Application of Integrable Systems to Phase Transitions - Hardcover

Wang, C.B.

Hardcover

ISBN 10: 3642385648 ISBN 13: 9783642385643

Publisher: Springer, 2013

Synopsis

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.

About this title

About the Author

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

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2013
• Language: English
• ISBN 10: 3642385648
• ISBN 13: 9783642385643
• Binding: Hardcover
• Number of pages: 229