Phase Transition Dynamics
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 p
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ase Transition Dynamics Second Edition
Phase Transition Dynamics
Tian Ma • Shouhong Wang
Phase Transition Dynamics Second Edition
Tian Ma Department of Mathematics Sichuan University Sichuan, China
Shouhong Wang Department of Mathematics Indiana University Bloomington, IN, USA
ISBN 978-3-030-29259-1 ISBN 978-3-030-29260-7 (eBook) https://doi.org/10.1007/978-3-030-29260-7 Mathematics Subject Classification: 76xxx, 82xxx, 35Qxx, 37Lxx 1st edition: © Springer New York Heidelberg Dordrecht London 2014 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
For Li and Ping
Preface to the Second Edition
Since the publication of the first edition of this book, progresses have been made on statistical physics, quantum physics, and topological phase transitions (TPTs). It is clear now that all phase transitions in nature that we have encountered can be categorized into the following two types: (a) Dynamical phase transitions (b) Topological phase transitions The fundamental law governing a physical system is given in the form of mathematical equations, often partial differential equations (PDEs). The solutions of these equations determine the states of the system. A dynamic phase transition refers to transitions of the underlying physical system from one state to another, as the control parameter crosses certain critical threshold. The notion of dynamic phase transitions is applicable to all dissipative systems, including nonlinear dissipative systems in statistical physics, quantum physics, fluid dynamics, atmospheric and oceanic sciences, biological and chemical systems, etc. TPTs are entirely different from dynamic phase transitions. Intuitively speaking, a TPT ref
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