Introduction to Conformal Invariance and Its Applications to Critical Phenomena

Introduction to Conformal Invariance and Its Applications to Critical Phenomena
Title Introduction to Conformal Invariance and Its Applications to Critical Phenomena PDF eBook
Author Philippe Christe
Publisher Springer Science & Business Media
Pages 260
Release 2008-09-11
Genre Science
ISBN 3540475753

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The history of critical phenomena goes back to the year 1869 when Andrews discovered the critical point of carbon dioxide, located at about 31°C and 73 atmospheres pressure. In the neighborhood ofthis point the carbon dioxide was observed to become opalescent, that is, light is strongly scattered. This is nowadays interpreted as comingfrom the strong fluctuations of the system close to the critical point. Subsequently, a wide varietyofphysicalsystems were realized to display critical points as well. Ofparticular importance was the observation of a critical point in ferromagnetic iron by Curie. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and may even extend to the quark-gluon plasmaand the early universe as a whole. Early theoretical investigationstried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations and culminating in Landau's general theory of critical phenomena. In a dramatic development, Onsager's exact solutionofthe two-dimensional Ising model made clear the important role of the critical fluctuations. Their role was taken into account in the subsequent developments leading to the scaling theories of critical phenomena and the renormalization group. These developements have achieved a precise description of the close neighborhood of the critical point and results are often in good agreement with experiments. In contrast to the general understanding a century ago, the presence of fluctuations on all length scales at a critical point is today emphasized.

Conformal Invariance and Critical Phenomena

Conformal Invariance and Critical Phenomena
Title Conformal Invariance and Critical Phenomena PDF eBook
Author Malte Henkel
Publisher Springer Science & Business Media
Pages 433
Release 2013-03-14
Genre Science
ISBN 3662039370

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Critical phenomena arise in a wide variety of physical systems. Classi cal examples are the liquid-vapour critical point or the paramagnetic ferromagnetic transition. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and fully developed tur bulence and may even extend to the quark-gluon plasma and the early uni verse as a whole. Early theoretical investigators tried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations, culminating in Landau's general theory of critical phenomena. Nowadays, it is understood that the common ground for all these phenomena lies in the presence of strong fluctuations of infinitely many coupled variables. This was made explicit first through the exact solution of the two-dimensional Ising model by Onsager. Systematic subsequent developments have been leading to the scaling theories of critical phenomena and the renormalization group which allow a precise description of the close neighborhood of the critical point, often in good agreement with experiments. In contrast to the general understanding a century ago, the presence of fluctuations on all length scales at a critical point is emphasized today. This can be briefly summarized by saying that at a critical point a system is scale invariant. In addition, conformal invaTiance permits also a non-uniform, local rescal ing, provided only that angles remain unchanged.

Introduction to Conformal Invariance and Its Applications to Critical Phenomena

Introduction to Conformal Invariance and Its Applications to Critical Phenomena
Title Introduction to Conformal Invariance and Its Applications to Critical Phenomena PDF eBook
Author Philippe Christe
Publisher
Pages 260
Release 1993
Genre Conformal invariants
ISBN

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Conformal Invariance And Applications To Statistical Mechanics

Conformal Invariance And Applications To Statistical Mechanics
Title Conformal Invariance And Applications To Statistical Mechanics PDF eBook
Author C Itzykson
Publisher World Scientific
Pages 992
Release 1998-09-29
Genre
ISBN 9814507598

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This volume contains Introductory Notes and major reprints on conformal field theory and its applications to 2-dimensional statistical mechanics of critical phenomena. The subject relates to many different areas in contemporary physics and mathematics, including string theory, integrable systems, representations of infinite Lie algebras and automorphic functions.

Chaos, Kinetics and Nonlinear Dynamics in Fluids and Plasmas

Chaos, Kinetics and Nonlinear Dynamics in Fluids and Plasmas
Title Chaos, Kinetics and Nonlinear Dynamics in Fluids and Plasmas PDF eBook
Author Sadruddin Benkadda
Publisher Springer Science & Business Media
Pages 462
Release 1998-07-16
Genre Science
ISBN 9783540646358

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Over the last few years it has become apparent that fluid turbulence shares many common features with plasma turbulence, such as coherent structures and self-organization phenomena, passive scalar transport and anomalous diffusion. This book gathers very high level, current papers on these subjects. It is intended for scientists and researchers, lecturers and graduate students because of the review style of the papers.

Inverse and Algebraic Quantum Scattering Theory

Inverse and Algebraic Quantum Scattering Theory
Title Inverse and Algebraic Quantum Scattering Theory PDF eBook
Author Barnabas Apagyi
Publisher Springer
Pages 402
Release 2013-12-30
Genre Science
ISBN 3662141450

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This volume contains three interrelated, beautiful, and useful topics of quantum scattering theory: inverse scattering theory, algebraic scattering theory and supersymmetrical quantum mechanics. The contributions cover such issues as coupled-channel inversions at fixed energy, inversion of pion-nucleon scattering cross-sections into potentials, inversions in neutron and x-ray reflection, 3-dimensional fixed-energy inversion, inversion of electron scattering data affected by dipole polarization, nucleon-nucleon potentials by inversion versus meson-exchange theory, potential reversal and reflectionless impurities in periodic structures, quantum design in spectral, scattering, and decay control, solution hierarchy of Toda lattices, etc.

From Instability to Intelligence

From Instability to Intelligence
Title From Instability to Intelligence PDF eBook
Author Michail Zak
Publisher Springer Science & Business Media
Pages 559
Release 2008-12-11
Genre Science
ISBN 3540691219

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So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality. -A. Einstein The word "instability" in day-to-day language is associated with some thing going wrong or being abnormal: exponential growth of cancer cells, irrational behavior of a patient, collapse of a structure, etc. This book, however, is about "good" instabilities, which lead to change, evolution, progress, creativity, and intelligence; they explain the paradox of irreversi bility in thermodynamics, the phenomena of chaos and turbulence in clas sical mechanics, and non-deterministic (multi-choice) behavior in biological and social systems. The concept of instability is an attribute of dynamical models that de scribe change in time of physical parameters, biological or social events, etc. Each dynamical model has a certain sensitivity to small changes or "errors" in initial values of its variables. These errors may grow in time, and if such growth is of an exponential rate, the behavior of the variable is defined as unstable. However, the overall effect of an unstable variable upon the dynamical system is not necessarily destructive. Indeed, there al ways exists such a group of variables that do not contribute to the energy of the system. In mechanics such variables are called ignorable or cyclic.