Application of Integrable Systems to Phase Transitions

ISBN-13: 9783642440243 / Angielski / Miękka / 2015 / 219 str.

C. B. Wang

Opis

This book practical book applies integrable systems to solve the phase transition problems. It provides a unified model for the densities of eigenvalues in quantum chromodynamics (QCD).

Recenzje

From the book reviews:

"The author addresses a large variety of integrable systems, their remarkable connections to orthogonal polynomials and to string equations, and the ensuing consequences for the associated free energies and critical behavior near phase transitions. This text contains much useful information and relevant techniques for researchers interested in specific integrable model systems whose features might be of relevance for some aspects of fundamental particle theory." (Uwe C. Täuber, Mathematical Reviews, July, 2014)

Spis treści

Introduction.- Densities in Hermitian Matrix Models.- Bifurcation Transitions and Expansions.- Large-N Transitions and Critical Phenomena.- Densities in Unitary Matrix Models.- Transitions in the Unitary Matrix Models.- Marcenko-Pastur Distribution and McKay’s Law.

O autorze

The author obtained his Ph.D in mathematics at University of Pittsburgh in 1998. Then he worked at University of California, Davis, as a visiting research assistant professor for one year before he started working in industry.  The Marcenko-Pastur distribution in econophysics inspired him to search a unified model for the eigenvalue densities in the matrix models. The phase transition models discussed in this book are based on the Gross-Witten third-order phase transition model and the researches on transition problems in complex systems and data clustering.  He is now a data scientist at Institute of Analysis, MI, USA. Email: chiebingwang@yahoo.com

Blurb

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.