Statistics of Knots and Entangled Random

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In this book, the author announces the class of problems called “entropy of knots” and gives an overview of modern physical applications of existing topological invariants.He constructs statistical models on knot diagrams and braids using the repres…
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    Om Statistics of Knots and Entangled Random

    In this book, the author announces the class of problems called “entropy of knots” and gives an overview of modern physical applications of existing topological invariants.He constructs statistical models on knot diagrams and braids using the representations of Jones–Kauffman and Alexander invariants and puts forward the question of limit distribution of these invariants for randomly generated knots. The relation of powers of corresponding algebraic invariants to the Lyapunov exponents of the products of noncommutative matrices is described. Also the problem of conditional joint limit distributions for “ brownian bridges” on braids is discussed. Special cases of noncommutative groups PSL(2,R), PSL(2,Z) and braid groups are considered in detail.In this volume, the author also discusses the application of conformal methods for explicit construction of topological invariants for random walks on multiconnected manifolds. The construction of these topological invariants and the monodromy properties of correlation function of some conformal theories are also discussed.The author also considers the physical applications of “knot entropy” problem in various physical systems, focussing on polymers.Contents:Knot Diagrams as Disordered Spin Systems:Introduction: Statistical Problems in TopologyReview of Abelian Problems in Statistics of Entangled Random Walks and Incompleteness of Gauss InvariantNonabelian Algebraic Knot InvariantsLattice Knot Diagrams as Disordered Potts ModelAnnealed and Quenched Realizations of Topological DisorderRandom Walks on Local Noncommutative Groups:IntroductionBrownian Bridges on Simplest Noncommutative Groups and Knot StatisticsRandom Walks on Locally Free GroupsBrownian Bridges on Lobachevskii Plane and Products of Noncommutative Random MatricesConformal Methods in Statistics of Entangled Random Walks:Introduction: Random Walk with Topological ConstraintsConstruction of Nonabelian Connections for Γ2 and PSL(2,Z) from Conformal MethodsRandom Walk on Double Punctured Plane and Conformal Field TheoryStatistics of Random Walks with Topological Constraints in 2D Lattice of ObstaclesPhysical Applications:Introduction: Polymer Language in Statistics of Entangled Chain-Like ObjectsPolymer Chain in 3D Array of Obstacles: Critical Exponents for Gyration RadiusHigh Elasticity of Polymer NetworksCollapsed Phase of Unknotted PolymerOrdering Phase Transition in Entangled “Directed Polymers”Readership: Mathematicians, mathematical physicists and polymer physicists.Key Features:In the present textbook/monograph, the concept of “optomechanics” is extended to “generalized optomechanics”Some quantum optical devices are proposed based on generalized optomechanical system in all-optical domain which merges optics and condensed matter science together and brings the field of light speed manipulation into a new chapter

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    Detaljer

    Format
    E-Bok
    Filformat
    PDF
    Utgivelsesår
    1996
    Forlag
    World Scientific Publishing Co
    Språk
    Engelsk
    ISBN
    9789812830463
    Sider
    204

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