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Application of Integrable Systems to Phase Transitions

2013-07-20 Mathematics
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Release : 2013-07-20
Genre : Mathematics
Kind : eBook
Book Rating : 656/5 ( reviews)

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Book Synopsis Application of Integrable Systems to Phase Transitions by : C.B. Wang

Download or read book Application of Integrable Systems to Phase Transitions written by C.B. Wang. This book was released on 2013-07-20. Available in PDF, EPUB and Kindle. Book excerpt: The eigenvalue densities in various matrix models in quantum chromodynamics (QCD) are ultimately unified in this book by a unified model derived from the integrable systems. Many new density models and free energy functions are consequently solved and presented. The phase transition models including critical phenomena with fractional power-law for the discontinuities of the free energies in the matrix models are systematically classified by means of a clear and rigorous mathematical demonstration. The methods here will stimulate new research directions such as the important Seiberg-Witten differential in Seiberg-Witten theory for solving the mass gap problem in quantum Yang-Mills theory. The formulations and results will benefit researchers and students in the fields of phase transitions, integrable systems, matrix models and Seiberg-Witten theory.

Theory of Phase Transitions

2014-05-20 Science
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Release : 2014-05-20
Genre : Science
Kind : eBook
Book Rating : 497/5 ( reviews)

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Book Synopsis Theory of Phase Transitions by : Ya. G. Sinai

Download or read book Theory of Phase Transitions written by Ya. G. Sinai. This book was released on 2014-05-20. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Phase Transitions: Rigorous Results is inspired by lectures on mathematical problems of statistical physics presented in the Mathematical Institute of the Hungarian Academy of Sciences, Budapest. The aim of the book is to expound a series of rigorous results about the theory of phase transitions. The book consists of four chapters, wherein the first chapter discusses the Hamiltonian, its symmetry group, and the limit Gibbs distributions corresponding to a given Hamiltonian. The second chapter studies the phase diagrams of lattice models that are considered at low temperatures. The notions of a ground state of a Hamiltonian and the stability of the set of the ground states of a Hamiltonian are also introduced. Chapter 3 presents the basic theorems about lattice models with continuous symmetry, and Chapter 4 focuses on the second-order phase transitions and on the theory of scaling probability distributions, connected to these phase transitions. Specialists in statistical physics and other related fields will greatly benefit from this publication.

Symmetries and Algebraic Structures in Physics: Integral systems, solid state physics and theory of phase transitions

1991 Mathematics
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Release : 1991
Genre : Mathematics
Kind : eBook
Book Rating : 386/5 ( reviews)

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Book Synopsis Symmetries and Algebraic Structures in Physics: Integral systems, solid state physics and theory of phase transitions by : V. V. Dodonov

Download or read book Symmetries and Algebraic Structures in Physics: Integral systems, solid state physics and theory of phase transitions written by V. V. Dodonov. This book was released on 1991. Available in PDF, EPUB and Kindle. Book excerpt:

Phase Transition Dynamics

2019-11-08 Mathematics
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Release : 2019-11-08
Genre : Mathematics
Kind : eBook
Book Rating : 606/5 ( reviews)

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Book Synopsis Phase Transition Dynamics by : Tian Ma

Download or read book Phase Transition Dynamics written by Tian Ma. This book was released on 2019-11-08. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to a comprehensive and unified dynamic transition theory for dissipative systems and to applications of the theory to a range of problems in the nonlinear sciences. The main objectives of this book are to introduce a general principle of dynamic transitions for dissipative systems, to establish a systematic dynamic transition theory, and to explore the physical implications of applications of the theory to a range of problems in the nonlinear sciences. The basic philosophy of the theory is to search for a complete set of transition states, and the general principle states that dynamic transitions of all dissipative systems can be classified into three categories: continuous, catastrophic and random. The audience for this book includes advanced graduate students and researchers in mathematics and physics as well as in other related fields. This second edition introduces a unified theory for topological phase transitions, provides a first-principle approach to statistical and quantum physics, and offers a microscopic mechanism of quantum condensates (Bose-Einstein condensation, superfluidity, and superconductivity). Reviews of first edition: “The goals of this interesting book are to derive a general principle of dynamic transitions for dissipative systems and to establish a systematic dynamic transition theory for a wide range of problems in the nonlinear sciences. ... The intended audience for this book includes students and researchers working on nonlinear problems in physics, meteorology, oceanography, biology, chemistry, and the social sciences.” (Carlo Bianca, Mathematical Reviews, December, 2014) “This is a clearly written book on numerous types of phase transitions taken in a broad sense when a dynamical dissipative system transforms from one physical state into another. ... The book is a very useful literature not only for the professionals in the field of dynamic systems and phase transitions but also for graduate students due to its interdisciplinary coverage and state-of-the-art level.” (Vladimir Čadež, zbMATH, Vol. 1285, 2014)

Phase Transitions and Relaxation in Systems with Competing Energy Scales

2012-12-06 Science
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Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 082/5 ( reviews)

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Book Synopsis Phase Transitions and Relaxation in Systems with Competing Energy Scales by : T. Riste

Download or read book Phase Transitions and Relaxation in Systems with Competing Energy Scales written by T. Riste. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Systems with competing energy scales are widespread and exhibit rich and subtle behaviour, although their systematic study is a relatively recent activity. This text presents lectures given at a NATO Advanced Study Institute reviewing the current knowledge and understanding of this fascinating subject, particularly with regard to phase transitions and dynamics, at an advanced tutorial level. Both general and specific aspects are considered, with competitions having several origins; differences in intrinsic interactions, interplay between intrinsic and extrinsic effects, such as geometry and disorder; irreversibility and non-equilibration. Among the specific physical application areas are supercooled liquids and glasses, high-temperature superconductors, flux or vortex pinning and motion, charge density waves, domain growth and coarsening, and electron solidification.

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