems amenable to TNS studies are still far from those achievable by 4-dimensional LGT tools, Tensor Networks can be readily used for problems which more standard techniques, such as Markov chain Monte Carlo simulations, cannot easily tackle. Examples of such problems are the presence of a chemical potential or out-of-equilibrium dynamics. We have explored the performance of Matrix Product States in the case of the Schwinger model, as a widely used testbench for lattice techniques. Using finite-size, open boundary MPS, we are able to determine the low energy states of the model in a fully non-perturbativemanner. The precision achieved by the method allows for accurate finite size and continuum limit extrapolations of the ground state energy, but also of the chiral condensate and the mass gaps, thus showing the feasibility of these techniques for gauge theory problems.

Chern-Simons matrix models and unoriented strings

International Nuclear Information System (INIS)

Halmagyi, Nick; Yasnov, Vadim

2004-01-01

For matrix models with measure on the Lie algebra of SO/Sp, the sub-leading free energy is given by F 1 (S) ±{1/4}({δF 0 (S)}/{δS}). Motivated by the fact that this relationship does not hold for Chern-Simons theory on S 3 , we calculate the sub-leading free energy in the matrix model for this theory, which is a Gaussian matrix model with Haar measure on the group SO/Sp. We derive a quantum loop equation for this matrix model and then find that F 1 is an integral of the leading order resolvent over the spectral curve. We explicitly calculate this integral for quadratic potential and find agreement with previous studies of SO/Sp Chern-Simons theory. (author)

Random matrix theory for heavy-tailed time series

DEFF Research Database (Denmark)

Heiny, Johannes

2017-01-01

This paper is a review of recent results for large random matrices with heavy-tailed entries. First, we outline the development of and some classical results in random matrix theory. We focus on large sample covariance matrices, their limiting spectral distributions, the asymptotic behavior...

Random matrix theory with an external source

CERN Document Server

Brézin, Edouard

2016-01-01

This is a first book to show that the theory of the Gaussian random matrix is essential to understand the universal correlations with random fluctuations and to demonstrate that it is useful to evaluate topological universal quantities. We consider Gaussian random matrix models in the presence of a deterministic matrix source. In such models the correlation functions are known exactly for an arbitrary source and for any size of the matrices. The freedom given by the external source allows for various tunings to different classes of universality. The main interest is to use this freedom to compute various topological invariants for surfaces such as the intersection numbers for curves drawn on a surface of given genus with marked points, Euler characteristics, and the Gromov–Witten invariants. A remarkable duality for the average of characteristic polynomials is essential for obtaining such topological invariants. The analysis is extended to nonorientable surfaces and to surfaces with boundaries.

On the processes of generation of particles in the extended S-matrix method

International Nuclear Information System (INIS)

Dushutin, N.K.; Mal'tsev, V.M.; Sinegovskij, S.I.

1975-01-01

In order to understand the processes of hadron multiple production very important are integral characteristics, such as the multiplicity distribution function Psub(n)=sigmasub(n)/sigmasub(inel) and correlation parameters of fsub(K). From the shape of distribution and the energy dependence of correlation parameters one may arrive at definite conclusions about the interaction dynamics. In the paper a possibility is studied of obtaining integral characteristics in the S matrix formulation of the quantum field theory. This technique is based on principles of the scattering matrix expanding beyond the energy surface (ES). This follows from the fact that the predetermination of the scattering matrix on the ES does not permit strict to determinate the condition for causality. The expansion of S matrix is performed by introducing some object described by a substantial function rho(x) and interacting with a quantum system, properties of rho(x) being such that the space of asymptotic states remains complete for the expanded matrix also, i.e., the unitarity condition is fulfilled for S(rho) too. The expansion of S-matrix over the function of the interaction insertion g(x) and the transition to the differential equations for the coupling constant allowed investigation of hadron inelastic processes at some simplifying suppositions. Experimental data do not contradict in the main the proposed picture of interactions [ru

Hardware matrix multiplier/accumulator for lattice gauge theory calculations

International Nuclear Information System (INIS)

Christ, N.H.; Terrano, A.E.

1984-01-01

The design and operating characteristics of a special-purpose matrix multiplier/accumulator are described. The device is connected through a standard interface to a host PDP11 computer. It provides a set of high-speed, matrix-oriented instructions which can be called from a program running on the host. The resulting operations accelerate the complex matrix arithmetic required for a class of Monte Carlo calculations currently of interest in high energy particle physics. A working version of the device is presently being used to carry out a pure SU(3) lattice gauge theory calculation using a PDP11/23 with a performance twice that obtainable on a VAX11/780. (orig.)

Discrete state moduli of string theory from c=1 matrix model

CERN Document Server

Dhar, A; Wadia, S R; Dhar, Avinash; Mandal, Gautam; Wadia, Spenta R

1995-01-01

We propose a new formulation of the space-time interpretation of the c=1 matrix model. Our formulation uses the well-known leg-pole factor that relates the matrix model amplitudes to that of the 2-dimensional string theory, but includes fluctuations around the fermi vacuum on {\\sl both sides} of the inverted harmonic oscillator potential of the double-scaled model, even when the fluctuations are small and confined entirely within the asymptotes in the phase plane. We argue that including fluctuations on both sides of the potential is essential for a consistent interpretation of the leg-pole transformed theory as a theory of space-time gravity. We reproduce the known results for the string theory tree level scattering amplitudes for flat space and linear dilaton background as a special case. We show that the generic case corresponds to more general space-time backgrounds. In particular, we identify the parameter corresponding to background metric perturbation in string theory (black hole mass) in terms of the ...

Quasiclassical R-matrix theory of inelastic processes in collisions of electrons with HCl molecules

International Nuclear Information System (INIS)

Fabrikant, I.I.

1991-01-01

The R-matrix theory for the vibrational excitation and dissociative attachment in e-HCl collisions is developed. Only one pole in the R-matrix expansion is included. This allows for making a connection between the R-matrix and the nonlocal-complex-potential theories, and for obtaining the expression for the dissociative-attachment cross section without using the R-matrix radius in the internuclear coordinate. All matrix elements in the equation for the vibrational-excitation and dissociative-attachment amplitudes are calculated using the quasiclassical approach. We study how the results depend on the number of vibrational levels of the neutral molecule included in the theory and show how to exclude the vibrational continuum by a modification of the nonlocal-complex potential. The results for the vibrational-excitation cross sections are extremely sensitive to the behavior of the R-matrix potential curve near the point of crossing this curve with the potential curve of the neutral molecule. Particularly in some cases the cross section at the threshold peak exhibits the boomerang oscillations earlier found for HCl by Domcke [in Aspects of Electron-Molecule Scattering and Photoionization, edited by A. Herzenberg (AIP, New Haven, 1989), p. 169]. The dissociative-attachment cross sections are in reasonable agreement with experiment and with other theories

Time dependent density matrix theory and effective interaction

Energy Technology Data Exchange (ETDEWEB)

Tohyama, Mitsuru [Kyorin Univ., Mitaka, Tokyo (Japan). School of Medicine

1998-07-01

A correlated ground state of {sup 16}O and an E2 giant resonance built on it are calculated using an extended version of the time-dependent Hartree-Fock theory called the time-dependent density-matrix theory (TDDM). The Skyrme force is used in the calculation of both a mean field and two-body correlations. It is found that TDDM gives reasonable ground-state correlations and a large spreading width of the E2 giant resonance when single-particle states in the continuum are treated appropriately. (author)

Numerical algebra, matrix theory, differential-algebraic equations and control theory festschrift in honor of Volker Mehrmann

CERN Document Server

Bollhöfer, Matthias; Kressner, Daniel; Mehl, Christian; Stykel, Tatjana

2015-01-01

This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on ...

Deformed type 0A matrix model and super-Liouville theory for fermionic black holes

International Nuclear Information System (INIS)

Ahn, Changrim; Kim, Chanju; Park, Jaemo; Suyama, Takao; Yamamoto, Masayoshi

2006-01-01

We consider a c-circumflex = 1 model in the fermionic black hole background. For this purpose we consider a model which contains both the N 1 and the N = 2 super-Liouville interactions. We propose that this model is dual to a recently proposed type 0A matrix quantum mechanics model with vortex deformations. We support our conjecture by showing that non-perturbative corrections to the free energy computed by both the matrix model and the super-Liouville theories agree exactly by treating the N = 2 interaction as a small perturbation. We also show that a two-point function on sphere calculated from the deformed type 0A matrix model is consistent with that of the N = 2 super-Liouville theory when the N = 1 interaction becomes small. This duality between the matrix model and super-Liouville theories leads to a conjecture for arbitrary n-point correlation functions of the N = 1 super-Liouville theory on the sphere

Complete axiomatization of the stutter-invariant fragment of the linear time µ-calculus

NARCIS (Netherlands)

Gheerbrant, A.

2010-01-01

The logic µ(U) is the fixpoint extension of the "Until"-only fragment of linear-time temporal logic. It also happens to be the stutter-invariant fragment of linear-time µ-calculus µ(◊). We provide complete axiomatizations of µ(U) on the class of finite words and on the class of ω-words. We introduce

Reformulation of the Hermitean 1-matrix model as an effective field theory

Energy Technology Data Exchange (ETDEWEB)

Klitz, Alexander

2009-07-15

The formal Hermitean 1-matrix model is shown to be equivalent to an effective field theory. The correlation functions and the free energy of the matrix model correspond directly to the correlation functions and the free energy of the effective field theory. The loop equation of the field theory coupling constants is stated. Despite its length, this loop equation is simpler than the loop equations in the matrix model formalism itself since it does not contain operator inversions in any sense, but consists instead only of derivative operators and simple projection operators. Therefore the solution of the loop equation could be given for an arbitrary number of cuts up to the fifth order in the topological expansion explicitly. Two different methods of obtaining the contributions to the free energy of the higher orders are given, one depending on an operator H and one not depending on it. (orig.)

Uncertainty theory

CERN Document Server

Liu, Baoding

2015-01-01

When no samples are available to estimate a probability distribution, we have to invite some domain experts to evaluate the belief degree that each event will happen. Perhaps some people think that the belief degree should be modeled by subjective probability or fuzzy set theory. However, it is usually inappropriate because both of them may lead to counterintuitive results in this case. In order to rationally deal with belief degrees, uncertainty theory was founded in 2007 and subsequently studied by many researchers. Nowadays, uncertainty theory has become a branch of axiomatic mathematics for modeling belief degrees. This is an introductory textbook on uncertainty theory, uncertain programming, uncertain statistics, uncertain risk analysis, uncertain reliability analysis, uncertain set, uncertain logic, uncertain inference, uncertain process, uncertain calculus, and uncertain differential equation. This textbook also shows applications of uncertainty theory to scheduling, logistics, networks, data mining, c...

Random matrix theory for transition strengths: Applications and open questions

Science.gov (United States)

Kota, V. K. B.

2017-12-01

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different) and so on. Using embedded ensembles (EE), there are efforts to derive a good statistical theory for transition strengths. With m fermions (or bosons) in N mean-field single particle levels and interacting via two-body forces, we have with GOE embedding, the so called EGOE(1+2). Now, the transition strength density (transition strength multiplied by the density of states at the initial and final energies) is a convolution of the density generated by the mean-field one-body part with a bivariate spreading function due to the two-body interaction. Using the embedding U(N) algebra, it is established, for a variety of transition operators, that the spreading function, for sufficiently strong interactions, is close to a bivariate Gaussian. Also, as the interaction strength increases, the spreading function exhibits a transition from bivariate Breit-Wigner to bivariate Gaussian form. In appropriate limits, this EE theory reduces to the polynomial theory of Draayer, French and Wong on one hand and to the theory due to Flambaum and Izrailev for one-body transition operators on the other. Using spin-cutoff factors for projecting angular momentum, the theory is applied to nuclear matrix elements for neutrinoless double beta decay (NDBD). In this paper we will describe: (i) various developments in the EE theory for transition strengths; (ii) results for nuclear matrix elements for 130Te and 136Xe NDBD; (iii) important open questions in the current form of the EE theory.

The foundation of quantum theory and noncommutative spectral theory: Part 2

International Nuclear Information System (INIS)

Kummer, H.

1991-01-01

The present paper comprises Sects. 5-8 of a work which proposes an axiomatic approach to quantum mechanics in which the concept of a filter is the central primitive concept. Having laid down the foundations in the first part of this work, the author arrived at a dual pair left-angle Y,M right-angle consisting of a base norm space Y and an order unit space M, being in order and norm duality with respect to each other. This is precisely the setting of noncommutative spectral theory, a theory which has been developed during the late nineteen seventies by Alfsen and Shultz. In this part he added to the four axioms (Axioms S, DP, R, SP) of Sect. 3 three further axioms (Axioms E, O, L). These axioms are suggested by the work of Alfsen and Shultz and and enable him to derive the JB-algebra structure of quantum mechanics (cf. Theorem 8.9)

Applications of Axiomatic Design in Developing Nuclear Systems

Energy Technology Data Exchange (ETDEWEB)

Heo, Gyunyoung [Kyung Hee University, Seoul (Korea, Republic of)

2007-10-15

The first step of designing nuclear systems starts with the identification of the top-level requirements given by stake holders and regulatory authorities. A detailed design of structure, system and component then follows. Design is divided into two processes: 'synthesis' and 'analysis.' While synthesis is the process of decision making on parameters, analysis is the process of optimizing the parameters selected. It is known from experience that the mistakes made in the synthesis process, particularly of a conceptual stage, are never completely corrected in the analysis process, which is more serious in designing complex safety critical systems such as nuclear power plants. It should be also noted that we normally believe that synthesis is only driven by engineers' heuristic knowledge. This paper proposes the applications of Axiomatic Design (AD), which is a design management tool as slightly opposed to this conventional view. I hypothesize that the design management using design axioms reduces uncertainty and subjectivity particularly at a conceptual phase so that a safer nuclear system can be developed while reducing cost in view of the system's entire life cycle. I will describe the notion of AD and introduce a few case studies.

Fuzzy Axiomatic Design approach based green supplier selection

DEFF Research Database (Denmark)

Kannan, Devika; Govindan, Kannan; Rajendran, Sivakumar

2015-01-01

proposes a multi-criteria decision-making (MCDM) approach called Fuzzy Axiomatic Design (FAD) to select the best green supplier for Singapore-based plastic manufacturing company. At first, the environmental criteria was developed along with the traditional criteria based on the literature review......Abstract Green Supply Chain Management (GSCM) is a developing concept recently utilized by manufacturing firms of all sizes. All industries, small or large, seek improvements in the purchasing of raw materials, manufacturing, allocation, transportation efficiency, in curbing storage time, importing...... responsible in addition to being efficiently managed. A significant way to implement responsible GSCM is to reconsider, in innovative ways, the purchase and supply cycle, and a preliminary step would be to ensure that the supplier of goods successfully incorporates green criteria. Therefore, this paper...

Phonon dispersion relations in monoatomic superlattices: a transfer matrix theory

International Nuclear Information System (INIS)

Albuquerque, E.L. de; Fulco, P.

1986-01-01

We present a lattice dynamical theory for monoatomic superlattices consisting of alternating layers of two different materials. Using a transfer matrix method we obtain explicit the equation for dispersion of the phonon's bulk modes, including the well known result in the long wave-length limit which can be obtained by elasticity theory. An illustation is shown and its features discussed. (Author) [pt

P A M Dirac meets M G Krein: matrix orthogonal polynomials and Dirac's equation

Energy Technology Data Exchange (ETDEWEB)

Duran, Antonio J [Departamento de Analisis Matematico, Universidad de Sevilla, Apdo (PO BOX) 1160, 41080 Sevilla (Spain); Gruenbaum, F Alberto [Department of Mathematics, University of California, Berkeley, CA 94720 (United States)

2006-04-07

The solution of several instances of the Schroedinger equation (1926) is made possible by using the well-known orthogonal polynomials associated with the names of Hermite, Legendre and Laguerre. A relativistic alternative to this equation was proposed by Dirac (1928) involving differential operators with matrix coefficients. In 1949 Krein developed a theory of matrix-valued orthogonal polynomials without any reference to differential equations. In Duran A J (1997 Matrix inner product having a matrix symmetric second order differential operator Rocky Mt. J. Math. 27 585-600), one of us raised the question of determining instances of these matrix-valued polynomials going along with second order differential operators with matrix coefficients. In Duran A J and Gruenbaum F A (2004 Orthogonal matrix polynomials satisfying second order differential equations Int. Math. Res. Not. 10 461-84), we developed a method to produce such examples and observed that in certain cases there is a connection with the instance of Dirac's equation with a central potential. We observe that the case of the central Coulomb potential discussed in the physics literature in Darwin C G (1928 Proc. R. Soc. A 118 654), Nikiforov A F and Uvarov V B (1988 Special Functions of Mathematical Physics (Basle: Birkhauser) and Rose M E 1961 Relativistic Electron Theory (New York: Wiley)), and its solution, gives rise to a matrix weight function whose orthogonal polynomials solve a second order differential equation. To the best of our knowledge this is the first instance of a connection between the solution of the first order matrix equation of Dirac and the theory of matrix-valued orthogonal polynomials initiated by M G Krein.

Application of some ideas from the axiomatic design principles for construction of a learning management system in Romanian higher engineering education

Directory of Open Access Journals (Sweden)

Iliescu Dragoş

2017-01-01

Full Text Available In education, the communication processes are critical. The result of education process depends on a significant manner by the quality of the incurred communication. To enhance learning in higher engineering education, an application of axiomatic design for the construction of a Learning Management System is proposed. The clients of such a system are identified, and their expectations were gathered as well. Functional requirements and design parameters to be designed are compiled regarding the two principles of axiomatic design. Finally, we investigate four design options to select the optimal design solution.

Intentionality forms the matrix of healing: a theory.

Science.gov (United States)

Zahourek, Rothlyn P

2004-01-01

The understanding of intentionality in a healing context has been incomplete and confusing. Attempts have been made to describe it as a concrete mental force in healing while healing has been accepted as a nonlocal phenomenon. This paper reviews several definitions and theoretical frameworks of intentionality. It proposes a new integrative theory of intentionality, Intentionality: the Matrix of Healing. The theory proposes definitions, forms, and phases of intentionality, a process of development and mediators that sculpt intentionality in healing. The theory has implications for conceptualizing intentionality and provides a framework for continued exploration of the nature of intentionality in healing for scholars as well as clinicians. This study was done as a Doctoral dissertation at New York University, School of Education, Division of Nursing.

Subjective Expected Utility Theory without States of the World

OpenAIRE

Edi Karni

2005-01-01

This paper develops an axiomatic theory of decision making under uncertainty that dispenses with the state space. The results are subjective expected utility models with unique, action-dependent, subjective probabilities, and a utility function defined over wealth-effect pairs that is unique up to positive linear transformation.

Correlated density matrix theory of spatially inhomogeneous Bose fluids

International Nuclear Information System (INIS)

Gernoth, K.A.; Clark, J.W.; Ristig, M.L.

1994-06-01

In this paper, the variational Hartree-Jastrow theory of the ground state of spatially inhomogeneous Bose systems is extended to finite temperatures. The theory presented here is a generalization also in the sense that it extends the correlated density matrix approach, formulated previously for uniform Bose fluids, to systems with nonuniform density profiles. The method provides a framework in which the effects of thermal excitations on the spatial structure of a Bose fluid, as represented by the density profile and the two-body distribution functions, may be discussed on the basis on an ab initio microscopic description of the system. Thermal excitations make their appearance through self-consistently determined one-body and two-body potentials which enter the nonlinear, coupled Euler-Lagrange equations for the one-body density and for the pair distribution function. Since back-flow correlations are neglected, the excitations are described by a Feynman eigenvalue equation, suitably generalized to nonzero temperatures. The only external quantities entering the correlated density matrix theory elaborated here are the bare two-body interaction potential and, in actual applications, the boundary conditions to be imposed on the one-body density. 30 refs

Evaluation of alternative public transportation systems in Izmit urban transportation via axiomatic design method

Directory of Open Access Journals (Sweden)

Gülşen AKMAN

2016-02-01

Full Text Available In the world and in our country, most of urban transportation is performed by public transportation. Public transportation is a system which provides transportation easiness and opportunity to people, not to vehicles. Therefore, giving priority to public transportation system is necessary in organizing urban transportation. In this study, in order to reduce traffic intensity and to facilitate passenger transportation in Izmit urban transportation, It is tried to determine appropriate public transportation system. For this, firstly, alternatives which could be used for public transportation were determined. These alternatives are metro, metrobus, tram, light rail system and monorail. Afterwards, the variables affecting decision making about public transportation were determined. These variables are cost, transportation line features, vehicle characteristics, sensitivity to environment and customer satisfaction. Lastly, most appropriate public transportation system is proposed by using the axiomatic design method. As a result, light trail system and metrobus are determined as the most appropriate alternatives for Izmit public transportation system.Keywords: Urban transportation, Multi criteria decision making, Axiomatic design

Einstein in matrix form. Exact derivation of the theory of special and general relativity without tensors

Energy Technology Data Exchange (ETDEWEB)

Ludyk, Guenter [Bremen Univ. (Germany). Physics and Electrical Engineering

2013-11-01

Derives the fundamental equations of Einstein's theory of special and general relativity using matrix calculus, without the help of tensors. Provides necessary mathematical tools in a user-friendly way, either directly in the text or in the appendices. Appendices contain an introduction to classical dynamics as a refresher of known fundamental physics. Rehearses vector and matrix calculus, differential geometry, and some special solutions of general relativity in the appendices. This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einsteins theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the ''Black Hole'' phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.

An Axiomatic Design Approach of Nanofluid-Engineered Nuclear Safety Features for Generation III+ React

International Nuclear Information System (INIS)

Bang, In Cheol; Heo, Gyun Young; Jeong, Yong Hoon; Heo, Sun

2009-01-01

A variety of Generation III/III+ reactor designs featuring enhanced safety and improved economics are being proposed by nuclear power industries around the world to solve the future energy supply shortfall. Nanofluid coolants showing an improved thermal performance are being considered as a new key technology to secure nuclear safety and economics. However, it should be noted that there is a lack of comprehensible design works to apply nanofluids to Generation III+ reactor designs. In this work, the review of accident scenarios that consider expected nanofluid mechanisms is carried out to seek detailed application spots. The Axiomatic Design (AD) theory is then applied to systemize the design of nanofluid-engineered nuclear safety systems such as Emergency Core Cooling System (ECCS) and External Reactor Vessel Cooling System (ERVCS). The various couplings between Gen-III/III+ nuclear safety features and nanofluids are investigated and they try to be reduced from the perspective of the AD in terms of prevention/mitigation of severe accidents. This study contributes to the establishment of a standard communication protocol in the design of nanofluid-engineered nuclear safety systems

LAMBDA < 0 quantum gravity in 2 + 1 dimensions: I. Quantum states and stringy S-matrix

CERN Document Server

Krasnov, K V

2002-01-01

We consider the theory of pure gravity in 2 + 1 dimensions, with negative cosmological constant. The theory contains simple matter in the form of point particles; the latter are classically described as lines of conical singularities. We propose a formalism in which quantum amplitudes for the process involving black holes and point particles are obtained as conformal field theory (CFT) correlation functions on Riemann surfaces X. Point particles are described by the CFT vertex operators; black holes (asymptotic regions) are in correspondence with boundaries of X. We consider two examples: the amplitude for emission of a particle by the BTZ black hole and the amplitude of black-hole creation by two point particles. We then define an inner product between quantum states. The value of this inner product can be interpreted as the amplitude for one set of point particles to go into another set producing black holes. The full particle S-matrix is then given by the sum of all such amplitudes. This S-matrix is that o...

Improving Reliability of a fire-fighting pump set with Axiomatic Design

Directory of Open Access Journals (Sweden)

Arcidiacono Gabriele

2017-01-01

Full Text Available This paper introduces a case study featuring Axiomatic Design and Multi-Level Hierarchical model (MLH applied to redesign a fire-fighting pump set. In particular, two different design concepts are presented to be applied to the supporting frame of the system to limit a vibration problem that can arise during potential malfunctioning of the fire-fighting pump. The selection of the best design has been carried out through reliability evaluation process and through the cost of failure based on the MLH model.

Probability and logical structure of statistical theories

International Nuclear Information System (INIS)

Hall, M.J.W.

1988-01-01

A characterization of statistical theories is given which incorporates both classical and quantum mechanics. It is shown that each statistical theory induces an associated logic and joint probability structure, and simple conditions are given for the structure to be of a classical or quantum type. This provides an alternative for the quantum logic approach to axiomatic quantum mechanics. The Bell inequalities may be derived for those statistical theories that have a classical structure and satisfy a locality condition weaker than factorizability. The relation of these inequalities to the issue of hidden variable theories for quantum mechanics is discussed and clarified

Matrix algebra and sampling theory : The case of the Horvitz-Thompson estimator

NARCIS (Netherlands)

Dol, W.; Steerneman, A.G.M.; Wansbeek, T.J.

Matrix algebra is a tool not commonly employed in sampling theory. The intention of this paper is to help change this situation by showing, in the context of the Horvitz-Thompson (HT) estimator, the convenience of the use of a number of matrix-algebra results. Sufficient conditions for the

Exploring multicollinearity using a random matrix theory approach.

Science.gov (United States)

Feher, Kristen; Whelan, James; Müller, Samuel

2012-01-01

Clustering of gene expression data is often done with the latent aim of dimension reduction, by finding groups of genes that have a common response to potentially unknown stimuli. However, what is poorly understood to date is the behaviour of a low dimensional signal embedded in high dimensions. This paper introduces a multicollinear model which is based on random matrix theory results, and shows potential for the characterisation of a gene cluster's correlation matrix. This model projects a one dimensional signal into many dimensions and is based on the spiked covariance model, but rather characterises the behaviour of the corresponding correlation matrix. The eigenspectrum of the correlation matrix is empirically examined by simulation, under the addition of noise to the original signal. The simulation results are then used to propose a dimension estimation procedure of clusters from data. Moreover, the simulation results warn against considering pairwise correlations in isolation, as the model provides a mechanism whereby a pair of genes with `low' correlation may simply be due to the interaction of high dimension and noise. Instead, collective information about all the variables is given by the eigenspectrum.

An introduction to conformal field theory in two dimensions and string theory

International Nuclear Information System (INIS)

Wadia, S.R.

1989-01-01

This paper provides information on The S-Matrix; Elements of conformally invariant field theory in 2-dim.; The Virasoro gauge conditions; Some representations of the Virasoro algebra; The S-matrix of the Bosonic string theory; Super conformal field theory; Superstring; superstring spectrum and GSO projection; The (β,γ) ghost system; BRST formulation; and String propagation in background fields

The Yangians, Bethe ansatz and combinatorics

International Nuclear Information System (INIS)

Kirillov, A.N.; Reshetikhin, N.Yu.

1986-01-01

An axiomatic definition of a quantum monodromy matrix and the representations of its corresponding Hopf algebra are discussed. The connection between the quantum inverse transform method and the representation theory of a symmetric group is considered. A new approach to the completeness problem of Bethe vectors is also given. (orig.)

Random matrix theory for pseudo-Hermitian systems: Cyclic blocks

Indian Academy of Sciences (India)

We discuss the relevance of random matrix theory for pseudo-Hermitian systems, and, for Hamiltonians that break parity and time-reversal invariance . In an attempt to understand the random Ising model, we present the treatment of cyclic asymmetric matrices with blocks and show that the nearest-neighbour spacing ...

S-matrix analysis of vibrational and alignment effects in intense-field multiphoton ionization of molecules

International Nuclear Information System (INIS)

Requate, A.

2007-03-01

Theoretical analysis of the vibrational excitation of small molecules during multiphoton ionization in intense laser fields of optical and infrared frequencies. Analysis of the alignment dependence of the electron impact ionization of diatomic molecules in the presence of an intense laser field as the final step in the process of Nonsequential Double Ionization. Quantum mechanical description using S-matrix theory in Strong Field Approximation (SFA), i.e. beyond perturbation theory. (orig.)

S-matrix analysis of vibrational and alignment effects in intense-field multiphoton ionization of molecules

Energy Technology Data Exchange (ETDEWEB)

Requate, A

2007-03-15

Theoretical analysis of the vibrational excitation of small molecules during multiphoton ionization in intense laser fields of optical and infrared frequencies. Analysis of the alignment dependence of the electron impact ionization of diatomic molecules in the presence of an intense laser field as the final step in the process of Nonsequential Double Ionization. Quantum mechanical description using S-matrix theory in Strong Field Approximation (SFA), i.e. beyond perturbation theory. (orig.)

Quasi-degenerate perturbation theory using matrix product states

Science.gov (United States)

Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali

2016-01-01

In this work, we generalize the recently proposed matrix product state perturbation theory (MPSPT) for calculating energies of excited states using quasi-degenerate (QD) perturbation theory. Our formulation uses the Kirtman-Certain-Hirschfelder canonical Van Vleck perturbation theory, which gives Hermitian effective Hamiltonians at each order, and also allows one to make use of Wigner's 2n + 1 rule. Further, our formulation satisfies Granovsky's requirement of model space invariance which is important for obtaining smooth potential energy curves. Thus, when we use MPSPT with the Dyall Hamiltonian, we obtain a model space invariant version of quasi-degenerate n-electron valence state perturbation theory (NEVPT), a property that the usual formulation of QD-NEVPT2 based on a multipartitioning technique lacked. We use our method on the benchmark problems of bond breaking of LiF which shows ionic to covalent curve crossing and the twist around the double bond of ethylene where significant valence-Rydberg mixing occurs in the excited states. In accordance with our previous work, we find that multi-reference linearized coupled cluster theory is more accurate than other multi-reference theories of similar cost.

Constrained Perturbation Regularization Approach for Signal Estimation Using Random Matrix Theory

KAUST Repository

Suliman, Mohamed Abdalla Elhag

2016-10-06

In this work, we propose a new regularization approach for linear least-squares problems with random matrices. In the proposed constrained perturbation regularization approach, an artificial perturbation matrix with a bounded norm is forced into the system model matrix. This perturbation is introduced to improve the singular-value structure of the model matrix and, hence, the solution of the estimation problem. Relying on the randomness of the model matrix, a number of deterministic equivalents from random matrix theory are applied to derive the near-optimum regularizer that minimizes the mean-squared error of the estimator. Simulation results demonstrate that the proposed approach outperforms a set of benchmark regularization methods for various estimated signal characteristics. In addition, simulations show that our approach is robust in the presence of model uncertainty.

Non-abelian action of D0-branes from Matrix theory in the longitudinal 5-brane background

International Nuclear Information System (INIS)

Asano, Masako; Sekino, Yasuhiro

2002-01-01

We study one-loop effective action of Berkooz-Douglas Matrix theory and obtain non-abelian action of D0-branes in the background field produced by longitudinal 5-branes. Since these 5-branes do not have D0-brane charge and are not present in BFSS Matrix theory, our analysis provides an independent test for the coupling of D-branes to general weak backgrounds proposed by Taylor and Van Raamsdonk from the analysis of the BFSS model. The proposed couplings appear in the Berkooz-Douglas effective action precisely as expected, which suggests the consistency of the two matrix models. We also point out the existence of the terms which are not given by the symmetrized trace prescription in the Matrix theory effective action

Personnel Selection Using Fuzzy Axiomatic Design Principles

Directory of Open Access Journals (Sweden)

Anant V. Khandekar

2016-09-01

Full Text Available Overall competency of the working personnel is often observed to ultimately affect the productivity of an organization. The globalised competitive atmosphere coupled with technological improvements demands for efficient and specialized manpower for the industrial operations. A set of typical technological skills and attitudes is thus demanded for every job profile. Most often, these skills and attitudes are expressed imprecisely and hence, necessitating the support of fuzzy sets for their effective understanding and further processing. In this paper, a method based on fuzzy axiomatic design principles is applied for solving the personnel selection problems. Selecting a middle management staff of a service department for a large scale organization is demonstrated here as a real life example. Five shortlisted candidates are assessed with respect to a set of 18 evaluation criteria, and the selection committee with experts from the related fields also realizes the outcome of the adopted approach to be quite appropriate, befitting and in agreement with their expectations.

Quantum field theory on curved spacetimes: Axiomatic framework and examples

International Nuclear Information System (INIS)

Fredenhagen, Klaus; Rejzner, Kasia

2016-01-01

In this review article, we want to expose a systematic development of quantum field theory on curved spacetimes. The leading principle is the emphasis on local properties. It turns out that this requires a reformulation of the QFT framework which also yields a new perspective for the theories on Minkowski space. The aim of the present work is to provide an almost self-contained introduction into the framework, which should be accessible for both mathematical physicists and mathematicians.

Quantum field theory on curved spacetimes: Axiomatic framework and examples

Energy Technology Data Exchange (ETDEWEB)

Fredenhagen, Klaus [II Institut fur Theoretische Physik, Universitat Hamburg, Hamburg 22761 (Germany); Rejzner, Kasia [Department of Mathematics, University of York, York YO10 5DD (United Kingdom)

2016-03-15

In this review article, we want to expose a systematic development of quantum field theory on curved spacetimes. The leading principle is the emphasis on local properties. It turns out that this requires a reformulation of the QFT framework which also yields a new perspective for the theories on Minkowski space. The aim of the present work is to provide an almost self-contained introduction into the framework, which should be accessible for both mathematical physicists and mathematicians.

Random matrix theory for pseudo-Hermitian systems: Cyclic blocks

Indian Academy of Sciences (India)

Abstract. We discuss the relevance of random matrix theory for pseudo-Hermitian sys- tems, and, for Hamiltonians that break parity P and time-reversal invariance T. In an attempt to understand the random Ising model, we present the treatment of cyclic asym- metric matrices with blocks and show that the nearest-neighbour ...

Time dependent mean field approximation to the many-body S-matrix

International Nuclear Information System (INIS)

Alhassid, Y.; Koonin, S.E.

1980-01-01

Time-dependent Hartree-Fock (TDHF) calculations are a good description of some inclusive properties of deep inelastic heavy-ion collisions. The first steps toward a mean-field theory that approximates specific elements of the many-body S matrix are presented. A many-body system with pairwise interactions excited by an external, time-dependent one-body field is considered. The methods are used to solve the forced Lipkin model. The moduli of elastic and excitation amplitudes are plotted. 3 figures

Random matrix theory and fund of funds portfolio optimisation

Science.gov (United States)

Conlon, T.; Ruskin, H. J.; Crane, M.

2007-08-01

The proprietary nature of Hedge Fund investing means that it is common practise for managers to release minimal information about their returns. The construction of a fund of hedge funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise. In this paper, random matrix theory (RMT) is applied to a cross-correlation matrix C, constructed using hedge fund returns data. The analysis reveals a number of eigenvalues that deviate from the spectrum suggested by RMT. The components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers. The inverse participation ratio is used to quantify the number of components that participate in each eigenvector. Finally, the correlation matrix is cleaned by separating the noisy part from the non-noisy part of C. This technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio, leading to an improved risk profile for a fund of hedge funds.

Introduction to game theory

Institute of Scientific and Technical Information of China (English)

无

2003-01-01

The basic ideas of game theory were originated from the problems of maximum and minimum given by J.Yon Neumann in 1928. Later, wars accelerated the study of game theory, there are many developments that contributed to the advancement of game theory, many problems of optimum appeared in economic development process. Scientists applied mathematic methods to studying game theory to make the theory more profound and perfect. The axiomatic structure of game theory was nearly complete in 1944. The path of the development of game theory started from finite to infinite, from two players to many players, from expressing gains with quantity to showing the ending of game theory with abstract result, and from certainty problems to random problems. Thus development of game theory is closely related to the economic development. In recent years, the research on the non-differentiability of Shapley value posed by Belgian Mertens is one of the advanced studies in game theory.

Incompatibility of the quantum and relativity theories and a possible resolution

International Nuclear Information System (INIS)

Sachs, M.

1982-01-01

This paper presents a comparison of the conceptual bases of the quantum theory and the theory of relativity, each considered as fundamental theories of elementary matter. From a study of the irreducible axiomatic bases of these respective approaches to elementary matter, it is concluded that they cannot peacefully co-exist because of logical incompatibility. Among the reasons discussed for this conclusion, one is the implication of the Hamiltonian form of quantum mechanics yielding an irreducible absolute frame of reference - that of the measuring apparatus - in the basic expression for the laws of elementary particles. This difficulty leads to logical inconsistency as well as a formulation of relativistic quantum field theory that is not demonstrably mathematically consistent. In spite of their logical incompatiability, it is argued that each of these theories logically requires the other, within its own framework. The conclusion is reached that, to make further progress in our understanding of elementary matter, it is necessary to abandon the axiomatic basis of one of these theories for the other, while keeping the formal structure of the abandoned theory as an accurate mathematical approximation (under special physical conditions) for a generalized form of the retained theory. An argument is presented for the author's retention of the theory of relativity as an authentic basis of elementary matter, and how its generalization is achieved by incorporating a fully (generally) covariant expression of the inertial manifestations of matter with its force manifestations

Schwinger's quantum action principle from Dirac’s formulation through Feynman’s path integrals, the Schwinger-Keldysh method, quantum field theory, to source theory

CERN Document Server

Milton, Kimball A

2015-01-01

Starting from the earlier notions of stationary action principles, these tutorial notes shows how Schwinger’s Quantum Action Principle descended from Dirac’s formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. Part I brings out in more detail the connection between the two formulations, and applications are discussed. Then, the Keldysh-Schwinger time-cycle method of extracting matrix elements is described. Part II will discuss the variational formulation of quantum electrodynamics and the development of source theory.

Non-supersymmetric matrix strings from generalized Yang-Mills theory on arbitrary Riemann surfaces

International Nuclear Information System (INIS)

Billo, M.; D'Adda, A.; Provero, P.

2000-01-01

We quantize pure 2d Yang-Mills theory on an arbitrary Riemann surface in the gauge where the field strength is diagonal. Twisted sectors originate, as in Matrix string theory, from permutations of the eigenvalues around homotopically non-trivial loops. These sectors, that must be discarded in the usual quantization due to divergences occurring when two eigenvalues coincide, can be consistently kept if one modifies the action by introducing a coupling of the field strength to the space-time curvature. This leads to a generalized Yang-Mills theory whose action reduces to the usual one in the limit of zero curvature. After integrating over the non-diagonal components of the gauge fields, the theory becomes a free string theory (sum over unbranched coverings) with a U(1) gauge theory on the world-sheet. This is shown to be equivalent to a lattice theory with a gauge group which is the semi-direct product of S N and U(1) N . By using well known results on the statistics of coverings, the partition function on arbitrary Riemann surfaces and the kernel functions on surfaces with boundaries are calculated. Extensions to include branch points and non-abelian groups on the world-sheet are briefly commented upon

Constructing the tree-level Yang-Mills S-matrix using complex factorization

Science.gov (United States)

Schuster, Philip C.; Toro, Natalia

2009-06-01

A remarkable connection between BCFW recursion relations and constraints on the S-matrix was made by Benincasa and Cachazo in 0705.4305, who noted that mutual consistency of different BCFW constructions of four-particle amplitudes generates non-trivial (but familiar) constraints on three-particle coupling constants — these include gauge invariance, the equivalence principle, and the lack of non-trivial couplings for spins > 2. These constraints can also be derived with weaker assumptions, by demanding the existence of four-point amplitudes that factorize properly in all unitarity limits with complex momenta. From this starting point, we show that the BCFW prescription can be interpreted as an algorithm for fully constructing a tree-level S-matrix, and that complex factorization of general BCFW amplitudes follows from the factorization of four-particle amplitudes. The allowed set of BCFW deformations is identified, formulated entirely as a statement on the three-particle sector, and using only complex factorization as a guide. Consequently, our analysis based on the physical consistency of the S-matrix is entirely independent of field theory. We analyze the case of pure Yang-Mills, and outline a proof for gravity. For Yang-Mills, we also show that the well-known scaling behavior of BCFW-deformed amplitudes at large z is a simple consequence of factorization. For gravity, factorization in certain channels requires asymptotic behavior ~ 1/z2.

Constructing the tree-level Yang-Mills S-matrix using complex factorization

International Nuclear Information System (INIS)

Schuster, Philip C.; Toro, Natalia

2009-01-01

A remarkable connection between BCFW recursion relations and constraints on the S-matrix was made by Benincasa and Cachazo in 0705.4305, who noted that mutual consistency of different BCFW constructions of four-particle amplitudes generates non-trivial (but familiar) constraints on three-particle coupling constants - these include gauge invariance, the equivalence principle, and the lack of non-trivial couplings for spins > 2. These constraints can also be derived with weaker assumptions, by demanding the existence of four-point amplitudes that factorize properly in all unitarity limits with complex momenta. From this starting point, we show that the BCFW prescription can be interpreted as an algorithm for fully constructing a tree-level S-matrix, and that complex factorization of general BCFW amplitudes follows from the factorization of four-particle amplitudes. The allowed set of BCFW deformations is identified, formulated entirely as a statement on the three-particle sector, and using only complex factorization as a guide. Consequently, our analysis based on the physical consistency of the S-matrix is entirely independent of field theory. We analyze the case of pure Yang-Mills, and outline a proof for gravity. For Yang-Mills, we also show that the well-known scaling behavior of BCFW-deformed amplitudes at large z is a simple consequence of factorization. For gravity, factorization in certain channels requires asymptotic behavior ∼ 1/z 2 .

Random matrix theory and portfolio optimization in Moroccan stock exchange

Science.gov (United States)

El Alaoui, Marwane

2015-09-01

In this work, we use random matrix theory to analyze eigenvalues and see if there is a presence of pertinent information by using Marčenko-Pastur distribution. Thus, we study cross-correlation among stocks of Casablanca Stock Exchange. Moreover, we clean correlation matrix from noisy elements to see if the gap between predicted risk and realized risk would be reduced. We also analyze eigenvectors components distributions and their degree of deviations by computing the inverse participation ratio. This analysis is a way to understand the correlation structure among stocks of Casablanca Stock Exchange portfolio.

Chern-Simons Theory, Matrix Models, and Topological Strings

International Nuclear Information System (INIS)

Walcher, J

2006-01-01

This book is a find. Marino meets the challenge of filling in less than 200 pages the need for an accessible review of topological gauge/gravity duality. He is one of the pioneers of the subject and a clear expositor. It is no surprise that reading this book is a great pleasure. The existence of dualities between gauge theories and theories of gravity remains one of the most surprising recent discoveries in mathematical physics. While it is probably fair to say that we do not yet understand the full reach of such a relation, the impressive amount of evidence that has accumulated over the past years can be regarded as a substitute for a proof, and will certainly help to delineate the question of what is the most fundamental quantum mechanical theory. Here is a brief summary of the book. The journey begins with matrix models and an introduction to various techniques for the computation of integrals including perturbative expansion, large-N approximation, saddle point analysis, and the method of orthogonal polynomials. The second chapter, on Chern-Simons theory, is the longest and probably the most complete one in the book. Starting from the action we meet Wilson loop observables, the associated perturbative 3-manifold invariants, Witten's exact solution via the canonical duality to WZW models, the framing ambiguity, as well as a collection of results on knot invariants that can be derived from Chern-Simons theory and the combinatorics of U (∞) representation theory. The chapter also contains a careful derivation of the large-N expansion of the Chern-Simons partition function, which forms the cornerstone of its interpretation as a closed string theory. Finally, we learn that Chern-Simons theory can sometimes also be represented as a matrix model. The story then turns to the gravity side, with an introduction to topological sigma models (chapter 3) and topological string theory (chapter 4). While this presentation is necessarily rather condensed (and the beginner may

An MEG signature corresponding to an axiomatic model of reward prediction error.

Science.gov (United States)

Talmi, Deborah; Fuentemilla, Lluis; Litvak, Vladimir; Duzel, Emrah; Dolan, Raymond J

2012-01-02

Optimal decision-making is guided by evaluating the outcomes of previous decisions. Prediction errors are theoretical teaching signals which integrate two features of an outcome: its inherent value and prior expectation of its occurrence. To uncover the magnetic signature of prediction errors in the human brain we acquired magnetoencephalographic (MEG) data while participants performed a gambling task. Our primary objective was to use formal criteria, based upon an axiomatic model (Caplin and Dean, 2008a), to determine the presence and timing profile of MEG signals that express prediction errors. We report analyses at the sensor level, implemented in SPM8, time locked to outcome onset. We identified, for the first time, a MEG signature of prediction error, which emerged approximately 320 ms after an outcome and expressed as an interaction between outcome valence and probability. This signal followed earlier, separate signals for outcome valence and probability, which emerged approximately 200 ms after an outcome. Strikingly, the time course of the prediction error signal, as well as the early valence signal, resembled the Feedback-Related Negativity (FRN). In simultaneously acquired EEG data we obtained a robust FRN, but the win and loss signals that comprised this difference wave did not comply with the axiomatic model. Our findings motivate an explicit examination of the critical issue of timing embodied in computational models of prediction errors as seen in human electrophysiological data. Copyright © 2011 Elsevier Inc. All rights reserved.

Exact perturbation theory of multiphoton processes at high intensities. [Schroedinger equation, perturbation theory, matrix

Energy Technology Data Exchange (ETDEWEB)

Faisal, F H.M. [Bielefeld Univ. (Germany, F.R.). Fakultaet fuer Physik

1976-06-11

In this work the perturbation theory for multiphoton processes at high intensities is investigated and it is described an analytical method of summing the perturbation series to extract the contribution from all terms that give rise to the absorption of N photons by an atomic system. The method is first applied to the solution of a simple model problem and the result is confirmed by direct integration of the model Schroedinger equation. The usual lowest (nonvanishing)-order perturbation-theoretical calculation is also carried out for this model to demonstrate explicitly that the full result correctly reproduces that of the lowest-order theory in the limit of low intensity. The method is then extended to the case of an atomic system with well-developed spectrum (e.g. H atom) and the N-photon T-matrix is derived in terms of a ''photon matrix'' asub(N), for which a three-term recurrence relation is established. Next, from the vantage point of the general result obtained here, A probe is made into the nature of several approximate nonperturbative solutions that have appeared in the literature in the past. It is shown here that their applicability is severely restricted by the requirement of the essential spectral degeneracy of the atomic system. Finally, appendix A outlines a prescription of computing the photon matrix asub(N), which (as in the usual lowest-order perturbation-theoretical calculation)requires a knowledge of the eigenfunctions and eigenvalues of the atomic Hamiltonian only.

Basic scattering theory

International Nuclear Information System (INIS)

Queen, N.M.

1978-01-01

This series of lectures on basic scattering theory were given as part of a course for postgraduate high energy physicists and were designed to acquaint the student with some of the basic language and formalism used for the phenomenological description of nuclear reactions and decay processes used for the study of elementary particle interactions. Well established and model independent aspects of scattering theory, which are the basis of S-matrix theory, are considered. The subject is considered under the following headings; the S-matrix, cross sections and decay rates, phase space, relativistic kinematics, the Mandelstam variables, the flux factor, two-body phase space, Dalitz plots, other kinematic plots, two-particle reactions, unitarity, the partial-wave expansion, resonances (single-channel case), multi-channel resonances, analyticity and crossing, dispersion relations, the one-particle exchange model, the density matrix, mathematical properties of the density matrix, the density matrix in scattering processes, the density matrix in decay processes, and the helicity formalism. Some exercises for the students are included. (U.K.)

A theory of Bayesian decision making

OpenAIRE

Karni, Edi

2009-01-01

This paper presents a complete, choice-based, axiomatic Bayesian decision theory. It introduces a new choice set consisting of information-contingent plans for choosing actions and bets and subjective expected utility model with effect-dependent utility functions and action-dependent subjective probabilities which, in conjunction with the updating of the probabilities using Bayes’ rule, gives rise to a unique prior and a set of action-dependent posterior probabilities representing the decisio...

Constrained Perturbation Regularization Approach for Signal Estimation Using Random Matrix Theory

KAUST Repository

Suliman, Mohamed Abdalla Elhag; Ballal, Tarig; Kammoun, Abla; Al-Naffouri, Tareq Y.

2016-01-01

random matrix theory are applied to derive the near-optimum regularizer that minimizes the mean-squared error of the estimator. Simulation results demonstrate that the proposed approach outperforms a set of benchmark regularization methods for various

A critical analysis of the quantum theory of measurement

International Nuclear Information System (INIS)

Fer, F.

1984-01-01

Keeping strictly in the positivist and probabilistic, hence hilbertian frame of Quantum Mechanics, the author tries to ascertain whether or not Quantum Mechanics, starting from its axioms, reaches the aim of any physical theory, that is, comparison with experiment. The answer is: no, as long as it keeps close to the existing axiomatics, and also to accurate mathematics. (Auth.)

R-Matrix Theory of Atomic Collisions Application to Atomic, Molecular and Optical Processes

CERN Document Server

Burke, Philip George

2011-01-01

Commencing with a self-contained overview of atomic collision theory, this monograph presents recent developments of R-matrix theory and its applications to a wide-range of atomic molecular and optical processes. These developments include electron and photon collisions with atoms, ions and molecules required in the analysis of laboratory and astrophysical plasmas, multiphoton processes required in the analysis of superintense laser interactions with atoms and molecules and positron collisions with atoms and molecules required in antimatter studies of scientific and technologial importance. Basic mathematical results and general and widely used R-matrix computer programs are summarized in the appendices.

q-Virasoro constraints in matrix models

Energy Technology Data Exchange (ETDEWEB)

Nedelin, Anton [Dipartimento di Fisica, Università di Milano-Bicocca and INFN, sezione di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano (Italy); Department of Physics and Astronomy, Uppsala university,Box 516, SE-75120 Uppsala (Sweden); Zabzine, Maxim [Department of Physics and Astronomy, Uppsala university,Box 516, SE-75120 Uppsala (Sweden)

2017-03-20

The Virasoro constraints play the important role in the study of matrix models and in understanding of the relation between matrix models and CFTs. Recently the localization calculations in supersymmetric gauge theories produced new families of matrix models and we have very limited knowledge about these matrix models. We concentrate on elliptic generalization of hermitian matrix model which corresponds to calculation of partition function on S{sup 3}×S{sup 1} for vector multiplet. We derive the q-Virasoro constraints for this matrix model. We also observe some interesting algebraic properties of the q-Virasoro algebra.

On the generalized eigenvalue method for energies and matrix elements in lattice field theory

Energy Technology Data Exchange (ETDEWEB)

Blossier, Benoit [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)]|[Paris-XI Univ., 91 - Orsay (France). Lab. de Physique Theorique; Morte, Michele della [CERN, Geneva (Switzerland). Physics Dept.]|[Mainz Univ. (Germany). Inst. fuer Kernphysik; Hippel, Georg von; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Mendes, Tereza [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)]|[Sao Paulo Univ. (Brazil). IFSC

2009-02-15

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E{sub N+1}-E{sub n}) t). The gap E{sub N+1}-E{sub n} can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m{sub b} in HQET. (orig.)

On the generalized eigenvalue method for energies and matrix elements in lattice field theory

International Nuclear Information System (INIS)

Blossier, Benoit; Mendes, Tereza; Sao Paulo Univ.

2009-02-01

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E N+1 -E n ) t). The gap E N+1 -E n can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m b in HQET. (orig.)

Asymptotic theory for the sample covariance matrix of a heavy-tailed multivariate time series

DEFF Research Database (Denmark)

Davis, Richard A.; Mikosch, Thomas Valentin; Pfaffel, Olivier

2016-01-01

In this paper we give an asymptotic theory for the eigenvalues of the sample covariance matrix of a multivariate time series. The time series constitutes a linear process across time and between components. The input noise of the linear process has regularly varying tails with index α∈(0,4) in...... particular, the time series has infinite fourth moment. We derive the limiting behavior for the largest eigenvalues of the sample covariance matrix and show point process convergence of the normalized eigenvalues. The limiting process has an explicit form involving points of a Poisson process and eigenvalues...... of a non-negative definite matrix. Based on this convergence we derive limit theory for a host of other continuous functionals of the eigenvalues, including the joint convergence of the largest eigenvalues, the joint convergence of the largest eigenvalue and the trace of the sample covariance matrix...

Theory of the particle matrix elements for Helium atom scattering in surfaces

International Nuclear Information System (INIS)

Khater, A.; Toennies, J.P.

2000-01-01

Full text.A brief review is presented for the recent development of the theory of the particle transition matrix elements, basic to the cross section for Helium and inert particle scattering at thermal energies in solid surfaces. the Jackson and Mott matrix elements are presented and discussed for surface scattering processes, habitually classified as elastic and inelastic. Modified transition matrix elements, introduced originally to account for the cut-off effects, are presented in a direct and simple manner. the Debye-Waller factor is introduced and discussed. A recent calculation for the particle transition matrix elements is presented for the specular and inelastic transition matrix elements and the corresponding inelastic scattering cross section is compared in detail to experimental data. the specular and inelastic transition matrix elements are found to be intrinsically similar owing to the intermediate role of a proposed virtual particle squeezed state near the surface

J-matrix method of scattering in one dimension: The nonrelativistic theory

International Nuclear Information System (INIS)

Alhaidari, A.D.; Bahlouli, H.; Abdelmonem, M.S.

2009-01-01

We formulate a theory of nonrelativistic scattering in one dimension based on the J-matrix method. The scattering potential is assumed to have a finite range such that it is well represented by its matrix elements in a finite subset of a basis that supports a tridiagonal matrix representation for the reference wave operator. Contrary to our expectation, the 1D formulation reveals a rich and highly nontrivial structure compared to the 3D formulation. Examples are given to demonstrate the utility and accuracy of the method. It is hoped that this formulation constitutes a viable alternative to the classical treatment of 1D scattering problem and that it will help unveil new and interesting applications.

The AdS5xS5 superstring worldsheet S matrix and crossing symmetry

International Nuclear Information System (INIS)

Janik, Romuald A.

2006-01-01

An S matrix satisfying the Yang-Baxter equation with symmetries relevant to the AdS 5 xS 5 superstring recently has been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations; however, due to the lack of conventional relativistic invariance, in this case its determination remained an open problem. In this paper we propose an algebraic way to implement crossing relations for the AdS 5 xS 5 superstring worldsheet S matrix. We base our construction on a Hopf-algebraic formulation of crossing in terms of the antipode and introduce generalized rapidities living on the universal cover of the parameter space which is constructed through an auxillary, coupling-constant dependent, elliptic curve. We determine the crossing transformation and write functional equations for the scalar factor of the S matrix in the generalized rapidity plane

Comments on fusion matrix in N=1 super Liouville field theory

Directory of Open Access Journals (Sweden)

Hasmik Poghosyan

2016-08-01

Full Text Available We study several aspects of the N=1 super Liouville theory. We show that certain elements of the fusion matrix in the Neveu–Schwarz sector are related to the structure constants according to the same rules which we observe in rational conformal field theory. We collect some evidences that these relations should hold also in the Ramond sector. Using them the Cardy–Lewellen equation for defects is studied, and defects are constructed.

Effects of the virtual particle number on the S matrix of the (phi4)/sub 1+1/ model

International Nuclear Information System (INIS)

Kroeger, H.; Girard, R.; Dufour, G.

1987-01-01

We present results of the S matrix in the (phi 4 )/sub 1 + 1/ model obtained by a nonperturbative calculation using a momentum-space discretization technique. First, we calculate the two-body S matrix in the strong-coupling regime (up to λ/sub eff/ = 3), with the restriction of taking into account only two-body virtual particle states. We find agreement with standard perturbation theory obtained by summing up the corresponding graphs to infinite order. We also estimate the effect of mass renormalization. Second, we investigate the effect of including higher virtual particle numbers in two-particle scattering in the cases λ/sub eff/ = (1/6) and λ/sub eff/ = 1. In both cases we find convergence of the S matrix with respect to increasing the virtual-particle-number cutoff

Variational principles are a powerful tool also for formulating field theories

OpenAIRE

Dell'Isola , Francesco; Placidi , Luca

2012-01-01

Variational principles and calculus of variations have always been an important tool for formulating mathematical models for physical phenomena. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest for scientists and engineers and are the main tool for the axiomatization of physical theories

arXiv The S-matrix Bootstrap I: QFT in AdS

CERN Document Server

Paulos, Miguel F.; Toledo, Jonathan; van Rees, Balt C.; Vieira, Pedro

2017-11-21

We propose a strategy to study massive Quantum Field Theory (QFT) using conformal bootstrap methods. The idea is to consider QFT in hyperbolic space and study correlation functions of its boundary operators. We show that these are solutions of the crossing equations in one lower dimension. By sending the curvature radius of the background hyperbolic space to infinity we expect to recover flat-space physics. We explain that this regime corresponds to large scaling dimensions of the boundary operators, and discuss how to obtain the flat-space scattering amplitudes from the corresponding limit of the boundary correlators. We implement this strategy to obtain universal bounds on the strength of cubic couplings in 2D flat-space QFTs using 1D conformal bootstrap techniques. Our numerical results match precisely the analytic bounds obtained in our companion paper using S-matrix bootstrap techniques.

Dirac operator, chirality and random matrix theory

International Nuclear Information System (INIS)

Pullirsch, R.

2001-05-01

Quantum Chromodynamics (QCD) is considered to be the correct theory which describes quarks and gluons and, thus, all strong interaction phenomena from the fundamental forces of nature. However, important properties of QCD such as the physical mechanism of color confinement and the spontaneous breaking of chiral symmetry are still not completely understood and under extensive discussion. Analytical calculations are limited, because in the low-energy regime where quarks are confined, application of perturbation theory is restricted due to the large gluon coupling. A powerful tool to investigate numerically and analytically the non-perturbative region is provided by the lattice formulation of QCD. From Monte Carlo simulations of lattice QCD we know that chiral symmetry is restored above a critical temperature. As the chiral condensate is connected to the spectral density of the Dirac operator via the Banks-Casher relation, the QCD Dirac spectrum is an interesting object for detailed studies. In search for an analytical expression of the infrared limit of the Dirac spectrum it has been realized that chiral random-matrix theory (chRMT) is a suitable tool to compare with the distribution and the correlations of the small Dirac eigenvalues. Further, it has been shown that the correlations of eigenvalues on the scale of mean level spacings are universal for complex physical systems and are given by random-matrix theory (Rm). This has been formulated as the Baghouse-Giannoni-Schmit conjecture which states that spectral correlations of a classically chaotic system are given by RMT on the quantum level. The aim of this work is to analyze the relationship between chiral phase transitions and chaos to order transitions in quantum field theories. We study the eigenvalues of the Dirac operator for Quantum Electrodynamics (QED) with compact gauge group U(1) on the lattice. This theory shows chiral symmetry breaking and confinement in the strong coupling region. Although being

One-point functions in AdS/dCFT from matrix product states

International Nuclear Information System (INIS)

Buhl-Mortensen, Isak; Leeuw, Marius de; Kristjansen, Charlotte; Zarembo, Konstantin

2016-01-01

One-point functions of certain non-protected scalar operators in the defect CFT dual to the D3-D5 probe brane system with k units of world volume flux can be expressed as overlaps between Bethe eigenstates of the Heisenberg spin chain and a matrix product state. We present a closed expression of determinant form for these one-point functions, valid for any value of k. The determinant formula factorizes into the k=2 result times a k-dependent pre-factor. Making use of the transfer matrix of the Heisenberg spin chain we recursively relate the matrix product state for higher even and odd k to the matrix product state for k=2 and k=3 respectively. We furthermore find evidence that the matrix product states for k=2 and k=3 are related via a ratio of Baxter’s Q-operators. The general k formula has an interesting thermodynamical limit involving a non-trivial scaling of k, which indicates that the match between string and field theory one-point functions found for chiral primaries might be tested for non-protected operators as well. We revisit the string computation for chiral primaries and discuss how it can be extended to non-protected operators.

S-matrix elements from T-duality

International Nuclear Information System (INIS)

Babaei Velni, Komeil; Garousi, Mohammad R.

2013-01-01

Recently it has been speculated that the S-matrix elements satisfy the Ward identity associated with the T-duality. This indicates that a group of S-matrix elements is invariant under the linear T-duality transformations on the external states. If one evaluates one component of such T-dual multiplet, then all other components may be found by the simple use of the linear T-duality. The assumption that fields must be independent of the Killing coordinate, however, may cause, in some cases, the T-dual multiplet not to be gauge invariant. In those cases, the S-matrix elements contain more than one T-dual multiplet which are intertwined by the gauge symmetry. In this paper, we apply the T-dual Ward identity on the S-matrix element of one RR (p−3)-form and two NSNS states on the world volume of a D p -brane to find its corresponding T-dual multiplet. In the case that the RR potential has two transverse indices, the T-dual multiplet is gauge invariant, however, in the case that it has one transverse index the multiplet is not gauge invariant. We find a new T-dual multiplet in this case by imposing the gauge symmetry. We show that the multiplets are reproduced by explicit calculation, and their low energy contact terms at order α ′2 are consistent with the existing couplings in the literature

An Exploratory Study of Cost Engineering in Axiomatic Design: Creation of the Cost Model Based on an FR-DP Map

Science.gov (United States)

Lee, Taesik; Jeziorek, Peter

2004-01-01

Large complex projects cost large sums of money throughout their life cycle for a variety of reasons and causes. For such large programs, the credible estimation of the project cost, a quick assessment of the cost of making changes, and the management of the project budget with effective cost reduction determine the viability of the project. Cost engineering that deals with these issues requires a rigorous method and systematic processes. This paper introduces a logical framework to a&e effective cost engineering. The framework is built upon Axiomatic Design process. The structure in the Axiomatic Design process provides a good foundation to closely tie engineering design and cost information together. The cost framework presented in this paper is a systematic link between the functional domain (FRs), physical domain (DPs), cost domain (CUs), and a task/process-based model. The FR-DP map relates a system s functional requirements to design solutions across all levels and branches of the decomposition hierarchy. DPs are mapped into CUs, which provides a means to estimate the cost of design solutions - DPs - from the cost of the physical entities in the system - CUs. The task/process model describes the iterative process ot-developing each of the CUs, and is used to estimate the cost of CUs. By linking the four domains, this framework provides a superior traceability from requirements to cost information.

Equations for formally real meadows

NARCIS (Netherlands)

Bergstra, J.A.; Bethke, I.; Ponse, A.

2015-01-01

We consider the signatures Σm = (0,1,−,+,⋅,−1)  of meadows and (Σm,s)  of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these signatures. In the first case, we extend the axiomatization of zero-totalized fields by a single axiom

Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient

Science.gov (United States)

Wang, Gang-Jin; Xie, Chi; Chen, Shou; Yang, Jiao-Jiao; Yang, Ming-Yan

2013-09-01

In this study, we first build two empirical cross-correlation matrices in the US stock market by two different methods, namely the Pearson’s correlation coefficient and the detrended cross-correlation coefficient (DCCA coefficient). Then, combining the two matrices with the method of random matrix theory (RMT), we mainly investigate the statistical properties of cross-correlations in the US stock market. We choose the daily closing prices of 462 constituent stocks of S&P 500 index as the research objects and select the sample data from January 3, 2005 to August 31, 2012. In the empirical analysis, we examine the statistical properties of cross-correlation coefficients, the distribution of eigenvalues, the distribution of eigenvector components, and the inverse participation ratio. From the two methods, we find some new results of the cross-correlations in the US stock market in our study, which are different from the conclusions reached by previous studies. The empirical cross-correlation matrices constructed by the DCCA coefficient show several interesting properties at different time scales in the US stock market, which are useful to the risk management and optimal portfolio selection, especially to the diversity of the asset portfolio. It will be an interesting and meaningful work to find the theoretical eigenvalue distribution of a completely random matrix R for the DCCA coefficient because it does not obey the Marčenko-Pastur distribution.

Universality in random matrix theory and chiral symmetry breaking in QCD

International Nuclear Information System (INIS)

Akemann, G.

2000-05-01

In this work we review the topic of random matrix model universality with particular stress on its application to the study of chiral symmetry breaking in QCD. We highlight the role of microscopic and macroscopic matrix model correlation functions played in the description of the deep infrared eigenvalue spectrum of the Dirac operator. The universal microscopic correlation functions are presented for all three chiral symmetry breaking patterns, and the corresponding random matrix universality proofs are given for massless and massive fermions in a unified way. These analytic results have been widely confirmed from QCD lattice data and we present a comparison with the most recent analytic calculations describing data for dynamical SU(2) staggered fermions. The microscopic matrix model results are then re-expressed in terms of the finite-volume partition functions of Leutwyler and Smilga, where some of these expressions have been recently obtained using field theory only. The macroscopic random matrix universality is reviewed for the most simplest examples of bosonic and supersymmetric models. We also give an example for a non-universal deformation of a random matrix model - the restricted trace ensemble. (orig.)

Kinematic matrix theory and universalities in self-propellers and active swimmers.

Science.gov (United States)

Nourhani, Amir; Lammert, Paul E; Borhan, Ali; Crespi, Vincent H

2014-06-01

We describe an efficient and parsimonious matrix-based theory for studying the ensemble behavior of self-propellers and active swimmers, such as nanomotors or motile bacteria, that are typically studied by differential-equation-based Langevin or Fokker-Planck formalisms. The kinematic effects for elementary processes of motion are incorporated into a matrix, called the "kinematrix," from which we immediately obtain correlators and the mean and variance of angular and position variables (and thus effective diffusivity) by simple matrix algebra. The kinematrix formalism enables us recast the behaviors of a diverse range of self-propellers into a unified form, revealing universalities in their ensemble behavior in terms of new emergent time scales. Active fluctuations and hydrodynamic interactions can be expressed as an additive composition of separate self-propellers.

Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory.

Science.gov (United States)

Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic

2010-01-14

We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu(2)O(2)](2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu(2)O(2)](2+).

The existence of superluminal particles is consistent with the kinematics of Einstein's special theory of relativity

OpenAIRE

Székely, Gergely

2012-01-01

Within an axiomatic framework of kinematics, we prove that the existence of faster than light particles is logically independent of Einstein's special theory of relativity. Consequently, it is consistent with the kinematics of special relativity that there might be faster than light particles.

Light-like big bang singularities in string and matrix theories

International Nuclear Information System (INIS)

Craps, Ben; Evnin, Oleg

2011-01-01

Important open questions in cosmology require a better understanding of the big bang singularity. In string and matrix theories, light-like analogues of cosmological singularities (singular plane wave backgrounds) turn out to be particularly tractable. We give a status report on the current understanding of such light-like big bang models, presenting both solved and open problems.

Matrix model approximations of fuzzy scalar field theories and their phase diagrams

Energy Technology Data Exchange (ETDEWEB)

Tekel, Juraj [Department of Theoretical Physics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska Dolina, Bratislava, 842 48 (Slovakia)

2015-12-29

We present an analysis of two different approximations to the scalar field theory on the fuzzy sphere, a nonperturbative and a perturbative one, which are both multitrace matrix models. We show that the former reproduces a phase diagram with correct features in a qualitative agreement with the previous numerical studies and that the latter gives a phase diagram with features not expected in the phase diagram of the field theory.

Spectral function from Reduced Density Matrix Functional Theory

Science.gov (United States)

Romaniello, Pina; di Sabatino, Stefano; Berger, Jan A.; Reining, Lucia

2015-03-01

In this work we focus on the calculation of the spectral function, which determines, for example, photoemission spectra, from reduced density matrix functional theory. Starting from its definition in terms of the one-body Green's function we derive an expression for the spectral function that depends on the natural occupation numbers and on an effective energy which accounts for all the charged excitations. This effective energy depends on the two-body as well as higher-order density matrices. Various approximations to this expression are explored by using the exactly solvable Hubbard chains.

Dielectric matrix, dynamical matrix and phonon dispersion in hcp transition metal scandium

International Nuclear Information System (INIS)

Singh, Joginder; Singh, Natthi; Prakash, S.

1976-01-01

Complete dielectric matrix is evaluated for hcp transition metal scandium using the non-interacting s- and d-band model. The local field corrections which are consequence of the non-diagonal part of the dielectric matrix are calculated explicitly. The free electron approximation is used for the s-electrons and the simple tight-binding approximation is used for the d-electrons. The theory developed by Singh and others is used to invert the dielectric matrix and the explicit expressions for the dynamical matrix are obtained. The phonon dispersion relations are investigated by using the renormalized Animalu transition metal model potential (TMMP) for bare ion potential. The contribution due to non-central forces which arise due to local fields is found to be 20%. The results are found in resonably good agreement with the experimental values. (author)

Noncommutative gauge theory and symmetry breaking in matrix models

International Nuclear Information System (INIS)

Grosse, Harald; Steinacker, Harold; Lizzi, Fedele

2010-01-01

We show how the fields and particles of the standard model can be naturally realized in noncommutative gauge theory. Starting with a Yang-Mills matrix model in more than four dimensions, an SU(n) gauge theory on a Moyal-Weyl space arises with all matter and fields in the adjoint of the gauge group. We show how this gauge symmetry can be broken spontaneously down to SU(3) c xSU(2) L xU(1) Q [resp. SU(3) c xU(1) Q ], which couples appropriately to all fields in the standard model. An additional U(1) B gauge group arises which is anomalous at low energies, while the trace-U(1) sector is understood in terms of emergent gravity. A number of additional fields arise, which we assume to be massive, in a pattern that is reminiscent of supersymmetry. The symmetry breaking might arise via spontaneously generated fuzzy spheres, in which case the mechanism is similar to brane constructions in string theory.

A Road Map for Knowledge Management Systems Design Using Axiomatic Design Approach

Directory of Open Access Journals (Sweden)

Houshmand Mahmoud

2017-01-01

Full Text Available Successful design and implementation of knowledge management systems have been the main concern of many researchers. It has been reported that more than 50% of knowledge management systems have failed, therefore, it is required to seek for a new and comprehensive scientific approach to design and implement it. In the design and implementation of a knowledge management system, it is required to know ’what we want to achieve’ and ’how and by what processes we will achieve it’. A literature review conducted and axiomatic design theory selected for this purpose. For the first time, this paper develops a conceptual design of knowledge management systems by means of a hierarchical structure, composed of ’Functional Requirements’ (FRs, ’Design Parameters’ (DPs, and ’Process Variables’ (PVs. The intersection of several studies conducted in the field of knowledge management systems has been used to design the knowledge management model. It reveals that six essential bases of knowledge management are organizational culture, organizational structure, human resources, management and leadership, information technology, and the external environment of the organization; that are represented as top DPs in the structure of the model. These essential factors are decomposed to lower levels by means of zigzagging. The model implemented in Tehran Urban and Suburban Railway Operation Corporation (TUSROC and the results were very promising. The most important result of this study is a roadmap to design successful and efficient knowledge management systems.

Weak Quantum Theory: Formal Framework and Selected Applications

International Nuclear Information System (INIS)

Atmanspacher, Harald; Filk, Thomas; Roemer, Hartmann

2006-01-01

Two key concepts of quantum theory, complementarity and entanglement, are considered with respect to their significance in and beyond physics. An axiomatically formalized, weak version of quantum theory, more general than the ordinary quantum theory of physical systems, is described. Its mathematical structure generalizes the algebraic approach to ordinary quantum theory. The crucial formal feature leading to complementarity and entanglement is the non-commutativity of observables.The ordinary Hilbert space quantum mechanics can be recovered by stepwise adding the necessary features. This provides a hierarchy of formal frameworks of decreasing generality and increasing specificity. Two concrete applications, more specific than weak quantum theory and more general than ordinary quantum theory, are discussed: (i) complementarity and entanglement in classical dynamical systems, and (ii) complementarity and entanglement in the bistable perception of ambiguous stimuli

Theory of quark mixing matrix and invariant functions of mass matrices

International Nuclear Information System (INIS)

Jarlskog, C.

1987-10-01

The outline of this talk is as follows: The origin of the quark mixing matrix. Super elementary theory of flavour projection operators. Equivalences and invariances. The commutator formalism and CP violation. CP conditions for any number of families. The 'angle' between the quark mass matrices. Application to Fritzsch and Stech matrices. References. (author)

A simplified density matrix minimization for linear scaling self-consistent field theory

International Nuclear Information System (INIS)

Challacombe, M.

1999-01-01

A simplified version of the Li, Nunes and Vanderbilt [Phys. Rev. B 47, 10891 (1993)] and Daw [Phys. Rev. B 47, 10895 (1993)] density matrix minimization is introduced that requires four fewer matrix multiplies per minimization step relative to previous formulations. The simplified method also exhibits superior convergence properties, such that the bulk of the work may be shifted to the quadratically convergent McWeeny purification, which brings the density matrix to idempotency. Both orthogonal and nonorthogonal versions are derived. The AINV algorithm of Benzi, Meyer, and Tuma [SIAM J. Sci. Comp. 17, 1135 (1996)] is introduced to linear scaling electronic structure theory, and found to be essential in transformations between orthogonal and nonorthogonal representations. These methods have been developed with an atom-blocked sparse matrix algebra that achieves sustained megafloating point operations per second rates as high as 50% of theoretical, and implemented in the MondoSCF suite of linear scaling SCF programs. For the first time, linear scaling Hartree - Fock theory is demonstrated with three-dimensional systems, including water clusters and estane polymers. The nonorthogonal minimization is shown to be uncompetitive with minimization in an orthonormal representation. An early onset of linear scaling is found for both minimal and double zeta basis sets, and crossovers with a highly optimized eigensolver are achieved. Calculations with up to 6000 basis functions are reported. The scaling of errors with system size is investigated for various levels of approximation. copyright 1999 American Institute of Physics

A vector space approach to geometry

CERN Document Server

Hausner, Melvin

2010-01-01

The effects of geometry and linear algebra on each other receive close attention in this examination of geometry's correlation with other branches of math and science. In-depth discussions include a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.

Microlocal study of S-matrix singularity structure

International Nuclear Information System (INIS)

Kawai, Takahiro; Kyoto Univ.; Stapp, H.P.

1975-01-01

Support is adduced for two related conjectures of simplicity of the analytic structure of the S-matrix and related function; namely, Sato's conjecture that the S-matrix is a solution of a maximally over-determined system of pseudo-differential equations, and our conjecture that the singularity spectrum of any bubble diagram function has the conormal structure with respect to a canonical decomposition of the solutions of the relevant Landau equations. This latter conjecture eliminates the open sets of allowed singularities that existing procedures permit. (orig.) [de

Flat-space singletons

International Nuclear Information System (INIS)

Fronsdal, C.

1987-01-01

Singletons exist, as particles and as local fields, only in 3+2 de Sitter space. Their kinematical properties make them natural candidates for constituents of massless fields, and perhaps for quarks. It is interesting to find out how to describe this type of compositeness in flat space. A theory of interacting singleton fields in de Sitter space is now available, and in this paper we study the flat-space limit of the Green's functions of that theory. The flat-space limit is an autonomous theory of Green's functions, but is not an operator field theory. The three-point function is calculated and its flat-space limit is found to reveal glimpses of a physical interpretation. Causal and spectral properties are in accord with the tenets of axiomatic field theory. The theory is a generalization of local field theory, in which photons appear as composite objects although the physical S matrix is the same as in conventional QED

Membranes from monopole operators in ABJM theory: Large angular momentum and M-theoretic AdS4/CFT3

International Nuclear Information System (INIS)

Kovacs, Stefano; Sato, Yuki; Shimada, Hidehiko

2014-01-01

We study the duality between M-theory in AdS 4 ×S 7 /ℤ k and the ABJM N=6 Chern–Simons-matter theory with gauge group U(N)×U(N) and level k, taking N large and k of order 1. In this M-theoretic regime the lack of an explicit formulation of M-theory in AdS 4 ×S 7 /ℤ k makes the gravity side difficult, while the CFT is strongly coupled and the planar approximation is not applicable. We focus on states on the gravity side with large angular momentum J≫1 associated with a single plane of rotation in S 7 and identify their dual operators in the CFT. We show that natural approximation schemes arise on both sides thanks to the presence of the small parameter 1/J. On the AdS side, we use the matrix model of M-theory on the maximally supersymmetric pp-wave background with matrices of size J/k. A perturbative treatment of this matrix model provides a good approximation to M-theory in AdS 4 ×S 7 /ℤ k when N 1/3 ≪J≪N 1/2 . On the CFT side, we study the theory on S 2 ×ℝ with magnetic flux J/k. A Born–Oppenheimer-type expansion arises naturally for large J in spite of the theory being strongly coupled. The energy spectra on the two sides agree at leading order. This provides a non-trivial test of the AdS 4 /CFT 3 correspondence including near-BPS observables associated with membrane degrees of freedom, thus verifying the duality beyond the previously studied sectors corresponding to either BPS observables or the type IIA string regime

Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models

CERN Document Server

Pasquetti, Sara

2010-01-01

We address the nonperturbative structure of topological strings and c=1 matrix models, focusing on understanding the nature of instanton effects alongside with exploring their relation to the large-order behavior of the 1/N expansion. We consider the Gaussian, Penner and Chern-Simons matrix models, together with their holographic duals, the c=1 minimal string at self-dual radius and topological string theory on the resolved conifold. We employ Borel analysis to obtain the exact all-loop multi-instanton corrections to the free energies of the aforementioned models, and show that the leading poles in the Borel plane control the large-order behavior of perturbation theory. We understand the nonperturbative effects in terms of the Schwinger effect and provide a semiclassical picture in terms of eigenvalue tunneling between critical points of the multi-sheeted matrix model effective potentials. In particular, we relate instantons to Stokes phenomena via a hyperasymptotic analysis, providing a smoothing of the nonp...

Mean-deviation analysis in the theory of choice.

Science.gov (United States)

Grechuk, Bogdan; Molyboha, Anton; Zabarankin, Michael

2012-08-01

Mean-deviation analysis, along with the existing theories of coherent risk measures and dual utility, is examined in the context of the theory of choice under uncertainty, which studies rational preference relations for random outcomes based on different sets of axioms such as transitivity, monotonicity, continuity, etc. An axiomatic foundation of the theory of coherent risk measures is obtained as a relaxation of the axioms of the dual utility theory, and a further relaxation of the axioms are shown to lead to the mean-deviation analysis. Paradoxes arising from the sets of axioms corresponding to these theories and their possible resolutions are discussed, and application of the mean-deviation analysis to optimal risk sharing and portfolio selection in the context of rational choice is considered. © 2012 Society for Risk Analysis.

Supplementary Appendix for: Constrained Perturbation Regularization Approach for Signal Estimation Using Random Matrix Theory

KAUST Repository

Suliman, Mohamed Abdalla Elhag; Ballal, Tarig; Kammoun, Abla; Alnaffouri, Tareq Y.

2016-01-01

In this supplementary appendix we provide proofs and additional simulation results that complement the paper (constrained perturbation regularization approach for signal estimation using random matrix theory).

An unprecedented multi attribute decision making using graph theory matrix approach

Directory of Open Access Journals (Sweden)

N.K. Geetha

2018-02-01

Full Text Available A frame work for investigating the best combination of functioning parameters on a variable compression ratio diesel engine is proposed in the present study using a multi attribute optimization methodology, Graph Theory Matrix Approach. The functioning parameters, attributes, sub attributes and functioning variables of sub attributes are chosen based on expert’s opinion and literature review. The directed graphs are developed for attributes and sub attributes. The ‘Parameter Index’ was calculated for all trials to choose the best trial. The experimental results are verified with the theoretical data. Functioning parameters with combination of compression ratio of 17, fuel injection pressure of 20 N/mm2 and fuel injection pressure of 21°bTDC was found to be best. The proposed method allows the decision maker to systematically and logically find the best combination of functioning parameters.

Hermiticity and CPT in string theory

International Nuclear Information System (INIS)

Sonoda, Hidenori

1989-01-01

In the application of conformal field theory to string theory S-matrix elements are obtained from correlation functions of vertex operators. By studying the relation between the vertex operators for the incoming states and those for the outgoing states we obtain two results: First we show that hermiticity of the string vertices is equivalent to the CPT invariance of the corresponding conformal field theory. Secondly we prove that the S-matrix elements in any string theory in flat space-time background are invariant under CPT. (orig.)

Axiomatic Quantum Field Theory in Terms of Operator Product Expansions: General Framework, and Perturbation Theory via Hochschild Cohomology

Directory of Open Access Journals (Sweden)

Stefan Hollands

2009-09-01

Full Text Available In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are ''associativity'' or ''factorization'' conditions on the operator product expansion (OPE of the theory, and are proposed to be the defining property of any quantum field theory. Our framework is presented in the Euclidean setting, and is applicable in principle to any quantum field theory, including non-conformal ones. In our framework, we obtain a characterization of perturbations of a given quantum field theory in terms of a certain cohomology ring of Hochschild-type. We illustrate our framework by the free field, but our constructions are general and apply also to interacting quantum field theories. For such theories, we propose a new scheme to construct the OPE which is based on the use of non-linear quantized field equations.

Towards an S-matrix Description of Gravitational Collapse

CERN Document Server

Amati, D; Veneziano, Gabriele

2008-01-01

Extending our previous results on trans-Planckian ($Gs \\gg \\hbar$) scattering of light particles in quantum string-gravity we present a calculation of the corresponding S-matrix from the region of large impact parameters ($b \\gg G\\sqrt{s}>\\lambda_s$) down to the regime where classical gravitational collapse is expected to occur. By solving the semiclassical equations of a previously introduced effective-action approximation, we find that the perturbative expansion around the leading eikonal result diverges at a critical value $b = b_c = O(G\\sqrt{s})$, signalling the onset of a new (black-hole related?) regime. We then discuss the main features of our explicitly unitary S-matrix -- and of the associated effective metric -- down to (and in the vicinity of) $b = b_c$, and present some ideas and results on its extension all the way to the $ b \\to 0$ region. We find that for $bS-matrix shows additional absorption, related to a new production mechanis...

Z4-symmetric factorized S-matrix in two space-time dimensions

International Nuclear Information System (INIS)

Zamolodchikov, A.B.

1979-01-01

The factorized S-matrix with internal symmetry Z 4 is constructed in two space-time dimensions. The two-particle amplitudes are obtained by means of solving the factorization, unitarity and analyticity equations. The solution of factorization equations can be expressed in terms of elliptic functions. The S-matrix cotains the resonance poles naturally. The simple formal relation between the general factorized S-matrices and the Baxter-type lattice transfer matrices is found. In the sense of this relation the Z 4 -symmetric S-matrix corresponds to the Baxter transfer matrix itself. (orig.)

Rigorous Quantum Field Theory A Festschrift for Jacques Bros

CERN Document Server

Monvel, Anne Boutet; Iagolnitzer, Daniel; Moschella, Ugo

2007-01-01

Jacques Bros has greatly advanced our present understanding of rigorous quantum field theory through numerous fundamental contributions. This book arose from an international symposium held in honour of Jacques Bros on the occasion of his 70th birthday, at the Department of Theoretical Physics of the CEA in Saclay, France. The impact of the work of Jacques Bros is evident in several articles in this book. Quantum fields are regarded as genuine mathematical objects, whose various properties and relevant physical interpretations must be studied in a well-defined mathematical framework. The key topics in this volume include analytic structures of Quantum Field Theory (QFT), renormalization group methods, gauge QFT, stability properties and extension of the axiomatic framework, QFT on models of curved spacetimes, QFT on noncommutative Minkowski spacetime. Contributors: D. Bahns, M. Bertola, R. Brunetti, D. Buchholz, A. Connes, F. Corbetta, S. Doplicher, M. Dubois-Violette, M. Dütsch, H. Epstein, C.J. Fewster, K....

Relations between the SU(2|4) symmetric theories and the gauge gravity correspondence

International Nuclear Information System (INIS)

Tsuchiya, Asato

2008-01-01

We study theories with SU(2|4) symmetry, which include N=4 SYM on R x S 3 /Z k , 2+1 SYM on R x S 2 and the plane wave matrix model. All these theories possess many vacua. From Lin-Maldacena's method which gives the gravity dual of each vacuum, it is suggested that the theory around each vacuum of N=4 SYM on R x S 3 /Z k and 2+1 SYM on R x S 2 is equivalent to the theory around a certain vacuum of the plane wave matrix model. We show this directly on the gauge theory side. We realize theories around multi-monopole backgrounds in matrix model, and extend Taylor's matrix T-duality to that on spheres. (author)

Hydrogel core flexible matrix composite (H-FMC) actuators: theory and preliminary modelling

International Nuclear Information System (INIS)

Dicker, M P M; Weaver, P M; Bond, I P; Rossiter, J M

2014-01-01

The underlying theory of a new actuator concept based on hydrogel core flexible matrix composites (H-FMC) is presented. The key principle that underlines the H-FMC actuator operation is that the three-dimensional swelling of a hydrogel is partially constrained in order to improve the amount of useful work done. The partial constraint is applied to the hydrogel by a flexible matrix composite (FMC) that minimizes the hydrogel's volume expansion while swelling. This constraint serves to maximize the fixed charge density and resulting osmotic pressure, the driving force behind actuation. In addition, for certain FMC fibre orientations the Poisson's ratio of the anisotropic FMC laminate converts previously unused hydrogel swelling in the radial and circumferential directions into useful axial strains. The potential benefit of the H-FMC concept to hydrogel actuator performance is shown through comparison of force–stroke curves and evaluation of improvements in useful actuation work. The model used to achieve this couples chemical and electrical components, represented with the Nernst–Plank and Poisson equations, as well as a linear elastic mechanical material model, encompassing limited geometric nonlinearities. It is found that improvements in useful actuation work in the order of 1500% over bare hydrogel performance are achieved by the H-FMC concept. A parametric study is also undertaken to determine the effect of various FMC design parameters on actuator free strain and blocking stress. A comparison to other actuator concepts is also included. (paper)

Factorizable S-matrix for SO(D)/SO(2) circle times SO(D - 2) non-linear σ models with fermions

International Nuclear Information System (INIS)

Abdalla, E.; Lima-Santos, A.

1988-01-01

The authors compute the exact S matrix for the non-linear sigma model with symmetry SO(D)/SO(2) circle times SO(D-2) coupled to fermions in a minimal or supersymmetric way. The model has some relevance in string theory with non-zero external curvature

Parametric Level Statistics in Random Matrix Theory: Exact Solution

International Nuclear Information System (INIS)

Kanzieper, E.

1999-01-01

During recent several years, the theory of non-Gaussian random matrix ensembles has experienced a sound progress motivated by new ideas in quantum chromodynamics (QCD) and mesoscopic physics. Invariant non-Gaussian random matrix models appear to describe universal features of low-energy part of the spectrum of Dirac operator in QCD, and electron level statistics in normal conducting-superconducting hybrid structures. They also serve as a basis for constructing the toy models of universal spectral statistics expected at the edge of the metal-insulator transition. While conventional spectral statistics has received a detailed study in the context of RMT, quite a bit is known about parametric level statistics in non-Gaussian random matrix models. In this communication we report about exact solution to the problem of parametric level statistics in unitary invariant, U(N), non-Gaussian ensembles of N x N Hermitian random matrices with either soft or strong level confinement. The solution is formulated within the framework of the orthogonal polynomial technique and is shown to depend on both the unfolded two-point scalar kernel and the level confinement through a double integral transformation which, in turn, provides a constructive tool for description of parametric level correlations in non-Gaussian RMT. In the case of soft level confinement, the formalism developed is potentially applicable to a study of parametric level statistics in an important class of random matrix models with finite level compressibility expected to describe a disorder-induced metal-insulator transition. In random matrix ensembles with strong level confinement, the solution presented takes a particular simple form in the thermodynamic limit: In this case, a new intriguing connection relation between the parametric level statistics and the scalar two-point kernel of an unperturbed ensemble is demonstrated to emerge. Extension of the results obtained to higher-order parametric level statistics is

Theory of convex structures

CERN Document Server

van de Vel, MLJ

1993-01-01

Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear si

Gauge amplitude identities by on-shell recursion relation in S-matrix program

International Nuclear Information System (INIS)

Feng Bo; Huang Rijun; Jia Yin

2011-01-01

Using only the Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion relation we prove color-order reversed relation, U(1)-decoupling relation, Kleiss-Kuijf (KK) relation and Bern-Carrasco-Johansson (BCJ) relation for color-ordered gauge amplitude in the framework of S-matrix program without relying on Lagrangian description. Our derivation is the first pure field theory proof of the new discovered BCJ identity, which substantially reduces the color-ordered basis from (n-2)! to (n-3)!. Our proof gives also its physical interpretation as the mysterious bonus relation with 1/(z 2 ) behavior under suitable on-shell deformation for no adjacent pair.

Integrable theories that are asymptotically CFT

CERN Document Server

Evans, J M; Jonathan M Evans; Timothy J Hollowood

1995-01-01

A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level k. In contrast to the more familiar situation of asymptotically free theories in which the fixed points are trivial, the sigma models considered here may be termed ``asymptotically CFT''. These theories have previously been conjectured to be quantum integrable; we confirm this by proposing a factorizable S-matrix to describe their infra-red behaviour and then carrying out a stringent test of this proposal. The test involves coupling the theory to a conserved charge and evaluating the response of the free-energy both in perturbation theory to one loop and directly from the S-matrix via the Thermodynamic Bethe Ansatz with a chemical potential at zero temperature. Comparison of these results provides convincing evidence in favour of the proposed S-matrix; it also yields the universal coefficients of the beta-func...

Application of random matrix theory to biological networks

Energy Technology Data Exchange (ETDEWEB)

Luo Feng [Department of Computer Science, Clemson University, 100 McAdams Hall, Clemson, SC 29634 (United States); Department of Pathology, U.T. Southwestern Medical Center, 5323 Harry Hines Blvd. Dallas, TX 75390-9072 (United States); Zhong Jianxin [Department of Physics, Xiangtan University, Hunan 411105 (China) and Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States)]. E-mail: zhongjn@ornl.gov; Yang Yunfeng [Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States); Scheuermann, Richard H. [Department of Pathology, U.T. Southwestern Medical Center, 5323 Harry Hines Blvd. Dallas, TX 75390-9072 (United States); Zhou Jizhong [Department of Botany and Microbiology, University of Oklahoma, Norman, OK 73019 (United States) and Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States)]. E-mail: zhouj@ornl.gov

2006-09-25

We show that spectral fluctuation of interaction matrices of a yeast protein-protein interaction network and a yeast metabolic network follows the description of the Gaussian orthogonal ensemble (GOE) of random matrix theory (RMT). Furthermore, we demonstrate that while the global biological networks evaluated belong to GOE, removal of interactions between constituents transitions the networks to systems of isolated modules described by the Poisson distribution. Our results indicate that although biological networks are very different from other complex systems at the molecular level, they display the same statistical properties at network scale. The transition point provides a new objective approach for the identification of functional modules.

Random matrix theory filters and currency portfolio optimisation

Science.gov (United States)

Daly, J.; Crane, M.; Ruskin, H. J.

2010-04-01

Random matrix theory (RMT) filters have recently been shown to improve the optimisation of financial portfolios. This paper studies the effect of three RMT filters on realised portfolio risk, using bootstrap analysis and out-of-sample testing. We considered the case of a foreign exchange and commodity portfolio, weighted towards foreign exchange, and consisting of 39 assets. This was intended to test the limits of RMT filtering, which is more obviously applicable to portfolios with larger numbers of assets. We considered both equally and exponentially weighted covariance matrices, and observed that, despite the small number of assets involved, RMT filters reduced risk in a way that was consistent with a much larger S&P 500 portfolio. The exponential weightings indicated showed good consistency with the value suggested by Riskmetrics, in contrast to previous results involving stocks. This decay factor, along with the low number of past moves preferred in the filtered, equally weighted case, displayed a trend towards models which were reactive to recent market changes. On testing portfolios with fewer assets, RMT filtering provided less or no overall risk reduction. In particular, no long term out-of-sample risk reduction was observed for a portfolio consisting of 15 major currencies and commodities.

An Axiomatic Analysis Approach for Large-Scale Disaster-Tolerant Systems Modeling

Directory of Open Access Journals (Sweden)

Theodore W. Manikas

2011-02-01

Full Text Available Disaster tolerance in computing and communications systems refers to the ability to maintain a degree of functionality throughout the occurrence of a disaster. We accomplish the incorporation of disaster tolerance within a system by simulating various threats to the system operation and identifying areas for system redesign. Unfortunately, extremely large systems are not amenable to comprehensive simulation studies due to the large computational complexity requirements. To address this limitation, an axiomatic approach that decomposes a large-scale system into smaller subsystems is developed that allows the subsystems to be independently modeled. This approach is implemented using a data communications network system example. The results indicate that the decomposition approach produces simulation responses that are similar to the full system approach, but with greatly reduced simulation time.

An ACL2 Mechanization of an Axiomatic Framework for Weak Memory

Directory of Open Access Journals (Sweden)

Benjamin Selfridge

2014-06-01

Full Text Available Proving the correctness of programs written for multiple processors is a challenging problem, due in no small part to the weaker memory guarantees afforded by most modern architectures. In particular, the existence of store buffers means that the programmer can no longer assume that writes to different locations become visible to all processors in the same order. However, all practical architectures do provide a collection of weaker guarantees about memory consistency across processors, which enable the programmer to write provably correct programs in spite of a lack of full sequential consistency. In this work, we present a mechanization in the ACL2 theorem prover of an axiomatic weak memory model (introduced by Alglave et al.. In the process, we provide a new proof of an established theorem involving these axioms.

Semiclassical S-matrix for black holes

CERN Document Server

Bezrukov, Fedor; Sibiryakov, Sergey

2015-01-01

We propose a semiclassical method to calculate S-matrix elements for two-stage gravitational transitions involving matter collapse into a black hole and evaporation of the latter. The method consistently incorporates back-reaction of the collapsing and emitted quanta on the metric. We illustrate the method in several toy models describing spherical self-gravitating shells in asymptotically flat and AdS space-times. We find that electrically neutral shells reflect via the above collapse-evaporation process with probability exp(-B), where B is the Bekenstein-Hawking entropy of the intermediate black hole. This is consistent with interpretation of exp(B) as the number of black hole states. The same expression for the probability is obtained in the case of charged shells if one takes into account instability of the Cauchy horizon of the intermediate Reissner-Nordstrom black hole. Our semiclassical method opens a new systematic approach to the gravitational S-matrix in the non-perturbative regime.

POLLA-NESC, Resonance Parameter R-Matrix to S-Matrix Conversion by Reich-Moore Method

International Nuclear Information System (INIS)

Saussure, G. de; Perez, R.B.

1975-01-01

1 - Description of problem or function: The program transforms a set of r-matrix nuclear resonance parameters into a set of equivalent s-matrix (or Kapur-Peierls) resonance parameters. 2 - Method of solution: The program utilizes the multilevel formalism of Reich and Moore and avoids diagonalization of the level matrix. The parameters are obtained by a direct partial fraction expansion of the Reich-Moore expression of the collision matrix. This approach appears simpler and faster when the number of fission channels is known and small. The method is particularly useful when a large number of levels must be considered because it does not require diagonalization of a large level matrix. 3 - Restrictions on the complexity of the problem: By DIMENSION statements, the program is limited to maxima of 100 levels and 5 channels

The S-matrix for abstract scattering systems

International Nuclear Information System (INIS)

Amrein, W.O.; Pearson, D.B.

1979-01-01

Let S(lambda) be the S-matrix at energy lambda for an abstract scattering system. A bound is derived in terms of the interaction, on integrals of the form ∫ h(lambda)/S(lambda) - I/ 2 sub(HS) dlambda, where /./sub(HS) denotes the Hilbert-Schmidt norm. (Auth.)

N=2 Minimal Conformal Field Theories and Matrix Bifactorisations of x d

Science.gov (United States)

Davydov, Alexei; Camacho, Ana Ros; Runkel, Ingo

2018-01-01

We establish an action of the representations of N = 2-superconformal symmetry on the category of matrix factorisations of the potentials x d and x d - y d , for d odd. More precisely we prove a tensor equivalence between (a) the category of Neveu-Schwarz-type representations of the N = 2 minimal super vertex operator algebra at central charge 3-6/d, and (b) a full subcategory of graded matrix factorisations of the potential x d - y d . The subcategory in (b) is given by permutation-type matrix factorisations with consecutive index sets. The physical motivation for this result is the Landau-Ginzburg/conformal field theory correspondence, where it amounts to the equivalence of a subset of defects on both sides of the correspondence. Our work builds on results by Brunner and Roggenkamp [BR], where an isomorphism of fusion rules was established.

Quantum theory as an emergent phenomenon the statistical mechanics of matrix models as the precursor of quantum field theory

CERN Document Server

Adler, Stephen L

2004-01-01

Quantum mechanics is our most successful physical theory. However, it raises conceptual issues that have perplexed physicists and philosophers of science for decades. This 2004 book develops an approach, based on the proposal that quantum theory is not a complete, final theory, but is in fact an emergent phenomenon arising from a deeper level of dynamics. The dynamics at this deeper level are taken to be an extension of classical dynamics to non-commuting matrix variables, with cyclic permutation inside a trace used as the basic calculational tool. With plausible assumptions, quantum theory is shown to emerge as the statistical thermodynamics of this underlying theory, with the canonical commutation/anticommutation relations derived from a generalized equipartition theorem. Brownian motion corrections to this thermodynamics are argued to lead to state vector reduction and to the probabilistic interpretation of quantum theory, making contact with phenomenological proposals for stochastic modifications to Schr�...

Matrix elements for the anti B{yields}X{sub s}{gamma} decay at NNLO

Energy Technology Data Exchange (ETDEWEB)

Schutzmeier, Thomas Paul

2009-12-17

In the context of the indirect search for non-standard physics in the flavour sector of the Standard Model (SM), one of the most interesting processes is the rare inclusive anti B{yields} X{sub s}{gamma} decay. On the one hand, being a flavour-changing neutral current, this B decay is sensitive to new physics, as it is loop-suppressed in the SM. On the other hand, it is only mildly affected by non-perturbative effects, and thus allows for precise theoretical predictions in the framework of renormalization-group improved perturbation theory. Accurate measurements as well as precise theoretical predictions with a good control over both perturbative and non-perturbative contributions have to be provided in order to derive stringent constraints on the parameter space of physics beyond the SM. On the experimental side, an outstanding accuracy in the measurement of the anti B{yields}X{sub s}{gamma} decay rate has been achieved, which is mainly due the specialized experiments BaBar and Belle at the so-called B factories. To match the small experimental uncertainty, higher order computations within an effective low-energy theory of the SM are mandatory. In fact, next-to-next-to-leading order (NNLO) QCD corrections are required to provide a prediction for the decay rate with the same precision as the measurement. The NNLO evaluation of the anti B{yields}X{sub s}{gamma} decay rate has been pursued by various groups over the last decade. The project was completed to a large extent and a first estimate at this level of perturbation theory was obtained in 2006. This prediction, however, lacks important contributions from yet unknown matrix elements, that were estimated from results which are only partially known to date. In this work, we provide a framework for the systematic study of the missing matrix elements at the NNLO. As main results of this thesis, we determine fermionic corrections to the charm quark mass dependent matrix elements of four-quark operators in the

Mathematical aspects of quantum field theories

CERN Document Server

Strobl, Thomas

2015-01-01

Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homolo...

Correlation Matrix Renormalization Theory: Improving Accuracy with Two-Electron Density-Matrix Sum Rules.

Science.gov (United States)

Liu, C; Liu, J; Yao, Y X; Wu, P; Wang, C Z; Ho, K M

2016-10-11

We recently proposed the correlation matrix renormalization (CMR) theory to treat the electronic correlation effects [Phys. Rev. B 2014, 89, 045131 and Sci. Rep. 2015, 5, 13478] in ground state total energy calculations of molecular systems using the Gutzwiller variational wave function (GWF). By adopting a number of approximations, the computational effort of the CMR can be reduced to a level similar to Hartree-Fock calculations. This paper reports our recent progress in minimizing the error originating from some of these approximations. We introduce a novel sum-rule correction to obtain a more accurate description of the intersite electron correlation effects in total energy calculations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.

Stochastic Gravity: Theory and Applications

Directory of Open Access Journals (Sweden)

Hu Bei Lok

2008-05-01

Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein–Langevin equation, which has, in addition, sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bitensor, which describes the fluctuations of quantum-matter fields in curved spacetimes. A new improved criterion for the validity of semiclassical gravity may also be formulated from the viewpoint of this theory. In the first part of this review we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to the correlation functions. The functional approach uses the Feynman–Vernon influence functional and the Schwinger–Keldysh closed-time-path effective action methods. In the second part, we describe three applications of stochastic gravity. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic-gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, using the Einstein–Langevin equation, we discuss the backreaction of Hawking radiation and the behavior of metric fluctuations for both the quasi-equilibrium condition of a black-hole in a box and the fully nonequilibrium condition of an evaporating black hole spacetime. Finally, we briefly discuss the theoretical structure of stochastic gravity in relation to quantum gravity and point out

Analysis of aeroplane boarding via spacetime geometry and random matrix theory

International Nuclear Information System (INIS)

Bachmat, E; Berend, D; Sapir, L; Skiena, S; Stolyarov, N

2006-01-01

We show that aeroplane boarding can be asymptotically modelled by two-dimensional Lorentzian geometry. Boarding time is given by the maximal proper time among curves in the model. Discrepancies between the model and simulation results are closely related to random matrix theory. The models can be used to explain why some commonly practiced airline boarding policies are ineffective and even detrimental. (letter to the editor)

Evaluation of E-Learning Web Sites Using Fuzzy Axiomatic Design Based Approach

Directory of Open Access Journals (Sweden)

2010-04-01

Full Text Available High quality web site has been generally recognized as a critical enabler to conduct online business. Numerous studies exist in the literature to measure the business performance in relation to web site quality. In this paper, an axiomatic design based approach for fuzzy group decision making is adopted to evaluate the quality of e-learning web sites. Another multi-criteria decision making technique, namely fuzzy TOPSIS, is applied in order to validate the outcome. The methodology proposed in this paper has the advantage of incorporating requirements and enabling reductions in the problem size, as compared to fuzzy TOPSIS. A case study focusing on Turkish e-learning websites is presented, and based on the empirical findings, managerial implications and recommendations for future research are offered.

Nano-fillers to tune Young’s modulus of silicone matrix

International Nuclear Information System (INIS)

Xia Lijin; Xu Zhonghua; Sun Leming; Caveney, Patrick M.; Zhang Mingjun

2013-01-01

In this study, we investigated nanoparticles, nanofibers, and nanoclays for their filler effects on tuning the Young’s modulus of silicone matrix, a material with broad in vivo applications. Nano-fillers with different shapes, sizes, and surface properties were added into silicone matrix, and then their filler effects were evaluated through experimental studies. It was found that spherical nanoparticles could clearly improve Young’s modulus of the silicone matrix, while nanoclays and carbon nanofibers had limited effects. Smaller spherical nanoparticles were better in performance compared to larger nanoparticles. In addition, enhanced distribution of the nanoparticles in the matrix has been observed to improve the filler effect. In order to minimize toxicity of the nanoparticles for in vivo applications, spherical nanoparticles coated with amine, acid, or hydroxide groups were also investigated, but they were found only to diminish the filler effect of nanoparticles. This study demonstrated that spherical nanoparticles could serve as fillers to tune Young’s modulus of silicone matrix for potential applications in medicine.

S-AMP: Approximate Message Passing for General Matrix Ensembles

DEFF Research Database (Denmark)

Cakmak, Burak; Winther, Ole; Fleury, Bernard H.

2014-01-01

the approximate message-passing (AMP) algorithm to general matrix ensembles with a well-defined large system size limit. The generalization is based on the S-transform (in free probability) of the spectrum of the measurement matrix. Furthermore, we show that the optimality of S-AMP follows directly from its......We propose a novel iterative estimation algorithm for linear observation models called S-AMP. The fixed points of S-AMP are the stationary points of the exact Gibbs free energy under a set of (first- and second-) moment consistency constraints in the large system limit. S-AMP extends...

Manufacturing system design based on axiomatic design: Case of assembly line

Energy Technology Data Exchange (ETDEWEB)

Hager, T.; Wafik, H.; Faouzi, M.

2017-07-01

In this paper, a combined Production Line Design (PLD) process which includes many design aspects is presented, developed and validated. Design/methodology/approach: The PLD process is based on the SADT (Structured Analysis and Design Technique) diagram and the Axiomatic Design (AD) method. Practical implications: For a purpose of validation, this proposed process has been applied in a manufacturing company and it has been validated by simulation. Findings: The results of the validation indicated that the production line designed by this process is outperformed the initial line of the company. Originality/value: Recently, the problems of production line design (PLD) have attracted the attention of many researchers. However, only a few studies have treated the PLD which includes all design aspects. In this work, a combined PLD process is presented. It should be noted that the proposed process is simple and effective.

Manufacturing system design based on axiomatic design: Case of assembly line

International Nuclear Information System (INIS)

Hager, T.; Wafik, H.; Faouzi, M.

2017-01-01

In this paper, a combined Production Line Design (PLD) process which includes many design aspects is presented, developed and validated. Design/methodology/approach: The PLD process is based on the SADT (Structured Analysis and Design Technique) diagram and the Axiomatic Design (AD) method. Practical implications: For a purpose of validation, this proposed process has been applied in a manufacturing company and it has been validated by simulation. Findings: The results of the validation indicated that the production line designed by this process is outperformed the initial line of the company. Originality/value: Recently, the problems of production line design (PLD) have attracted the attention of many researchers. However, only a few studies have treated the PLD which includes all design aspects. In this work, a combined PLD process is presented. It should be noted that the proposed process is simple and effective.

A variational approach to operator and matrix Pade approximation. Applications to potential scattering and field theory

International Nuclear Information System (INIS)

Mery, P.

1977-01-01

The operator and matrix Pade approximation are defined. The fact that these approximants can be derived from the Schwinger variational principle is emphasized. In potential theory, using this variational aspect it is shown that the matrix Pade approximation allow to reproduce the exact solution of the Lippman-Schwinger equation with any required accuracy taking only into account the knowledge of the first two coefficients in the Born expansion. The deep analytic structure of this variational matrix Pade approximation (hyper Pade approximation) is discussed

Models based on multichannel R-matrix theory for evaluating light element reactions

International Nuclear Information System (INIS)

Dodder, D.C.; Hale, G.M.; Nisley, R.A.; Witte, K.; Young, P.G.

1975-01-01

Multichannel R-matrix theory has been used as a basis for models for analysis and evaluation of light nuclear systems. These models have the characteristic that data predictions can be made utilizing information derived from other reactions related to the one of primary interest. Several examples are given where such an approach is valid and appropriate. (auth.)

Stochastic Gravity: Theory and Applications

Directory of Open Access Journals (Sweden)

Hu Bei Lok

2004-01-01

Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction

Quantum information theory

CERN Document Server

Wilde, Mark M

2017-01-01

Developing many of the major, exciting, pre- and post-millennium developments from the ground up, this book is an ideal entry point for graduate students into quantum information theory. Significant attention is given to quantum mechanics for quantum information theory, and careful studies of the important protocols of teleportation, superdense coding, and entanglement distribution are presented. In this new edition, readers can expect to find over 100 pages of new material, including detailed discussions of Bell's theorem, the CHSH game, Tsirelson's theorem, the axiomatic approach to quantum channels, the definition of the diamond norm and its interpretation, and a proof of the Choi–Kraus theorem. Discussion of the importance of the quantum dynamic capacity formula has been completely revised, and many new exercises and references have been added. This new edition will be welcomed by the upcoming generation of quantum information theorists and the already established community of classical information theo...

Theory of Brownian motion with the Alder-Wainwright effect

International Nuclear Information System (INIS)

Okabe, Y.

1986-01-01

The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process with T-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, the authors obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. The authors interested in whether or not it can be measured experimentally

Introduction to field theory

CERN Multimedia

CERN. Geneva; CERN. Geneva

2001-01-01

Starting from the notion of path integrals as developed by Feynman, we discuss field theory in zero spacetime dimensions. The concepts of perturbation expansions, connected amplitudes, Feynman diagrams, classical solutions, renormalization and the effective action are developed. The model is extended to four spacetime dimensions, and the full Feynman rules for relativisitc scalar theory derived. The S matrix and the concept of unitarity are discussed, leading to the amputation rules for S matrix elements from considerations of unitarity. The rules are extended to include particles with spin-1/2 and spin-1. The high-energy behaviour of the theory is discussed as a method to derive the gauge symmetry of the various models.

Genetic Algorithm and Graph Theory Based Matrix Factorization Method for Online Friend Recommendation

Directory of Open Access Journals (Sweden)

Qu Li

2014-01-01

Full Text Available Online friend recommendation is a fast developing topic in web mining. In this paper, we used SVD matrix factorization to model user and item feature vector and used stochastic gradient descent to amend parameter and improve accuracy. To tackle cold start problem and data sparsity, we used KNN model to influence user feature vector. At the same time, we used graph theory to partition communities with fairly low time and space complexity. What is more, matrix factorization can combine online and offline recommendation. Experiments showed that the hybrid recommendation algorithm is able to recommend online friends with good accuracy.

Approaching the axiomatic enrichment of the Gene Ontology from a lexical perspective.

Science.gov (United States)

Quesada-Martínez, Manuel; Mikroyannidi, Eleni; Fernández-Breis, Jesualdo Tomás; Stevens, Robert

2015-09-01

The main goal of this work is to measure how lexical regularities in biomedical ontology labels can be used for the automatic creation of formal relationships between classes, and to evaluate the results of applying our approach to the Gene Ontology (GO). In recent years, we have developed a method for the lexical analysis of regularities in biomedical ontology labels, and we showed that the labels can present a high degree of regularity. In this work, we extend our method with a cross-products extension (CPE) metric, which estimates the potential interest of a specific regularity for axiomatic enrichment in the lexical analysis, using information on exact matches in external ontologies. The GO consortium recently enriched the GO by using so-called cross-product extensions. Cross-products are generated by establishing axioms that relate a given GO class with classes from the GO or other biomedical ontologies. We apply our method to the GO and study how its lexical analysis can identify and reconstruct the cross-products that are defined by the GO consortium. The label of the classes of the GO are highly regular in lexical terms, and the exact matches with labels of external ontologies affect 80% of the GO classes. The CPE metric reveals that 31.48% of the classes that exhibit regularities have fragments that are classes into two external ontologies that are selected for our experiment, namely, the Cell Ontology and the Chemical Entities of Biological Interest ontology, and 18.90% of them are fully decomposable into smaller parts. Our results show that the CPE metric permits our method to detect GO cross-product extensions with a mean recall of 62% and a mean precision of 28%. The study is completed with an analysis of false positives to explain this precision value. We think that our results support the claim that our lexical approach can contribute to the axiomatic enrichment of biomedical ontologies and that it can provide new insights into the engineering of

An introduction to the general boundary formulation of quantum field theory

International Nuclear Information System (INIS)

Colosi, Daniele

2015-01-01

We give a brief introduction to the so-called general boundary formulation (GBF) of quantum theory. This new axiomatic formulation provides a description of the quantum dynamics which is manifestly local and does not rely on a metric background structure for its definition. We present the basic ingredients of the GBF, in particular we review the core axioms that assign algebraic structures to geometric ones, the two quantisation schemes so far developed for the GBF and the probability interpretation which generalizes the standard Born rule. Finally we briefly discuss some of the results obtained studying specific quantum field theories within the GBF. (paper)

Skew-orthogonal polynomials and random matrix theory

CERN Document Server

Ghosh, Saugata

2009-01-01

Orthogonal polynomials satisfy a three-term recursion relation irrespective of the weight function with respect to which they are defined. This gives a simple formula for the kernel function, known in the literature as the Christoffel-Darboux sum. The availability of asymptotic results of orthogonal polynomials and the simple structure of the Christoffel-Darboux sum make the study of unitary ensembles of random matrices relatively straightforward. In this book, the author develops the theory of skew-orthogonal polynomials and obtains recursion relations which, unlike orthogonal polynomials, depend on weight functions. After deriving reduced expressions, called the generalized Christoffel-Darboux formulas (GCD), he obtains universal correlation functions and non-universal level densities for a wide class of random matrix ensembles using the GCD. The author also shows that once questions about higher order effects are considered (questions that are relevant in different branches of physics and mathematics) the ...

Direct integration of the S-matrix applied to rigorous diffraction

International Nuclear Information System (INIS)

Iff, W; Lindlein, N; Tishchenko, A V

2014-01-01

A novel Fourier method for rigorous diffraction computation at periodic structures is presented. The procedure is based on a differential equation for the S-matrix, which allows direct integration of the S-matrix blocks. This results in a new method in Fourier space, which can be considered as a numerically stable and well-parallelizable alternative to the conventional differential method based on T-matrix integration and subsequent conversions from the T-matrices to S-matrix blocks. Integration of the novel differential equation in implicit manner is expounded. The applicability of the new method is shown on the basis of 1D periodic structures. It is clear however, that the new technique can also be applied to arbitrary 2D periodic or periodized structures. The complexity of the new method is O(N 3 ) similar to the conventional differential method with N being the number of diffraction orders. (fast track communication)

Big bang/big crunch cosmologies in matrix theory and AdS/CFT

Science.gov (United States)

Das, Sumit R.

2008-11-01

Recently several versions of gauge-gravity duality in string theory have been used to understand null and space-like singularities. In many cases, the gauge theory description allows a smooth evolution across what appears as a singularity in the gravity description.

Transport properties of clean and disordered superconductors in matrix field theory

International Nuclear Information System (INIS)

Zhou Lubo; Kirkpatrick, T.R.

2004-01-01

A comprehensive field theory is developed for superconductors with quenched disorder. We first show that the matrix field theory, used previously to describe a disordered Fermi liquid and a disordered itinerant ferromagnet, also has a saddle-point solution that describes a disordered superconductor. A general gap equation is obtained. We then expand about the saddle point to Gaussian order to explicitly obtain the physical correlation functions. The ultrasonic attenuation, number density susceptibility, spin-density susceptibility, and the electrical conductivity are used as examples. Results in the clean limit and in the disordered case are discussed, respectively. This formalism is expected to be a powerful tool to study the quantum phase transitions between the normal-metal state and the superconductor state

Matrix theory selected topics and useful results

CERN Document Server

Mehta, Madan Lal

1989-01-01

Matrices and operations on matrices ; determinants ; elementary operations on matrices (continued) ; eigenvalues and eigenvectors, diagonalization of normal matrices ; functions of a matrix ; positive definiteness, various polar forms of a matrix ; special matrices ; matrices with quaternion elements ; inequalities ; generalised inverse of a matrix ; domain of values of a matrix, location and dispersion of eigenvalues ; symmetric functions ; integration over matrix variables ; permanents of doubly stochastic matrices ; infinite matrices ; Alexander matrices, knot polynomials, torsion numbers.

On a Formalization of Cantor Set Theory for Natural Models of the Physical Phenomena

Directory of Open Access Journals (Sweden)

Nudel'man A. S.

2010-01-01

Full Text Available This article presents a set theory which is an extension of ZFC . In contrast to ZFC , a new theory admits absolutely non-denumerable sets. It is feasible that a symbiosis of the proposed theory and Vdovin set theory will permit to formulate a (presumably non- contradictory axiomatic set theory which will represent the core of Cantor set theory in a maximally full manner as to the essence and the contents of the latter. This is possible due to the fact that the generalized principle of choice and the generalized continuum hypothesis are proved in Vdovin theory. The theory, being more complete than ZF and more natural according to Cantor, will allow to construct and study (in its framework only natural models of the real physical phenomena.

On a Formalization of Cantor Set Theory for Natural Models of the Physical Phenomena

Directory of Open Access Journals (Sweden)

Nudel'man A. S.

2010-01-01

Full Text Available This article presents a set theory which is an extension of $ZFC$. In contrast to $ZFC$, a new theory admits absolutely non-denumerable sets. It is feasible that a symbiosis of the proposed theory and Vdovin set theory will permit to formulate a (presumably non-contradictory axiomatic set theory which will represent the core of Cantor set theory in a maximally full manner as to the essence and the contents of the latter. This is possible due to the fact that the generalized principle of choice and the generalized continuum hypothesis are proved in Vdovin theory. The theory, being more complete than $ZF$ and more natural according to Cantor, will allow to construct and study (in its framework only natural models of the real physical phenomena.

Einstein in matrix form. Exact derivation of the theory of special and general relativity without tensors

International Nuclear Information System (INIS)

Ludyk, Guenter

2013-01-01

Derives the fundamental equations of Einstein's theory of special and general relativity using matrix calculus, without the help of tensors. Provides necessary mathematical tools in a user-friendly way, either directly in the text or in the appendices. Appendices contain an introduction to classical dynamics as a refresher of known fundamental physics. Rehearses vector and matrix calculus, differential geometry, and some special solutions of general relativity in the appendices. This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einsteins theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the ''Black Hole'' phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.

Blind Measurement Selection: A Random Matrix Theory Approach

KAUST Repository

Elkhalil, Khalil

2016-12-14

This paper considers the problem of selecting a set of $k$ measurements from $n$ available sensor observations. The selected measurements should minimize a certain error function assessing the error in estimating a certain $m$ dimensional parameter vector. The exhaustive search inspecting each of the $n\\\\choose k$ possible choices would require a very high computational complexity and as such is not practical for large $n$ and $k$. Alternative methods with low complexity have recently been investigated but their main drawbacks are that 1) they require perfect knowledge of the measurement matrix and 2) they need to be applied at the pace of change of the measurement matrix. To overcome these issues, we consider the asymptotic regime in which $k$, $n$ and $m$ grow large at the same pace. Tools from random matrix theory are then used to approximate in closed-form the most important error measures that are commonly used. The asymptotic approximations are then leveraged to select properly $k$ measurements exhibiting low values for the asymptotic error measures. Two heuristic algorithms are proposed: the first one merely consists in applying the convex optimization artifice to the asymptotic error measure. The second algorithm is a low-complexity greedy algorithm that attempts to look for a sufficiently good solution for the original minimization problem. The greedy algorithm can be applied to both the exact and the asymptotic error measures and can be thus implemented in blind and channel-aware fashions. We present two potential applications where the proposed algorithms can be used, namely antenna selection for uplink transmissions in large scale multi-user systems and sensor selection for wireless sensor networks. Numerical results are also presented and sustain the efficiency of the proposed blind methods in reaching the performances of channel-aware algorithms.

Supersymmetrical dual string theories and their field theory limits: A review

International Nuclear Information System (INIS)

Green, M.B.

1985-01-01

This paper outlines the construction and properties of supersymmetric string theories. Such theories, which describe the quantum mechanics of relativistic strings in ten-space time dimensions contain both N=4 Yang-Mills and N=8 supergravity field theories as special limits in which the string tension becomes infinite. Calculations of one-loop S-matrix elements reveal remarkable finiteness properties

Scattering theory of space-time non-commutative abelian gauge field theory

International Nuclear Information System (INIS)

Rim, Chaiho; Yee, Jaehyung

2005-01-01

The unitary S-matrix for space-time non-commutative quantum electrodynamics is constructed using the *-time ordering which is needed in the presence of derivative interactions. Based on this S-matrix, we formulate the perturbation theory and present the Feynman rule. We then apply this perturbation analysis to the Compton scattering process to the lowest order and check the gauge invariance of the scattering amplitude at this order.

Quantum mechanics in matrix form

CERN Document Server

Ludyk, Günter

2018-01-01

This book gives an introduction to quantum mechanics with the matrix method. Heisenberg's matrix mechanics is described in detail. The fundamental equations are derived by algebraic methods using matrix calculus. Only a brief description of Schrödinger's wave mechanics is given (in most books exclusively treated), to show their equivalence to Heisenberg's matrix  method. In the first part the historical development of Quantum theory by Planck, Bohr and Sommerfeld is sketched, followed by the ideas and methods of Heisenberg, Born and Jordan. Then Pauli's spin and exclusion principles are treated. Pauli's exclusion principle leads to the structure of atoms. Finally, Dirac´s relativistic quantum mechanics is shortly presented. Matrices and matrix equations are today easy to handle when implementing numerical algorithms using standard software as MAPLE and Mathematica.

The problem of the universal density functional and the density matrix functional theory

International Nuclear Information System (INIS)

Bobrov, V. B.; Trigger, S. A.

2013-01-01

The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.

Axiomation of quantum mechanics

International Nuclear Information System (INIS)

Kotecky, R.

1975-01-01

Deeper understanding of the basic structure of the formalism of the modern quantum theory (as has been established during its 50 years' stormy development) has been brought about by its axiomatization - by founding the formalism merely on experimentally directly accountable postulates without referring to historical development, without any a priori nonessential or empirically nonexplicable assumptions. A summary is given of the common formalism of quantum mechanics and its most significant axiomatizations. The assumptions are discussed under which respective axiomatically described abstract structures may be modelled by means of the common formalisn of quantum theory (established on the theory of Hilbert spaces). (author)

Three-body forces for electrons by the S-matrix method

International Nuclear Information System (INIS)

Margaritelli, R.

1989-01-01

A electromagnetic three-body potential between eletrons is derived by the S-matrix method. This potential can be compared up to a certain point with other electromagnetic potentials (obtained by other methods) encountered in the literature. However, since the potential derived here is far more complete than others, this turns direct comparison with the potentials found in the literature somewhat difficult. These calculations allow a better understanding of the S-matrix method as applied to problems which involve the calculations of three-body nuclear forces (these calculations are performed in order to understand the 3 He form factor). Furthermore, these results enable us to decide between two discrepant works which derive the two-pion exchange three-body potential, both by the S-matrix method. (author) [pt

Theory of direct interparticle action

International Nuclear Information System (INIS)

Vladimirov, Yu.S.; Turygin, A.Yu.

1986-01-01

Unusual point of view on the physical picture of the Universe and ratio between main physical categories is considered. Principal moments and theory peculiarities based on the conception of direct interparticle action are underlined. The direct interparticle action theory (DIAT) is considered from the position of choosing one or another axiomatics. At first the Fokker action principle is postulated there and then identical satisfiability of field equations is proved. All that relates to vacuum DIAT ignores and actions of matter formations are used as the basis. DIAT bears up against a global factor-account of absrbers of all surroundings (the Mach principle). The DIAT pretended to relativistic description of only additional concepts with the previously asigned space-time ratios. Concept for construction of the physical picture of the Universe, where classical space-time ratios being of secondary character, is suggested

Equational theories of tropical sernirings

DEFF Research Database (Denmark)

Aceto, Luca; Esik, Zoltan; Ingolfsdottir, Anna

2003-01-01

examples of such structures are the (max,+) semiring and the tropical semiring. It is shown that none of the exotic semirings commonly considered in the literature has a finite basis for its equations, and that similar results hold for the commutative idempotent weak semirings that underlie them. For each......This paper studies the equational theories of various exotic semirings presented in the literature. Exotic semirings are semirings whose underlying carrier set is some subset of the set of real numbers equipped with binary operations of minimum or maximum as sum, and addition as product. Two prime...... of these commutative idempotent weak semirings, the paper offers characterizations of the equations that hold in them, decidability results for their equational theories, explicit descriptions of the free algebras in the varieties they generate, and relative axiomatization results. Udgivelsesdato: APR 11...

Quantum field theory with a momentum space of constant curvature (perturbation theory)

International Nuclear Information System (INIS)

Mir-Kasimov, R.M.

1978-01-01

In the framework of the field-theoretical approach in which the off-the-mass shell extension proceeds in the p-space of constant curvature, the perburbation theory is developed. The configurational representation of the de Sitter space is introduced with the help of the Fourier transformation of the group of motions. On the basis of a natural generalization of the Bogolyubov causality condition to the case of the new configurational representation a perturbation theory is constructed with the local in xi space Lagrangian density fucntion. The obtained S matrix obeys the reguirement of translation invariance. The S matrix elements are given by convergent expressions

Super Yang-Mills theory in 10+2 dimensions, The 2T-physics Source for N=4 SYM and M(atrix) Theory

CERN Document Server

Bars, Itzhak

2010-01-01

In this paper we construct super Yang-Mills theory in 10+2 dimensions, a number of dimensions that was not reached before in a unitary supersymmetric field theory, and show that this is the 2T-physics source of some cherished lower dimensional field theories. The much studied conformally exact N=4 Super Yang-Mills field theory in 3+1 dimensions is known to be a compactified version of N=1 SYM in 9+1 dimensions, while M(atrix) theory is obtained by compactifications of the 9+1 theory to 0 dimensions (also 0+1 and others). We show that there is a deeper origin of these theories in two higher dimensions as they emerge from the new theory with two times. Pursuing various alternatives of gauge choices, solving kinematic equations and/or dimensional reductions of the 10+2 theory, we suggest a web of connections that include those mentioned above and a host of new theories that relate 2T-physics and 1T-physics field theories, all of which have the 10+2 theory as the parent. In addition to establishing the higher spa...

Matrix transformations and sequence spaces

International Nuclear Information System (INIS)

Nanda, S.

1983-06-01

In most cases the most general linear operator from one sequence space into another is actually given by an infinite matrix and therefore the theory of matrix transformations has always been of great interest in the study of sequence spaces. The study of general theory of matrix transformations was motivated by the special results in summability theory. This paper is a review article which gives almost all known results on matrix transformations. This also suggests a number of open problems for further study and will be very useful for research workers. (author)

Note on dual superconformal symmetry of the N=4 super Yang-Mills S matrix

International Nuclear Information System (INIS)

Brandhuber, Andreas; Heslop, Paul; Travaglini, Gabriele

2008-01-01

We present a supersymmetric recursion relation for tree-level scattering amplitudes in N=4 super Yang-Mills. Using this recursion relation, we prove that the tree-level S matrix of the maximally supersymmetric theory is covariant under dual superconformal transformations. We further analyze the consequences that the transformation properties of the trees under this symmetry have on those of the loops. In particular, we show that the coefficients of the expansion of generic one-loop amplitudes in a basis of pseudoconformally invariant scalar box functions transform covariantly under dual superconformal symmetry, and in exactly the same way as the corresponding tree-level amplitudes.

Matrix elements of Δ B =0 operators in heavy hadron chiral perturbation theory

Science.gov (United States)

Lee, Jong-Wan

2015-05-01

We study the light-quark mass and spatial volume dependence of the matrix elements of Δ B =0 four-quark operators relevant for the determination of Vu b and the lifetime ratios of single-b hadrons. To this end, one-loop diagrams are computed in the framework of heavy hadron chiral perturbation theory with partially quenched formalism for three light-quark flavors in the isospin limit; flavor-connected and -disconnected diagrams are carefully analyzed. These calculations include the leading light-quark flavor and heavy-quark spin symmetry breaking effects in the heavy hadron spectrum. Our results can be used in the chiral extrapolation of lattice calculations of the matrix elements to the physical light-quark masses and to infinite volume. To provide insight on such chiral extrapolation, we evaluate the one-loop contributions to the matrix elements containing external Bd, Bs mesons and Λb baryon in the QCD limit, where sea and valence quark masses become equal. In particular, we find that the matrix elements of the λ3 flavor-octet operators with an external Bd meson receive the contributions solely from connected diagrams in which current lattice techniques are capable of precise determination of the matrix elements. Finite volume effects are at most a few percent for typical lattice sizes and pion masses.

Absence of particle production and factorization of the s-matrix in 1 + 1 dimensional models

International Nuclear Information System (INIS)

Parke, S.

1980-01-01

In massive, 1 + 1 dimensional, local, quantum field theories the existence of two conserved charges is shown to be a sufficient condition for the absence of particle production and factorization of the s-matrix. These charges must commute and be integrals of local current densities. Their transformation properties under the Lorentz group must be different and also different from the transformation properties under the Lorentz group must be different and also different from the transformation properties pf a vector or a scalar. Also, they must not annihilate any single-particle momentum eigenstate. (orig.)

Phenomenology with F-theory S U (5 )

Science.gov (United States)

Leontaris, George K.; Shafi, Qaisar

2017-09-01

We explore the low-energy phenomenology of an F-theory-based S U (5 ) model which, in addition to the known quarks and leptons, contains Standard Model (SM) singlets and vectorlike color triplets and S U (2 ) doublets. Depending on their masses and couplings, some of these new particles may be observed at the LHC and future colliders. We discuss the restrictions by Cabibbo-Kobayashi-Maskawa matrix constraints on their mixing with the ordinary down quarks of the three chiral families. The model is consistent with gauge coupling unification at the usual supersymmetric GUT scale; dimension-five proton decay is adequately suppressed, while dimension-six decay mediated by the superheavy gauge bosons is enhanced by a factor of 5-7. The third generation charged fermion Yukawa couplings yield the corresponding low-energy masses in reasonable agreement with observations. The hierarchical nature of the masses of lighter generations is accounted for via nonrenormalizable interactions, with the perturbative vacuum expectation values (VEVs) of the SM singlet fields playing an essential role.

In search of the "lost capital". A theory for valuation, investment decisions, performance measurement

OpenAIRE

Magni, Carlo Alberto

2007-01-01

This paper presents a theoretical framework for valuation, investment decisions, and performance measurement based on a nonstandard theory of residual income. It is derived from the notion of "unrecovered" capital, which is here named "lost" capital because it represents the capital foregone by the investors. Its theoretical strength and meaningfulness is shown by deriving it from four main perspectives: financial, microeconomic, axiomatic, accounting. Implications for asset valuation, cap...

Axiomatics of Fermat’s problem, another Way

Directory of Open Access Journals (Sweden)

Amelent A.E.

2017-05-01

Full Text Available the researcher of this article attempts to develop another Way to address the Fermat’s problem based on a different logical space, limited by other axioms, which have been described in the previous article of the author.

Literature survey of matrix diffusion theory and of experiments and data including natural analogues

International Nuclear Information System (INIS)

Ohlsson, Yvonne; Neretnieks, I.

1995-08-01

Diffusion theory in general and matrix diffusion in particular has been outlined, and experimental work has been reviewed. Literature diffusion data has been systematized in the form of tables and data has been compared and discussed. Strong indications of surface diffusion and anion exclusion have been found, and natural analogue studies and in-situ experiments suggest pore connectivity in the scale of meters. Matrix diffusion, however, mostly seem to be confined to zones of higher porosity extending only a few centimeters into the rock. Surface coating material do not seem to hinder sorption or diffusion into the rock. 54 refs, 18 tabs

Living in the Matrix: How a Scientific Conjecture was Turned into a Conspiracy Theory

Directory of Open Access Journals (Sweden)

Paura Roberto

2017-11-01

Full Text Available In recent years the simulation argument, namely, the idea that our reality is a kind of computer-generated simulation developed for hidden purposes, has acquired some credit and has been appropriated by the conspiracy culture, especially in the works of David Icke, author of paranoid bestsellers and known for his pseudo-theory about Reptilian aliens who secretly rule our world. To understand the reasons for the success of such an implausible pseudo-theory, it is necessary to analyze its genealogy inside popular culture. The methodological proposal underlying this paper is that the analysis of conspiracy theories and pseudo-scientific beliefs can benefit from the contribution of the history of ideas, which traditionally focuses on the reconstruction of the genealogy and the metamorphosis of unit-ideas over time and through different cultural levels. In this way, it is possible to shed light on the background and the peculiar rationality behind these pseudo-theories. The paper highlights New Age appropriation mechanisms of the theories of physicist David Bohm and neuropsychiatrist Karl Pribram (holographic principle, in particular through the pseudoscientific works of the McKenna Brothers (The Invisibile Landscape, 1975 and Michael Talbot (The Holographic Universe, 1991 as well as the impact of some sci-fi works based on the simulation argument, especially Philip K. Dick’s novels and The Matrix movie (1999, in exposing the paranoid and conspiracy implications of this argument. The paper also highlights the role of pseudo-scientific concepts as a characteristic aspect of contemporary superconspiracies, which in the age of rationalization and disenchantment seek to embrace a patina of science in order to be better accepted by the public. Wider application of this perspective to other cases of pseudo-scientific beliefs and contemporary conspiracy theories (e.g. flat Earth or chemtrails could provide useful suggestions on the most effective way of

Exact results for integrable asymptotically-free field theories

CERN Document Server

Evans, J M; Evans, Jonathan M; Hollowood, Timothy J

1995-01-01

An account is given of a technique for testing the equivalence between an exact factorizable S-matrix and an asymptotically-free Lagrangian field theory in two space-time dimensions. The method provides a way of resolving CDD ambiguities in the S-matrix and it also allows for an exact determination of the physical mass in terms of the Lambda parameter of perturbation theory. The results for various specific examples are summarized. (To appear in the Proceedings of the Conference on Recent Developments in Quantum Field Theory and Statistical Mechanics, ICTP, Trieste, Easter 1995).

Reduced density matrix functional theory at finite temperature

Energy Technology Data Exchange (ETDEWEB)

Baldsiefen, Tim

2012-10-15

Density functional theory (DFT) is highly successful in many fields of research. There are, however, areas in which its performance is rather limited. An important example is the description of thermodynamical variables of a quantum system in thermodynamical equilibrium. Although the finite-temperature version of DFT (FT-DFT) rests on a firm theoretical basis and is only one year younger than its brother, groundstate DFT, it has been successfully applied to only a few problems. Because FT-DFT, like DFT, is in principle exact, these shortcomings can be attributed to the difficulties of deriving valuable functionals for FT-DFT. In this thesis, we are going to present an alternative theoretical description of quantum systems in thermal equilibrium. It is based on the 1-reduced density matrix (1RDM) of the system, rather than on its density and will rather cumbersomly be called finite-temperature reduced density matrix functional theory (FT-RDMFT). Its zero-temperature counterpart (RDMFT) proved to be successful in several fields, formerly difficult to address via DFT. These fields include, for example, the calculation of dissociation energies or the calculation of the fundamental gap, also for Mott insulators. This success is mainly due to the fact that the 1RDM carries more directly accessible ''manybody'' information than the density alone, leading for example to an exact description of the kinetic energy functional. This sparks the hope that a description of thermodynamical systems employing the 1RDM via FT-RDMFT can yield an improvement over FT-DFT. Giving a short review of RDMFT and pointing out difficulties when describing spin-polarized systems initiates our work. We then lay the theoretical framework for FT-RDMFT by proving the required Hohenberg-Kohn-like theorems, investigating and determining the domain of FT-RDMFT functionals and by deriving several properties of the exact functional. Subsequently, we present a perturbative method to

Reduced density matrix functional theory at finite temperature

International Nuclear Information System (INIS)

Baldsiefen, Tim

2012-10-01

Density functional theory (DFT) is highly successful in many fields of research. There are, however, areas in which its performance is rather limited. An important example is the description of thermodynamical variables of a quantum system in thermodynamical equilibrium. Although the finite-temperature version of DFT (FT-DFT) rests on a firm theoretical basis and is only one year younger than its brother, groundstate DFT, it has been successfully applied to only a few problems. Because FT-DFT, like DFT, is in principle exact, these shortcomings can be attributed to the difficulties of deriving valuable functionals for FT-DFT. In this thesis, we are going to present an alternative theoretical description of quantum systems in thermal equilibrium. It is based on the 1-reduced density matrix (1RDM) of the system, rather than on its density and will rather cumbersomly be called finite-temperature reduced density matrix functional theory (FT-RDMFT). Its zero-temperature counterpart (RDMFT) proved to be successful in several fields, formerly difficult to address via DFT. These fields include, for example, the calculation of dissociation energies or the calculation of the fundamental gap, also for Mott insulators. This success is mainly due to the fact that the 1RDM carries more directly accessible ''manybody'' information than the density alone, leading for example to an exact description of the kinetic energy functional. This sparks the hope that a description of thermodynamical systems employing the 1RDM via FT-RDMFT can yield an improvement over FT-DFT. Giving a short review of RDMFT and pointing out difficulties when describing spin-polarized systems initiates our work. We then lay the theoretical framework for FT-RDMFT by proving the required Hohenberg-Kohn-like theorems, investigating and determining the domain of FT-RDMFT functionals and by deriving several properties of the exact functional. Subsequently, we present a perturbative method to iteratively construct

[Taxonomic theory for non-classical systematics].

Science.gov (United States)

Pavlinov, I Ia

2012-01-01

Outlined briefly are basic principles of construing general taxonomic theory for biological systematics considered in the context of non-classical scientific paradigm. The necessity of such kind of theory is substantiated, and some key points of its elaboration are exposed: its interpretation as a framework concept for the partial taxonomic theories in various schools of systematics; elaboration of idea of cognitive situation including three interrelated components, namely subject, object, and epistemic ones; its construing as a content-wisely interpreted quasi-axiomatics, with strong structuring of its conceptual space including demarcation between axioms and inferring rules; its construing as a "conceptual pyramid" of concepts of various levels of generality; inclusion of a basic model into definition of the taxonomic system (classification) regulating its content. Two problems are indicated as fundamental: definition of taxonomic diversity as a subject domain for the systematics as a whole; definition of onto-epistemological status of taxonomic system (classification) in general and of taxa in particular.

Random matrix theory and analysis of nucleus-nucleus collision at high energies

International Nuclear Information System (INIS)

Shahaliev, E.I.; Inst. of Radiation Problems, Baku; ); Kuznetsov, A.A.; Suleymanov, M.K.; ); Teryaev, O.V.; )

2006-01-01

A novel method for analysis of experimental data obtained at relativistic nucleus-nucleus collisions is proposed. The method, based on the ideas of Random Matrix Theory, is applied to detect systematic errors that occur at measurements of momentum distributions of emitted particles. The unfolded momentum distribution is well described by the Gaussian orthogonal ensemble of random matrices, when the uncertainty in the momentum distribution is maximal. The method is free from unwanted background contributions [ru

Applied linear algebra and matrix analysis

CERN Document Server

Shores, Thomas S

2018-01-01

In its second edition, this textbook offers a fresh approach to matrix and linear algebra. Its blend of theory, computational exercises, and analytical writing projects is designed to highlight the interplay between these aspects of an application. This approach places special emphasis on linear algebra as an experimental science that provides tools for solving concrete problems. The second edition’s revised text discusses applications of linear algebra like graph theory and network modeling methods used in Google’s PageRank algorithm. Other new materials include modeling examples of diffusive processes, linear programming, image processing, digital signal processing, and Fourier analysis. These topics are woven into the core material of Gaussian elimination and other matrix operations; eigenvalues, eigenvectors, and discrete dynamical systems; and the geometrical aspects of vector spaces. Intended for a one-semester undergraduate course without a strict calculus prerequisite, Applied Linear Algebra and M...

Kant’s Theory of Progress

OpenAIRE

McCloughan, Meade

2008-01-01

My topic is Kant’s theory of historical progress. My approach is primarily textual and contextual. I analyse in some detail Kant’s three most important essays on the topic: ‘Idea for a Universal History’, the third part of ‘Theory and Practice’ and the second part of The Conflict of the Faculties. I devote particular attention to the Kant-Herder debate about progress, but also discuss Rousseau, Mendelssohn, Hegel and others. In presenting, on Kant’s behalf, a strong case for his theory of pro...

Meaning of the BRS Lagrangian theory

International Nuclear Information System (INIS)

Cheng, H.; Tsai, E.

1989-01-01

A simplified treatment of the Becchi-Rouet-Stora (BRS) Lagrangian theory is presented. With this treatment we show that the BRS Lagrangian theory in general, and the Feynman-gauge field theory in particular, are effective theories, not the physical theory, and the Feynman gauge is not, strictly speaking, a gauge. The relationship between the quantum states in the BRS Lagrangian theory and those in the physical theory is explicitly given. We also show that one may obtain matrix elements of gauge-invariant operators in the physical theory by calculating corresponding ones in the BRS Lagrangian theory. The formulas which equate such matrix elements are called correspondence formulas. The correspondence formula for the S matrix enables us to equate the scattering amplitudes in the physical theory with those in the BRS Lagrangian theory, thus a proof of the unitary of the Feynman-gauge (as well as other covariant gauges) Feynman rules is rendered unnecessary. This treatment can be applied to various gauge field theories and the examples of the pure Yang-Mills theory and a gauge field theory with a Higgs field is explicitly worked out

How Axiomatic Design can promote creativity in the design of new products

Directory of Open Access Journals (Sweden)

Gabriel-Santos António

2017-01-01

Full Text Available In product development, creativity is the driving force for doing something that leads to innovation. A typical ideation background has three subsystems: inspiration, dematerialization and recombination. The most basic concepts of Axiomatic Design, i.e. domains, hierarchies and zigzagging, as well as the two design axioms, provide a powerful framework to implement ideation, as to make creativity easier when developing a new product. The result of dematerialization is in the functional domain, which is the place where the customer needs are presented by functional requirements and purged of any kind of physical bias. The recombination creates the design parameters, at the physical domain, which are the set of elements of the design object that have been chosen to satisfy the functional requirements, into a new materialization profile of a new product. In this paper, a concrete case illustrating the above-mentioned concepts is presented.

Decay of autoionizing states in time-dependent density functional and reduced density matrix functional theory

Energy Technology Data Exchange (ETDEWEB)

Kapoor, Varun; Brics, Martins; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)

2013-07-01

Autoionizing states are inaccessible to time-dependent density functional theory (TDDFT) using known, adiabatic Kohn-Sham (KS) potentials. We determine the exact KS potential for a numerically exactly solvable model Helium atom interacting with a laser field that is populating an autoionizing state. The exact single-particle density of the population in the autoionizing state corresponds to that of the energetically lowest quasi-stationary state in the exact KS potential. We describe how this exact potential controls the decay by a barrier whose height and width allows for the density to tunnel out and decay with the same rate as in the ab initio time-dependent Schroedinger calculation. However, devising a useful exchange-correlation potential that is capable of governing such a scenario in general and in more complex systems is hopeless. As an improvement over TDDFT, time-dependent reduced density matrix functional theory has been proposed. We are able to obtain for the above described autoionization process the exact time-dependent natural orbitals (i.e., the eigenfunctions of the exact, time-dependent one-body reduced density matrix) and study the potentials that appear in the equations of motion for the natural orbitals and the structure of the two-body density matrix expanded in them.

Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theoryCohomological gauge theory, quiver matrix models and Donaldson-Thomas theory

NARCIS (Netherlands)

Cirafici, M.; Sinkovics, A.; Szabo, R.J.

2009-01-01

We study the relation between Donaldson–Thomas theory of Calabi–Yau threefolds and a six-dimensional topological Yang–Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its partition function we use equivariant localization techniques

Implementation of the CCGM approximation for surface diffraction using Wigner R-matrix theory

International Nuclear Information System (INIS)

Lauderdale, J.G.; McCurdy, C.W.

1983-01-01

The CCGM approximation for surface scattering proposed by Cabrera, Celli, Goodman, and Manson [Surf. Sci. 19, 67 (1970)] is implemented for realistic surface interaction potentials using Wigner R-matrix theory. The resulting procedure is highly efficient computationally and is in no way limited to hard wall or purely repulsive potentials. Comparison is made with the results of close-coupling calculations of other workers which include the same diffraction channels in order to fairly evaluate the CCGM approximation which is an approximation to the coupled channels Lippman--Schwinger equation for the T matrix. The shapes of selective adsorption features, whether maxima or minima, in the scattered intensity are well represented in this approach for cases in which the surface corrugation is not too strong

Transformation Matrix for Time Discretization Based on Tustin’s Method

Directory of Open Access Journals (Sweden)

Yiming Jiang

2014-01-01

Full Text Available This paper studies rules in transformation of transfer function through time discretization. A method of using transformation matrix to realize bilinear transform (also known as Tustin’s method is presented. This method can be described as the conversion between the coefficients of transfer functions, which are expressed as transform by certain matrix. For a polynomial of degree n, the corresponding transformation matrix of order n exists and is unique. Furthermore, the transformation matrix can be decomposed into an upper triangular matrix multiplied with another lower triangular matrix. And both have obvious regularity. The proposed method can achieve rapid bilinear transform used in automatic design of digital filter. The result of numerical simulation verifies the correctness of the theoretical results. Moreover, it also can be extended to other similar problems. Example in the last throws light on this point.

Classical-limit S-matrix for heavy ion scattering

International Nuclear Information System (INIS)

Donangelo, R.J.

1977-01-01

An integral representation for the classical limit of the quantum mechanical S-matrix is developed and applied to heavy-ion Coulomb excitation and Coulomb-nuclear interference. The method combines the quantum principle of superposition with exact classical dynamics to describe the projectile-target system. A detailed consideration of the classical trajectories and of the dimensionless parameters that characterize the system is carried out. The results are compared, where possible, to exact quantum mechanical calculations and to conventional semiclassical calculations. It is found that in the case of backscattering the classical limit S-matrix method is able to almost exactly reproduce the quantum-mechanical S-matrix elements, and therefore the transition probabilities, even for projectiles as light as protons. The results also suggest that this approach should be a better approximation for heavy-ion multiple Coulomb excitation than earlier semiclassical methods, due to a more accurate description of the classical orbits in the electromagnetic field of the target nucleus. Calculations using this method indicate that the rotational excitation probabilities in the Coulomb-nuclear interference region should be very sensitive to the details of the potential at the surface of the nucleus, suggesting that heavy-ion rotational excitation could constitute a sensitive probe of the nuclear potential in this region. The application to other problems as well as the present limits of applicability of the formalism are also discussed

1/2-BPS correlators as c = 1 S-matrix

International Nuclear Information System (INIS)

Jevicki, Antal; Yoneya, Tamiaki

2007-01-01

We argue from two complementary viewpoints of Holography that the 2-point correlation functions of 1/2-BPS multi-trace operators in the large-N (planar) limit are nothing but the (Wick-rotated) S-matrix elements of c = 1 matrix model. On the bulk side, we consider an Euclideanized version of the so-called bubbling geometries and show that the corresponding droplets reach the conformal boundary. Then the scattering matrix of fluctuations of the droplets gives directly the two-point correlators through the GKPW prescription. On the Yang-Mills side, we show that the two-point correlators of holomorphic and anti-holomorphic operators are essentially equivalent with the transformation functions between asymptotic in- and out-states of c = 1 matrix model. Extension to non-planar case is also discussed

A comparative analysis for multiattribute selection among renewable energy alternatives using fuzzy axiomatic design and fuzzy analytic hierarchy process

Energy Technology Data Exchange (ETDEWEB)

Kahraman, Cengiz; Kaya, Ihsan; Cebi, Selcuk [Istanbul Technical University, Department of Industrial Engineering, 34367, Macka-Istanbul (Turkey)

2009-10-15

Renewable energy is the energy generated from natural resources such as sunlight, wind, rain, tides and geothermal heat which are renewable. Energy resources are very important in perspective of economics and politics for all countries. Hence, the selection of the best alternative for any country takes an important role for energy investments. Among decision-making methodologies, axiomatic design (AD) and analytic hierarchy process (AHP) are often used in the literature. The fuzzy set theory is a powerful tool to treat the uncertainty in case of incomplete or vague information. In this paper, fuzzy multicriteria decision- making methodologies are suggested for the selection among renewable energy alternatives. The first methodology is based on the AHP which allows the evaluation scores from experts to be linguistic expressions, crisp, or fuzzy numbers, while the second is based on AD principles under fuzziness which evaluates the alternatives under objective or subjective criteria with respect to the functional requirements obtained from experts. The originality of the paper comes from the fuzzy AD application to the selection of the best renewable energy alternative and the comparison with fuzzy AHP. In the application of the proposed methodologies the most appropriate renewable energy alternative is determined for Turkey. (author)

2016 MATRIX annals

CERN Document Server

Praeger, Cheryl; Tao, Terence

2018-01-01

MATRIX is Australia’s international, residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each lasting 1-4 weeks. This book is a scientific record of the five programs held at MATRIX in its first year, 2016: Higher Structures in Geometry and Physics (Chapters 1-5 and 18-21); Winter of Disconnectedness (Chapter 6 and 22-26); Approximation and Optimisation (Chapters 7-8); Refining C*-Algebraic Invariants for Dynamics using KK-theory (Chapters 9-13); Interactions between Topological Recursion, Modularity, Quantum Invariants and Low-dimensional Topology (Chapters 14-17 and 27). The MATRIX Scientific Committee selected these programs based on their scientific excellence and the participation rate of high-profile international participants. Each program included ample unstructured time to encourage collaborative research; some of the longer programs also included an embedded conference or lecture series. The artic...

On the algebraic theory of kink sectors: Application to quantum field theory models and collision theory

International Nuclear Information System (INIS)

Schlingemann, D.

1996-10-01

Several two dimensional quantum field theory models have more than one vacuum state. An investigation of super selection sectors in two dimensions from an axiomatic point of view suggests that there should be also states, called soliton or kink states, which interpolate different vacua. Familiar quantum field theory models, for which the existence of kink states have been proven, are the Sine-Gordon and the φ 4 2 -model. In order to establish the existence of kink states for a larger class of models, we investigate the following question: Which are sufficient conditions a pair of vacuum states has to fulfill, such that an interpolating kink state can be constructed? We discuss the problem in the framework of algebraic quantum field theory which includes, for example, the P(φ) 2 -models. We identify a large class of vacuum states, including the vacua of the P(φ) 2 -models, the Yukawa 2 -like models and special types of Wess-Zumino models, for which there is a natural way to construct an interpolating kink state. In two space-time dimensions, massive particle states are kink states. We apply the Haag-Ruelle collision theory to kink sectors in order to analyze the asymptotic scattering states. We show that for special configurations of n kinks the scattering states describe n freely moving non interacting particles. (orig.)

Rainbows, supernumerary rainbows and interference effects in the angular scattering of chemical reactions: an investigation using Heisenberg's S matrix programme.

Science.gov (United States)

Shan, Xiao; Xiahou, Chengkui; Connor, J N L

2018-01-03

In earlier research, we have demonstrated that broad "hidden" rainbows can occur in the product differential cross sections (DCSs) of state-to-state chemical reactions. Here we ask the question: can pronounced and localized rainbows, rather than broad hidden ones, occur in reactive DCSs? Further motivation comes from recent measurements by H. Pan and K. Liu, J. Phys. Chem. A, 2016, 120, 6712, of a "bulge" in a reactive DCS, which they conjecture is a rainbow. Our theoretical approach uses a "weak" version of Heisenberg's scattering matrix program (wHSMP) introduced by X. Shan and J. N. L. Connor, Phys. Chem. Chem. Phys., 2011, 13, 8392. This wHSMP uses four general physical principles for chemical reactions to suggest simple parameterized forms for the S matrix; it does not employ a potential energy surface. We use a parameterization in which the modulus of the S matrix is a smooth-step function of the total angular momentum quantum number, J, and (importantly) its phase is a cubic polynomial in J. We demonstrate for a Legendre partial wave series (PWS) the existence of pronounced rainbows, supernumerary rainbows, and other interference effects, in reactive DCSs. We find that reactive rainbows can be more complicated in their structure than the familiar rainbows of elastic scattering. We also analyse the angular scattering using Nearside-Farside (NF) PWS theory and NF PWS Local Angular Momentum (LAM) theory, including resummations of the PWS. In addition, we apply full and NF asymptotic (semiclassical) rainbow theories to the PWS - in particular, the uniform Airy and transitional Airy approximations for the farside scattering. This lets us prove that structure in the DCSs are indeed rainbows, supernumerary rainbows as well as other interference effects.

Random matrix theory of multi-antenna communications: the Ricean channel

International Nuclear Information System (INIS)

Moustakas, Aris L; Simon, Steven H

2005-01-01

The use of multi-antenna arrays in wireless communications through disordered media promises huge increases in the information transmission rate. It is therefore important to analyse the information capacity of such systems in realistic situations of microwave transmission, where the statistics of the transmission amplitudes (channel) may be coloured. Here, we present an approach that provides analytic expressions for the statistics, i.e. the moments of the distribution, of the mutual information for general Gaussian channel statistics. The mathematical method applies tools developed originally in the context of coherent wave propagation in disordered media, such as random matrix theory and replicas. Although it is valid formally for large antenna numbers, this approach produces extremely accurate results even for arrays with as few as two antennas. We also develop a method to analytically optimize over the input signal distribution, which enables us to calculate analytic capacities when the transmitter has knowledge of the statistics of the channel. The emphasis of this paper is on elucidating the novel mathematical methods used. We do this by analysing a specific case when the channel matrix is a complex Gaussian with arbitrary mean and unit covariance, which is usually called the Ricean channel

Decision making by hybrid probabilistic: Possibilistic utility theory

Directory of Open Access Journals (Sweden)

Pap Endre

2009-01-01

Full Text Available It is presented an approach to decision theory based upon nonprobabilistic uncertainty. There is an axiomatization of the hybrid probabilistic possibilistic mixtures based on a pair of triangular conorm and triangular norm satisfying restricted distributivity law, and the corresponding non-additive Smeasure. This is characterized by the families of operations involved in generalized mixtures, based upon a previous result on the characterization of the pair of continuous t-norm and t-conorm such that the former is restrictedly distributive over the latter. The obtained family of mixtures combines probabilistic and idempotent (possibilistic mixtures via a threshold.

Application of R-Matrix with Time-dependence Theory to Double Ionisation Using a 2-electron Outer Region

International Nuclear Information System (INIS)

Wragg, Jack; Parker, J S; Van der Hart, H W

2015-01-01

R-Matrix with Time-dependence (RMT) theory has been extended to cover double-ionisation processes. An application to photoionisation of He is demonstrated, with an emphasis on double-ionisation cross sections. (paper)

Complex Masses in the S-Matrix

International Nuclear Information System (INIS)

Rupp, G.; Coito, S.; Beveren, E. van

2010-01-01

Most excited hadrons have multiparticle strong decay modes, which can often be described as resulting from intermediate states containing one or two resonances. In a theoretical approach, such a description in terms of quasi-two-particle initial and final states leads to unitarity violations, because of the complex masses of the involved resonances. In the present paper, an empirical algebraic procedure is presented to restore unitarity of the S-matrix while preserving its symmetry. Preliminary results are presented in a first application to S-wave ππ scattering, in the framework of the Resonance-Spectrum Expansion. (author)

Determination of Thermal Conductivity of Silicate Matrix for Applications in Effective Media Theory

Science.gov (United States)

Fiala, Lukáš; Jerman, Miloš; Reiterman, Pavel; Černý, Robert

2018-02-01

Silicate materials have an irreplaceable role in the construction industry. They are mainly represented by cement-based- or lime-based materials, such as concrete, cement mortar, or lime plaster, and consist of three phases: the solid matrix and air and water present in the pores. Therefore, their effective thermal conductivity depends on thermal conductivities of the involved phases. Due to the time-consuming experimental determination of the effective thermal conductivity, its calculation by means of homogenization techniques presents a reasonable alternative. In the homogenization theory, both volumetric content and particular property of each phase need to be identified. For porous materials the most problematic part is to accurately identify thermal conductivity of the solid matrix. Due to the complex composition of silicate materials, the thermal conductivity of the matrix can be determined only approximately, based on the knowledge of thermal conductivities of its major compounds. In this paper, the thermal conductivity of silicate matrix is determined using the measurement of a sufficiently large set of experimental data. Cement pastes with different open porosities are prepared, dried, and their effective thermal conductivity is determined using a transient heat-pulse method. The thermal conductivity of the matrix is calculated by means of extrapolation of the effective thermal conductivity versus porosity functions to zero porosity. Its practical applicability is demonstrated by calculating the effective thermal conductivity of a three-phase silicate material and comparing it with experimental data.

String states, loops and effective actions in noncommutative field theory and matrix models

Directory of Open Access Journals (Sweden)

Harold C. Steinacker

2016-09-01

Full Text Available Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string states as a tool for loop computations in noncommutative field theory and matrix models. Defined in terms of coherent states, they exhibit the stringy features of noncommutative field theory. This leads to a closed form for the 1-loop effective action in position space, capturing the long-range non-local UV/IR mixing for scalar fields. The formalism applies to generic fuzzy spaces. The non-locality is tamed in the maximally supersymmetric IKKT or IIB model, where it gives rise to supergravity. The linearized supergravity interactions are obtained directly in position space at one loop using string states on generic noncommutative branes.

String states, loops and effective actions in noncommutative field theory and matrix models

Energy Technology Data Exchange (ETDEWEB)

Steinacker, Harold C., E-mail: harold.steinacker@univie.ac.at

2016-09-15

Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string states as a tool for loop computations in noncommutative field theory and matrix models. Defined in terms of coherent states, they exhibit the stringy features of noncommutative field theory. This leads to a closed form for the 1-loop effective action in position space, capturing the long-range non-local UV/IR mixing for scalar fields. The formalism applies to generic fuzzy spaces. The non-locality is tamed in the maximally supersymmetric IKKT or IIB model, where it gives rise to supergravity. The linearized supergravity interactions are obtained directly in position space at one loop using string states on generic noncommutative branes.

A new approach to quantum field theory and a spacetime quantization

International Nuclear Information System (INIS)

Banai, I.

1982-09-01

A quantum logical approach to achieve a sound kinematical picture for LQFT (local quantum field theory) is reviewed. Then a general language in the framework of axiomatic set theory is presented, in which the 'local' description of a LQFT can be formulated in almost the same form as quantum mechanics was formulated by von Neumann. The main physical implication of this approach is that, in this framework, the quantization of a CRLFT (classical relativistic local field theory) requires not only the quantization of physical fields over M 4 but the quantization of spacetime M 4 itself, too. The uncertainty priciple is compatible with the Heisenberg uncertainty principle, but it requires the generalization of Poincare symmetries to all unitary symmetries. Some indications show that his approach might be successful in describing low laying hadronic phenomena. (author)

S-matrix analysis of the baryon electric charge correlation

Science.gov (United States)

Lo, Pok Man; Friman, Bengt; Redlich, Krzysztof; Sasaki, Chihiro

2018-03-01

We compute the correlation of the net baryon number with the electric charge (χBQ) for an interacting hadron gas using the S-matrix formulation of statistical mechanics. The observable χBQ is particularly sensitive to the details of the pion-nucleon interaction, which are consistently incorporated in the current scheme via the empirical scattering phase shifts. Comparing to the recent lattice QCD studies in the (2 + 1)-flavor system, we find that the natural implementation of interactions and the proper treatment of resonances in the S-matrix approach lead to an improved description of the lattice data over that obtained in the hadron resonance gas model.

S-matrix formulation of thermodynamics with N-body scatterings

Energy Technology Data Exchange (ETDEWEB)

Lo, Pok Man [University of Wroclaw, Institute of Theoretical Physics, Wroclaw (Poland); Extreme Matter Institute EMMI, GSI, Darmstadt (Germany)

2017-08-15

We apply a phase space expansion scheme to incorporate the N-body scattering processes in the S-matrix formulation of statistical mechanics. A generalized phase shift function suitable for studying the thermal contribution of N → N processes is motivated and examined in various models. Using the expansion scheme, we revisit how the hadron resonance gas model emerges from the S-matrix framework, and consider an example of structureless scattering in which the phase shift function can be exactly worked out. Finally we analyze the influence of dynamics on the phase shift function in a simple example of 3- and 4-body scattering. (orig.)

Construction of fuzzy spaces and their applications to matrix models

Science.gov (United States)

Abe, Yasuhiro

Quantization of spacetime by means of finite dimensional matrices is the basic idea of fuzzy spaces. There remains an issue of quantizing time, however, the idea is simple and it provides an interesting interplay of various ideas in mathematics and physics. Shedding some light on such an interplay is the main theme of this dissertation. The dissertation roughly separates into two parts. In the first part, we consider rather mathematical aspects of fuzzy spaces, namely, their construction. We begin with a review of construction of fuzzy complex projective spaces CP k (k = 1, 2, · · ·) in relation to geometric quantization. This construction facilitates defining symbols and star products on fuzzy CPk. Algebraic construction of fuzzy CPk is also discussed. We then present construction of fuzzy S 4, utilizing the fact that CP3 is an S2 bundle over S4. Fuzzy S4 is obtained by imposing an additional algebraic constraint on fuzzy CP3. Consequently it is proposed that coordinates on fuzzy S4 are described by certain block-diagonal matrices. It is also found that fuzzy S8 can analogously be constructed. In the second part of this dissertation, we consider applications of fuzzy spaces to physics. We first consider theories of gravity on fuzzy spaces, anticipating that they may offer a novel way of regularizing spacetime dynamics. We obtain actions for gravity on fuzzy S2 and on fuzzy CP3 in terms of finite dimensional matrices. Application to M(atrix) theory is also discussed. With an introduction of extra potentials to the theory, we show that it also has new brane solutions whose transverse directions are described by fuzzy S 4 and fuzzy CP3. The extra potentials can be considered as fuzzy versions of differential forms or fluxes, which enable us to discuss compactification models of M(atrix) theory. In particular, compactification down to fuzzy S4 is discussed and a realistic matrix model of M-theory in four-dimensions is proposed.

Investigation of properties of time-dependent bell inequalities in Wigner’s form for nonstationary and open quantum systems

Energy Technology Data Exchange (ETDEWEB)

Nikitin, N. V., E-mail: nnikit@mail.cern.ch; Sotnikov, V.P., E-mail: sotnikov@physics.msu.ru [Moscow State University, Faculty of Physics (Russian Federation); Toms, K. S., E-mail: ktoms@mail.cern.ch [The University of New Mexico, Department of Physics and Astronomy (United States)

2015-10-15

A radically new class of Bell inequalities in Wigner’s form was obtained on the basis of Kolmorov’s axiomatization of probability theory and the hypothesis of locality. These inequalities take explicitly into account the dependence on time (time-dependent Bell inequalities in Wigner’s form). By using these inequalities, one can propose a means for experimentally testing Bohr’ complementarity principle in the relativistic region. The inequalities in question open broad possibilities for studying correlations of nonrelativistic and relativistic quantum systems in external fields. The violation of the time-dependent inequalities in quantum mechanics was studied by considering the behavior of a pair of anticorrelated spins in a constant external magnetic field and oscillations of neutral pseudoscalar mesons. The decay of a pseudoscalar particle to a fermion–antifermion pair is considered within quantum field theory. In order to test experimentally the inequalities proposed in the present study, it is not necessary to perform dedicated noninvasive measurements required in the Leggett–Garg approach, for example.

Investigation of properties of time-dependent bell inequalities in Wigner’s form for nonstationary and open quantum systems

International Nuclear Information System (INIS)

Nikitin, N. V.; Sotnikov, V.P.; Toms, K. S.

2015-01-01

A radically new class of Bell inequalities in Wigner’s form was obtained on the basis of Kolmorov’s axiomatization of probability theory and the hypothesis of locality. These inequalities take explicitly into account the dependence on time (time-dependent Bell inequalities in Wigner’s form). By using these inequalities, one can propose a means for experimentally testing Bohr’ complementarity principle in the relativistic region. The inequalities in question open broad possibilities for studying correlations of nonrelativistic and relativistic quantum systems in external fields. The violation of the time-dependent inequalities in quantum mechanics was studied by considering the behavior of a pair of anticorrelated spins in a constant external magnetic field and oscillations of neutral pseudoscalar mesons. The decay of a pseudoscalar particle to a fermion–antifermion pair is considered within quantum field theory. In order to test experimentally the inequalities proposed in the present study, it is not necessary to perform dedicated noninvasive measurements required in the Leggett–Garg approach, for example

Ceramic matrix and resin matrix composites - A comparison

Science.gov (United States)

Hurwitz, Frances I.

1987-01-01

The underlying theory of continuous fiber reinforcement of ceramic matrix and resin matrix composites, their fabrication, microstructure, physical and mechanical properties are contrasted. The growing use of organometallic polymers as precursors to ceramic matrices is discussed as a means of providing low temperature processing capability without the fiber degradation encountered with more conventional ceramic processing techniques. Examples of ceramic matrix composites derived from particulate-filled, high char yield polymers and silsesquioxane precursors are provided.

Ceramic matrix and resin matrix composites: A comparison

Science.gov (United States)

Hurwitz, Frances I.

1987-01-01

The underlying theory of continuous fiber reinforcement of ceramic matrix and resin matrix composites, their fabrication, microstructure, physical and mechanical properties are contrasted. The growing use of organometallic polymers as precursors to ceramic matrices is discussed as a means of providing low temperature processing capability without the fiber degradation encountered with more conventional ceramic processing techniques. Examples of ceramic matrix composites derived from particulate-filled, high char yield polymers and silsesquioxane precursors are provided.

An iterative method to invert the LTSn matrix

Energy Technology Data Exchange (ETDEWEB)

Cardona, A.V.; Vilhena, M.T. de [UFRGS, Porto Alegre (Brazil)

1996-12-31

Recently Vilhena and Barichello proposed the LTSn method to solve, analytically, the Discrete Ordinates Problem (Sn problem) in transport theory. The main feature of this method consist in the application of the Laplace transform to the set of Sn equations and solve the resulting algebraic system for the transport flux. Barichello solve the linear system containing the parameter s applying the definition of matrix invertion exploiting the structure of the LTSn matrix. In this work, it is proposed a new scheme to invert the LTSn matrix, decomposing it in blocks and recursively inverting this blocks.

Moral Capital : Bourdieu’s theory of practice and moral climate theory

NARCIS (Netherlands)

Hans Bennink

2012-01-01

To many scholars and researchers in organisation and management studies, Bourdieu’s theory of practice as one of the grand sociological conceptual framework turns out to be an appealing toolkit to think with. What can Bourdieu’s theory of practice entail for moral climate theory as a relative new

Classes and Theories of Trees Associated with a Class Of Linear Orders

DEFF Research Database (Denmark)

Goranko, Valentin; Kellerman, Ruaan

2011-01-01

Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the set-theoretic relationships between...... these classes of trees and between their corresponding first-order theories. We then obtain some general results about the axiomatization of the first-order theories of some of these classes of trees in terms of the first-order theory of the generating class C, and indicate the problems obstructing such general...... results for the other classes. These problems arise from the possible existence of nondefinable paths in trees, that need not satisfy the first-order theory of C, so we have started analysing first order definable and undefinable paths in trees....

Matrix thermalization

International Nuclear Information System (INIS)

Craps, Ben; Evnin, Oleg; Nguyen, Kévin

2017-01-01

Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.

Matrix thermalization

Science.gov (United States)

Craps, Ben; Evnin, Oleg; Nguyen, Kévin

2017-02-01

Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.

Matrix thermalization

Energy Technology Data Exchange (ETDEWEB)

Craps, Ben [Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB), and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium); Evnin, Oleg [Department of Physics, Faculty of Science, Chulalongkorn University, Thanon Phayathai, Pathumwan, Bangkok 10330 (Thailand); Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB), and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium); Nguyen, Kévin [Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB), and International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium)

2017-02-08

Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing shell solutions in the gravitational bulk correspond in this setting to thermalization processes in the dual quantum mechanical theory. We construct an explicit, fully nonlinear supergravity solution describing a generic collapsing dilaton shell, specify the holographic renormalization prescriptions necessary for computing the relevant boundary observables, and apply them to evaluating thermalizing two-point correlation functions in the dual matrix theory.

TD-S-HF single determinantal reaction theory and the description of many-body processes, including fission

International Nuclear Information System (INIS)

Griffin, J.J.; Lichtner, P.C.; Dworzecka, M.; Kan, K.K.

1979-01-01

The restrictions implied for the time dependent many-body reaction theory by the (TDHF) single determinantal assumption are explored by constructive analysis. A restructured TD-S-HF reaction theory is modelled, not after the initial-value form of the Schroedinger reaction theory, but after the (fully equivalent) S-matrix form, under the conditions that only self-consistent TDHF solutions occur in the theory, every wave function obeys the fundamental statistical interpretation of quantum mechanics, and the theory reduces to the exact Schroedinger theory for exact solutions which are single determinantal. All of these conditions can be accomodated provided that the theory is interpreted on a time-averaged basis, i.e., physical constants of the Schroedinger theory which are time-dependent in the TDHF theory, are interpreted in TD-S-HF in terms of their time averaged values. The resulting reaction theory, although formulated heuristically, prescribes a well defined and unambiguous calculational program which, although somewhat more demanding technically than the conventional initial-value TDHF method, is nevertheless more consonant with first principles, structurally and mechanistically. For its physical predictions do not depend upon the precise location of the distant measuring apparatus, and are in no way influenced by the spurious cross channel correlations which arise whenever the description of many reaction channels is imposed upon one single-determinantal solution. For nuclear structure physics, the TDHF-eigenfunctions provide the first plausible description of exact eigenstates in the time-dependent framework; moreover, they are unencumbered by any restriction to small amplitudes. 14 references

Abelian dominance in Einstein’s theory

International Nuclear Information System (INIS)

Cho, Y M; Oh, S H; Kim, Sang-Woo

2012-01-01

We conjecture the Abelian dominance in Einstein’s theory, that is, the Abelian part of the theory plays the central role in the dynamics. Treating Einstein’s theory as a gauge theory of the Lorentz group, we show that Einstein’s theory can be decomposed into the restricted part made up of the restricted connection which has the full Lorentz gauge invariance and the valence part made up of the valence connection which plays the role of gravitational source of the restricted gravity. In this decomposition, the role of the metric g μν is replaced by a four-index metric tensor g μν which transforms covariantly under the Lorentz group, and the metric-compatibility condition ∇ α g μν = 0 of the connection is replaced by the gauge and generally covariant condition D μ g μν = 0. We show that there are two different Abelian decompositions, the light-like (or null) decomposition and the non-light-like (or non-null) decomposition, because the Lorentz group has two maximal Abelian subgroups. The decomposition shows the existence of the restricted gravity which has the full general invariance but is much simpler than Einstein’s theory. Moreover, it tells us that the restricted gravity can be written as an Abelian gauge theory, which implies that the graviton can be described by a massless spin-1 field. This establishes the Abelian dominance in Einstein’s theory. (paper)

Time-dependent reduced density matrix functional theory applied to laser-driven, correlated two-electron dynamics

Energy Technology Data Exchange (ETDEWEB)

Brics, Martins; Kapoor, Varun; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)

2013-07-01

Time-dependent density functional theory (TDDFT) with known and practicable exchange-correlation potentials does not capture highly correlated electron dynamics such as single-photon double ionization, autoionization, or nonsequential ionization. Time-dependent reduced density matrix functional theory (TDRDMFT) may remedy these problems. The key ingredients in TDRDMFT are the natural orbitals (NOs), i.e., the eigenfunctions of the one-body reduced density matrix (1-RDM), and the occupation numbers (OCs), i.e., the respective eigenvalues. The two-body reduced density matrix (2-RDM) is then expanded in NOs, and equations of motion for the NOs can be derived. If the expansion coefficients of the 2-RDM were known exactly, the problem at hand would be solved. In practice, approximations have to be made. We study the prospects of TDRDMFT following a top-down approach. We solve the exact two-electron time-dependent Schroedinger equation for a model Helium atom in intense laser fields in order to study highly correlated phenomena such as the population of autoionizing states or single-photon double ionization. From the exact wave function we calculate the exact NOs, OCs, the exact expansion coefficients of the 2-RDM, and the exact potentials in the equations of motion. In that way we can identify how many NOs and which level of approximations are necessary to capture such phenomena.

Exact S-matrices for dn+1(2) affine Toda solitons and their bound states

International Nuclear Information System (INIS)

Gandenberger, G.M.; MacKay, N.J.

1995-01-01

We conjecture an exact S-matrix for the scattering of solitons in d n+1 (2) affine Toda field theory in terms of the R-matrix of the quantum group U q (c n (1) ). From this we construct the scattering amplitudes for all scalar bound states (breathers) of the theory. This S-matrix conjecture is justified by detailed examination of its pole structure. We show that a breather-particle identification holds by comparing the S-matrix elements for the lowest breathers with the S-matrix for the quantum particles in real affine Toda field theory, and discuss the implications for various forms of duality. (orig.)

Matrix Information Geometry

CERN Document Server

Bhatia, Rajendra

2013-01-01

This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR).  During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented  are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.  

Inclusive fitness maximization: An axiomatic approach.

Science.gov (United States)

Okasha, Samir; Weymark, John A; Bossert, Walter

2014-06-07

Kin selection theorists argue that evolution in social contexts will lead organisms to behave as if maximizing their inclusive, as opposed to personal, fitness. The inclusive fitness concept allows biologists to treat organisms as akin to rational agents seeking to maximize a utility function. Here we develop this idea and place it on a firm footing by employing a standard decision-theoretic methodology. We show how the principle of inclusive fitness maximization and a related principle of quasi-inclusive fitness maximization can be derived from axioms on an individual׳s 'as if preferences' (binary choices) for the case in which phenotypic effects are additive. Our results help integrate evolutionary theory and rational choice theory, help draw out the behavioural implications of inclusive fitness maximization, and point to a possible way in which evolution could lead organisms to implement it. Copyright © 2014 Elsevier Ltd. All rights reserved.

Vacuum states and the S matrix in dS/CFT

International Nuclear Information System (INIS)

Spradlin, Marcus; Volovich, Anastasia

2002-01-01

We propose a definition of dS/CFT correlation functions by equating them to S-matrix elements for scattering particles from I - to I + . In planar coordinates, which cover half of de Sitter space, we consider instead the S vector obtained by specifying a fixed state on the horizon. We construct the one-parameter family of de Sitter invariant vacuum states for a massive scalar field in these coordinates, and show that the vacuum obtained by analytic continuation from the sphere has no particles on the past horizon. We use this formalism to provide evidence that the one-parameter family of vacua corresponds to marginal deformations of the CFT by computing a three-point function

Random matrix theory filters in portfolio optimisation: A stability and risk assessment

Science.gov (United States)

Daly, J.; Crane, M.; Ruskin, H. J.

2008-07-01

Random matrix theory (RMT) filters, applied to covariance matrices of financial returns, have recently been shown to offer improvements to the optimisation of stock portfolios. This paper studies the effect of three RMT filters on the realised portfolio risk, and on the stability of the filtered covariance matrix, using bootstrap analysis and out-of-sample testing. We propose an extension to an existing RMT filter, (based on Krzanowski stability), which is observed to reduce risk and increase stability, when compared to other RMT filters tested. We also study a scheme for filtering the covariance matrix directly, as opposed to the standard method of filtering correlation, where the latter is found to lower the realised risk, on average, by up to 6.7%. We consider both equally and exponentially weighted covariance matrices in our analysis, and observe that the overall best method out-of-sample was that of the exponentially weighted covariance, with our Krzanowski stability-based filter applied to the correlation matrix. We also find that the optimal out-of-sample decay factors, for both filtered and unfiltered forecasts, were higher than those suggested by Riskmetrics [J.P. Morgan, Reuters, Riskmetrics technical document, Technical Report, 1996. http://www.riskmetrics.com/techdoc.html], with those for the latter approaching a value of α=1. In conclusion, RMT filtering reduced the realised risk, on average, and in the majority of cases when tested out-of-sample, but increased the realised risk on a marked number of individual days-in some cases more than doubling it.

Random matrix analysis of human EEG data

Czech Academy of Sciences Publication Activity Database

Šeba, Petr

2003-01-01

Roč. 91, - (2003), s. 198104-1 - 198104-4 ISSN 0031-9007 R&D Projects: GA ČR GA202/02/0088 Institutional research plan: CEZ:AV0Z1010914 Keywords : random matrix theory * EEG signal Subject RIV: BE - Theoretical Physics Impact factor: 7.035, year: 2003

Theory of threshold phenomena

International Nuclear Information System (INIS)

Hategan, Cornel

2002-01-01

Theory of Threshold Phenomena in Quantum Scattering is developed in terms of Reduced Scattering Matrix. Relationships of different types of threshold anomalies both to nuclear reaction mechanisms and to nuclear reaction models are established. Magnitude of threshold effect is related to spectroscopic factor of zero-energy neutron state. The Theory of Threshold Phenomena, based on Reduced Scattering Matrix, does establish relationships between different types of threshold effects and nuclear reaction mechanisms: the cusp and non-resonant potential scattering, s-wave threshold anomaly and compound nucleus resonant scattering, p-wave anomaly and quasi-resonant scattering. A threshold anomaly related to resonant or quasi resonant scattering is enhanced provided the neutron threshold state has large spectroscopic amplitude. The Theory contains, as limit cases, Cusp Theories and also results of different nuclear reactions models as Charge Exchange, Weak Coupling, Bohr and Hauser-Feshbach models. (author)

A wave propagation matrix method in semiclassical theory

International Nuclear Information System (INIS)

Lee, S.Y.; Takigawa, N.

1977-05-01

A wave propagation matrix method is used to derive the semiclassical formulae of the multiturning point problem. A phase shift matrix and a barrier transformation matrix are introduced to describe the processes of a particle travelling through a potential well and crossing a potential barrier respectively. The wave propagation matrix is given by the products of phase shift matrices and barrier transformation matrices. The method to study scattering by surface transparent potentials and the Bloch wave in solids is then applied

Design evaluation of emergency core cooling systems using Axiomatic Design

Energy Technology Data Exchange (ETDEWEB)

Heo, Gyunyoung [Massachusetts Institute of Technology, Department of Mechanical Engineering, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States)]. E-mail: gheo@mit.edu; Lee, Song Kyu [Korea Advanced Institute of Science and Technology, Department of Nuclear and Quantum Engineering, 373-1 Guseong-dong, Yuseong-gu, Daejeon (Korea, Republic of)

2007-01-15

In designing nuclear power plants (NPPs), the evaluation of safety is one of the important issues. As a measure for evaluating safety, this paper proposes a methodology to examine the design process of emergency core cooling systems (ECCSs) in NPPs using Axiomatic Design (AD). This is particularly important for identifying vulnerabilities and creating solutions. Korean Advanced Power Reactor 1400 MWe (APR1400) adopted the ECCS, which was improved to meet the stronger safety regulations than that of the current Optimized Power Reactor 1000 MWe (OPR1000). To improve the performance and safety of the ECCS, the various design strategies such as independency or redundancy were implemented, and their effectiveness was confirmed by calculating core damage frequency. We suggest an alternative viewpoint of evaluating the deployment of design strategies in terms of AD methodology. AD suggests two design principles and the visualization tools for organizing design process. The important benefit of AD is that it is capable of providing suitable priorities for deploying design strategies. The reverse engineering driven by AD has been able to show that the design process of the ECCS of APR1400 was improved in comparison to that of OPR1000 from the viewpoint of the coordination of design strategies.

Lattice gauge theories

International Nuclear Information System (INIS)

Petronzio, R.

1992-01-01

Lattice gauge theories are about fifteen years old and I will report on the present status of the field without making the elementary introduction that can be found in the proceedings of the last two conferences. The talk covers briefly the following subjects: the determination of α s , the status of spectroscopy, heavy quark physics and in particular the calculation of their hadronic weak matrix elements, high temperature QCD, non perturbative Higgs bounds, chiral theories on the lattice and induced theories

Towards a simple mathematical theory of citation distributions.

Science.gov (United States)

Katchanov, Yurij L

2015-01-01

The paper is written with the assumption that the purpose of a mathematical theory of citation is to explain bibliometric regularities at the level of mathematical formalism. A mathematical formalism is proposed for the appearance of power law distributions in social citation systems. The principal contributions of this paper are an axiomatic characterization of citation distributions in terms of the Ekeland variational principle and a mathematical exploration of the power law nature of citation distributions. Apart from its inherent value in providing a better understanding of the mathematical underpinnings of bibliometric models, such an approach can be used to derive a citation distribution from first principles.

Influence of electron correlation and degeneracy on the Fukui matrix and extension of frontier molecular orbital theory to correlated quantum chemical methods.

Science.gov (United States)

Bultinck, Patrick; Van Neck, Dimitri; Acke, Guillaume; Ayers, Paul W

2012-02-21

The Fukui function is considered as the diagonal element of the Fukui matrix in position space, where the Fukui matrix is the derivative of the one particle density matrix (1DM) with respect to the number of electrons. Diagonalization of the Fukui matrix, expressed in an orthogonal orbital basis, explains why regions in space with negative Fukui functions exist. Using a test set of molecules, electron correlation is found to have a remarkable effect on the eigenvalues of the Fukui matrix. The Fukui matrices at the independent electron model level are mathematically proven to always have an eigenvalue equal to exactly unity while the rest of the eigenvalues possibly differ from zero but sum to zero. The loss of idempotency of the 1DM at correlated levels of theory causes the loss of these properties. The influence of electron correlation is examined in detail and the frontier molecular orbital concept is extended to correlated levels of theory by defining it as the eigenvector of the Fukui matrix with the largest eigenvalue. The effect of degeneracy on the Fukui matrix is examined in detail, revealing that this is another way by which the unity eigenvalue and perfect pairing of eigenvalues can disappear.

Reduced density-matrix functional theory: Correlation and spectroscopy.

Science.gov (United States)

Di Sabatino, S; Berger, J A; Reining, L; Romaniello, P

2015-07-14

In this work, we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard dimer at 1/4 and 1/2 fillings as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison, we also report the results of the GW approximation, where the self-energy functional is approximated, but no further hypothesis is made concerning the approximations of the observables. In particular, we focus on the atomic limit, where the two sites of the dimer are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard dimer at 1/2 filling with or without a spin-symmetry-broken ground state allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in GW, the signature of strong correlation is present, when looking at the removal/addition energies and spectral function from the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover, we show how the spectroscopic properties change from one spin structure to the other.

Optical excitation and electron relaxation dynamics at semiconductor surfaces: a combined approach of density functional and density matrix theory applied to the silicon (001) surface

Energy Technology Data Exchange (ETDEWEB)

Buecking, N

2007-11-05

In this work a new theoretical formalism is introduced in order to simulate the phononinduced relaxation of a non-equilibrium distribution to equilibrium at a semiconductor surface numerically. The non-equilibrium distribution is effected by an optical excitation. The approach in this thesis is to link two conventional, but approved methods to a new, more global description: while semiconductor surfaces can be investigated accurately by density-functional theory, the dynamical processes in semiconductor heterostructures are successfully described by density matrix theory. In this work, the parameters for density-matrix theory are determined from the results of density-functional calculations. This work is organized in two parts. In Part I, the general fundamentals of the theory are elaborated, covering the fundamentals of canonical quantizations as well as the theory of density-functional and density-matrix theory in 2{sup nd} order Born approximation. While the formalism of density functional theory for structure investigation has been established for a long time and many different codes exist, the requirements for density matrix formalism concerning the geometry and the number of implemented bands exceed the usual possibilities of the existing code in this field. A special attention is therefore attributed to the development of extensions to existing formulations of this theory, where geometrical and fundamental symmetries of the structure and the equations are used. In Part II, the newly developed formalism is applied to a silicon (001)surface in a 2 x 1 reconstruction. As first step, density-functional calculations using the LDA functional are completed, from which the Kohn-Sham-wave functions and eigenvalues are used to calculate interaction matrix elements for the electron-phonon-coupling an the optical excitation. These matrix elements are determined for the optical transitions from valence to conduction bands and for electron-phonon processes inside the

A periodic table of effective field theories

Energy Technology Data Exchange (ETDEWEB)

Cheung, Clifford [Walter Burke Institute for Theoretical Physics,California Institute of Technology,Pasadena, CA (United States); Kampf, Karol; Novotny, Jiri [Institute of Particle and Nuclear Physics,Faculty of Mathematics and Physics, Charles University,Prague (Czech Republic); Shen, Chia-Hsien [Walter Burke Institute for Theoretical Physics,California Institute of Technology,Pasadena, CA (United States); Trnka, Jaroslav [Center for Quantum Mathematics and Physics (QMAP),Department of Physics, University of California,Davis, CA (United States)

2017-02-06

We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix. To do so we define an EFT classification based on four parameters characterizing 1) the number of derivatives per interaction, 2) the soft properties of amplitudes, 3) the leading valency of the interactions, and 4) the spacetime dimension. Carving out the allowed space of EFTs, we prove that exceptional EFTs like the non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using on-shell momentum shifts and recursion relations, we prove that EFTs with arbitrarily soft behavior are forbidden and EFTs with leading valency much greater than the spacetime dimension cannot have enhanced soft behavior. We then enumerate all single scalar EFTs in d<6 and verify that they correspond to known theories in the literature. Our results suggest that the exceptional theories are the natural EFT analogs of gauge theory and gravity because they are one-parameter theories whose interactions are strictly dictated by properties of the S-matrix.

Measuring order in disordered systems and disorder in ordered systems: Random matrix theory for isotropic and nematic liquid crystals and its perspective on pseudo-nematic domains

Science.gov (United States)

Zhao, Yan; Stratt, Richard M.

2018-05-01

Surprisingly long-ranged intermolecular correlations begin to appear in isotropic (orientationally disordered) phases of liquid crystal forming molecules when the temperature or density starts to close in on the boundary with the nematic (ordered) phase. Indeed, the presence of slowly relaxing, strongly orientationally correlated, sets of molecules under putatively disordered conditions ("pseudo-nematic domains") has been apparent for some time from light-scattering and optical-Kerr experiments. Still, a fully microscopic characterization of these domains has been lacking. We illustrate in this paper how pseudo-nematic domains can be studied in even relatively small computer simulations by looking for order-parameter tensor fluctuations much larger than one would expect from random matrix theory. To develop this idea, we show that random matrix theory offers an exact description of how the probability distribution for liquid-crystal order parameter tensors converges to its macroscopic-system limit. We then illustrate how domain properties can be inferred from finite-size-induced deviations from these random matrix predictions. A straightforward generalization of time-independent random matrix theory also allows us to prove that the analogous random matrix predictions for the time dependence of the order-parameter tensor are similarly exact in the macroscopic limit, and that relaxation behavior of the domains can be seen in the breakdown of the finite-size scaling required by that random-matrix theory.

Probability Estimation in the Framework of Intuitionistic Fuzzy Evidence Theory

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Yafei Song

2015-01-01

Full Text Available Intuitionistic fuzzy (IF evidence theory, as an extension of Dempster-Shafer theory of evidence to the intuitionistic fuzzy environment, is exploited to process imprecise and vague information. Since its inception, much interest has been concentrated on IF evidence theory. Many works on the belief functions in IF information systems have appeared. Although belief functions on the IF sets can deal with uncertainty and vagueness well, it is not convenient for decision making. This paper addresses the issue of probability estimation in the framework of IF evidence theory with the hope of making rational decision. Background knowledge about evidence theory, fuzzy set, and IF set is firstly reviewed, followed by introduction of IF evidence theory. Axiomatic properties of probability distribution are then proposed to assist our interpretation. Finally, probability estimations based on fuzzy and IF belief functions together with their proofs are presented. It is verified that the probability estimation method based on IF belief functions is also potentially applicable to classical evidence theory and fuzzy evidence theory. Moreover, IF belief functions can be combined in a convenient way once they are transformed to interval-valued possibilities.

Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: theory and application to the study of chromium dimer.

Science.gov (United States)

Kurashige, Yuki; Yanai, Takeshi

2011-09-07

We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian. © 2011 American Institute of Physics

Iterative approach as alternative to S-matrix in modal methods

Science.gov (United States)

Semenikhin, Igor; Zanuccoli, Mauro

2014-12-01

The continuously increasing complexity of opto-electronic devices and the rising demands of simulation accuracy lead to the need of solving very large systems of linear equations making iterative methods promising and attractive from the computational point of view with respect to direct methods. In particular, iterative approach potentially enables the reduction of required computational time to solve Maxwell's equations by Eigenmode Expansion algorithms. Regardless of the particular eigenmodes finding method used, the expansion coefficients are computed as a rule by scattering matrix (S-matrix) approach or similar techniques requiring order of M3 operations. In this work we consider alternatives to the S-matrix technique which are based on pure iterative or mixed direct-iterative approaches. The possibility to diminish the impact of M3 -order calculations to overall time and in some cases even to reduce the number of arithmetic operations to M2 by applying iterative techniques are discussed. Numerical results are illustrated to discuss validity and potentiality of the proposed approaches.

Classical representations for quantum-like systems through an axiomatics for context dependence

International Nuclear Information System (INIS)

Coecke, B.

1997-01-01

We introduce a definition for a 'hidden measurement system', i.e., a physical entity for which there exist: (i) 'a set of non-contextual states of the entity under study' and (ii) 'a set of states of the measurement context', and which are such that all uncertainties are due to a lack of knowledge on the actual state of the measurement context. First we identify an explicit criterion that enables us to verify whether a given hidden measurement system is a representation of a given couple Σ, ε consisting of a set of states Σ and a set of measurements ε (= measurement system). Then we prove for every measurement system that there exists at least one representation as a hidden measurement system with [0, 1] as set of states of the measurement context. Thus, we can apply this definition of a hidden measurement system to impose an axiomatics for context dependence. We show that in this way we always find classical representations (hidden measurement representations) for general non-classical entities (e.g. quantum entities). (orig.)

INTRODUCTION IN TECHNOLOGY CONCEPTUALIZATION THE SUBJECT DOMAIN OF SOCIOLOGY: EXPANSION OF THE THEORY (in the example of relationship/kinship

Directory of Open Access Journals (Sweden)

A. Yu. Ivanov

2017-01-01

Full Text Available Presented article is the second of two articles, the aim of which is to introduce the reader has no special mathematical training, with the possibilities of application of mathematical methods developed in the scientific direction of “Conceptual analysis and design of systems of organizational management (CAD SOM”, designed to solve a variety of tasks, such as technical and humanitarian spheres on the basis of the proposed methodological approach to the mathematization of the theoretical knowledge. At the heart of this methodological approach is a process of conceptualization, which is understood as a theoretical study of qualitative aspects of a selected domain using mathematical forms (axiomatic theory, the locking connection between the concepts of logical derivability characterizing this subject area. Designed axiomatic theory – conceptual scheme – is the basis for building database structures, decision-making processes, a variety of phenomena subject area, structure and genesis of domain analysis and other tasks. One of the main advantages of the sending of methodological approach is the ability to work with complex regions based on the controlled synthesis tool terminal theory of conceptual schemes, explicated simple fragments of the subject area. Given the non-mathematical preparation of the reader, the contents of the methods illustrated by conceptualizing a conceptually simple subject areas – areas related relations, as well as the choice of one of the most simple goals conceptualization – structuring the domain and build a variety of its phenomena. The first article was given a brief description of mathematical methods, describes the main stages of the conceptualization of the subject areas, ranging from the definition of the boundaries of the domain and ending with the theory of the synthesis of the terminal and determine its compliance with the tasks of conceptualizing. In the chosen example – areas related relations �

Efficient perturbation theory to improve the density matrix renormalization group

Science.gov (United States)

Tirrito, Emanuele; Ran, Shi-Ju; Ferris, Andrew J.; McCulloch, Ian P.; Lewenstein, Maciej

2017-02-01

The density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. It has been applied to solve many physical problems, including the calculation of ground states and dynamical properties. In this work, we develop a perturbation theory of the DMRG (PT-DMRG) to greatly increase its accuracy in an extremely simple and efficient way. Using the canonical matrix product state (MPS) representation for the ground state of the considered system, a set of orthogonal basis functions {| ψi> } is introduced to describe the perturbations to the ground state obtained by the conventional DMRG. The Schmidt numbers of the MPS that are beyond the bond dimension cutoff are used to define these perturbation terms. The perturbed Hamiltonian is then defined as H˜i j= ; its ground state permits us to calculate physical observables with a considerably improved accuracy compared to the original DMRG results. We benchmark the second-order perturbation theory with the help of a one-dimensional Ising chain in a transverse field and the Heisenberg chain, where the precision of the DMRG is shown to be improved O (10 ) times. Furthermore, for moderate L the errors of the DMRG and PT-DMRG both scale linearly with L-1 (with L being the length of the chain). The linear relation between the dimension cutoff of the DMRG and that of the PT-DMRG at the same precision shows a considerable improvement in efficiency, especially for large dimension cutoffs. In the thermodynamic limit we show that the errors of the PT-DMRG scale with √{L-1}. Our work suggests an effective way to define the tangent space of the ground-state MPS, which may shed light on the properties beyond the ground state. This second-order PT-DMRG can be readily generalized to higher orders, as well as applied to models in higher dimensions.

Complete S-matrix of the O(2N) Gross-Neveu model

International Nuclear Information System (INIS)

Karowski, M.; Thun, H.J.

1980-11-01

We present the complete S-matrix of the O(2N) Gross-Neveu model including kinks, elementary fermions, and higher bound states. In addition to the S-matrix factorization, unitarity, and crossing conditions we make essential use of constraints which follow from the fact that particles in the spectrum are bound states of each other. A consistent solution can only be obtained if the kinks obey generalized statistics. Remarkably, some quantities related to this such as 'spins' and Klein factors show Bott periodicity. (orig.)

String Theory and M-Theory

Science.gov (United States)

Becker, Katrin; Becker, Melanie; Schwarz, John H.

String theory is one of the most exciting and challenging areas of modern theoretical physics. This book guides the reader from the basics of string theory to recent developments. It introduces the basics of perturbative string theory, world-sheet supersymmetry, space-time supersymmetry, conformal field theory and the heterotic string, before describing modern developments, including D-branes, string dualities and M-theory. It then covers string geometry and flux compactifications, applications to cosmology and particle physics, black holes in string theory and M-theory, and the microscopic origin of black-hole entropy. It concludes with Matrix theory, the AdS/CFT duality and its generalizations. This book is ideal for graduate students and researchers in modern string theory, and will make an excellent textbook for a one-year course on string theory. It contains over 120 exercises with solutions, and over 200 homework problems with solutions available on a password protected website for lecturers at www.cambridge.org/9780521860697. Comprehensive coverage of topics from basics of string theory to recent developments Ideal textbook for a one-year course in string theory Includes over 100 exercises with solutions Contains over 200 homework problems with solutions available to lecturers on-line

The Axiomatic Basis of Anticipated Utility: A Clarification

NARCIS (Netherlands)

J. Quiggin (John); P.P. Wakker (Peter)

1994-01-01

textabstractQuiggin (J. Econ. Behav. Organization3 (1982), 323-345) introduced anticipated ("rank-dependent") utility theory into decision making under risk. Questions have been raised about mathematical aspects of Quiggin′s analysis. This paper settles these questions and shows that a minor

THE AESTHETIC AXIOMATIC: DECONSTRUCTION

Directory of Open Access Journals (Sweden)

IRINA VASKES SANTCHES

2007-08-01

Full Text Available Resumen: El presente trabajo contribuye al debate sobre la actualidad estética, abordando diferentes enfoques del polémico concepto de deconstrucción, introducido por Jacques Derrida. Esta categoría es de referencia casi obligatoriacuando se habla sobre teoría estética contemporánea, forma parte de su nuevo aparato conceptual y expresa bien la nueva realidad que no tiene análogos históricos en lo que antes llamaban arte, estética y cultura. La elaboracióndel concepto de deconstrucción, el análisis de cómo funciona esa nueva forma del pensamiento crítico, y el método creativo de la interpretación y de la producción del texto artístico, nos permite entrar en el código de muchas obras artísticas actuales donde el espacio entre arte y teoría del arte es cada vez más incierto, especialmente en las diversas formas de arte conceptual o “performance art”.Abstract: Tackling polemic concept of deconstruction, introduced by Jacqes Derrida, from different approaches this article contributes to the debate on aesthetic current issues. This category is of almost obligatory reference when discussing about contemporary aesthetic theory. Deconstruction belongs to its new conceptual apparatus, and expresses well new reality that does not have historical analogy with what before was called art, aesthetics and culture. The elaboration of the concept of deconstruction, and the analysis of how this new form of strategical “procedure” of interpretation and production of the text (as textual reading is functioning allow us to enter the code of many current art works where the space between art and theory of the art is more and more uncertain, specially in the diverse forms of conceptual art or “performance art“.

Group manifold approach to gravity and supergravity theories

International Nuclear Information System (INIS)

d'Auria, R.; Fre, P.; Regge, T.

1981-05-01

Gravity theories are presented from the point of view of group manifold formulation. The differential geometry of groups and supergroups is discussed first; the notion of connection and related Yang-Mills potentials is introduced. Then ordinary Einstein gravity is discussed in the Cartan formulation. This discussion provides a first example which will then be generalized to more complicated theories, in particular supergravity. The distinction between ''pure'' and ''impure' theories is also set forth. Next, the authors develop an axiomatic approach to rheonomic theories related to the concept of Chevalley cohomology on group manifolds, and apply these principles to N = 1 supergravity. Then the panorama of so far constructed pure and impure group manifold supergravities is presented. The pure d = 5 N = 2 case is discussed in some detail, and N = 2 and N = 3 in d = 4 are considered as examples of the impure theories. The way a pure theory becomes impure after dimensional reduction is illustrated. Next, the role of kinematical superspace constraints as a subset of the group-manifold equations of motion is discussed, and the use of this approach to obtain the auxiliary fields is demonstrated. Finally, the application of the group manifold method to supersymmetric Super Yang-Mills theories is addressed

Graph theory

CERN Document Server

Gould, Ronald

2012-01-01

This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S

Vertex operators, semiclassical limit for soliton S-matrices and the number of bound states in Affine Toda Field Theories

International Nuclear Information System (INIS)

Kneipp, Marco A.C.

1999-10-01

Soliton time delays and the semiclassical limit for soliton S-matrices are calculated for non-simply laced Affine Toda Field Theories. The phase shift is written as a sum over bilinears on the soliton conserved charges. The results apply to any two solitons of any Affine Toda Field Theory. As a by-product, a general expression for the number of bound states and the values of the coupling in which the S-matrix can be diagonal are obtained. In order to arrive at these results, a vertex operator is constructed, in the principal gradation, for non-simply laced affine Lie algebras, extending the previous constructions for simply laced and twisted affine Lie algebras. (author)

String Theory on AdS Spaces

NARCIS (Netherlands)

de Boer, J.

2000-01-01

In these notes we discuss various aspects of string theory in AdS spaces. We briefly review the formulation in terms of Green-Schwarz, NSR, and Berkovits variables, as well as the construction of exact conformal field theories with AdS backgrounds. Based on lectures given at the Kyoto YITP Workshop

Type II pp-wave matrix models from point-like gravitons

International Nuclear Information System (INIS)

Lozano, Yolanda; RodrIguez-Gomez, Diego

2006-01-01

The BMN Matrix model can be regarded as a theory of coincident M-theory gravitons, which expand by Myers dielectric effect into the 2-sphere and 5-sphere giant graviton vacua of the theory. In this note we show that, in the same fashion, Matrix String theory in Type IIA pp-wave backgrounds arises from the action for coincident Type IIA gravitons. In Type IIB, we show that the action for coincident gravitons in the maximally supersymmetric pp-wave background gives rise to a Matrix model which supports fuzzy 3-sphere giant graviton vacua with the right behavior in the classical limit. We discuss the relation between our Matrix model and the Tiny Graviton Matrix theory

Low Complexity Precoder and Receiver Design for Massive MIMO Systems: A Large System Analysis using Random Matrix Theory

KAUST Repository

Sifaou, Houssem

2016-01-01

transceivers. Using tools from random matrix theory, we determine deterministic approximations of the SINR and the transmit power in the asymptotic regime. Then, the optimal per-user weight coe cients that solve the max-min SINR problem are derived

Husserl’s theory of noematic sense

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Nikolić Olga

2016-01-01

Full Text Available After Husserl’s transcendental turn and the discovery of the correlation between consciousness and the world the concept of the noema becomes one of the constant leitmotifs of Husserl’s philosophy. My paper will be devoted to the clarification of this concept and its implications for Husserl’s theory of sense. The leading question will be: How can the noema play the role of both the sense and the objective correlate of the intentional act? I will start with presenting the problematic of sense in Husserl’s phenomenology from the Logical Investigations to the Ideas I. The central part of my paper will be devoted to the influential debate regarding the interpretation of the noema. Finally, I intend to point out the most important ways in which the notion of the noema becomes enriched in later Husserl’s philosophy, as well as the difference between linguisitic and non-linguistic sense, based on the Analyses Concerning Passive and Active Synthesis. I hope to show that Husserl’s phenomenological theory of sense offers a valuable alternative to the exclusively language-oriented theories of sense. [This paper is the abridged and reworked version of my Master’s Thesis "Husser’s Notion of the Noema: The Phenomenological Theory of Sense" defended at KU Leuven in January 2016.

Axiomatic field theory and quantum electrodynamics: the massive case. [Gauge invariance, Maxwell equations, high momentum behavior

Energy Technology Data Exchange (ETDEWEB)

Steinmann, O [Bielefeld Univ. (F.R. Germany). Fakultaet fuer Physik

1975-01-01

Massive quantum electrodynamics of the electron is formulated as an LSZ theory of the electromagnetic field F(..mu nu..) and the electron-positron fields PSI. The interaction is introduced with the help of mathematically well defined subsidiary conditions. These are: 1) gauge invariance of the first kind, assumed to be generated by a conserved current j(..mu..); 2) the homogeneous Maxwell equations and a massive version of the inhomogeneous Maxwell equations; 3) a minimality condition concerning the high momentum behaviour of the theory. The inhomogeneous Maxwell equation is a linear differential equation connecting Fsub(..mu nu..) with the current Jsub(..mu..). No Lagrangian, no non-linear field equations, and no explicit expression of Jsub(..mu..) in terms of PSI, anti-PSI are needed. It is shown in perturbation theory that the proposed conditions fix the physically relevant (i.e. observable) quantities of the theory uniquely.

Moyal Deformations of Gravity via SU ( N ) Gauge Theories, Branes and Topological Chern-Simons Matrix Models