Nonlinear Adiabatic Evolution of Quantum Systems Geometric Phase and
This book systematically introduces the nonlinear adiabatic evolution theory of quantum many-body systems. The nonlinearity stems from a mean-field treatment of the interactions between particles, and the adiabatic dynamics of the system can be accurately
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Nonlinear Adiabatic Evolution of Quantum Systems Geometric Phase and Virtual Magnetic Monopole
Nonlinear Adiabatic Evolution of Quantum Systems
Jie Liu Sheng-Chang Li Li-Bin Fu Di-Fa Ye •
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Nonlinear Adiabatic Evolution of Quantum Systems Geometric Phase and Virtual Magnetic Monopole
123
Jie Liu Institute of Applied Physics and Computational Mathematics Beijing, China Sheng-Chang Li Xi’an Jiaotong University Xi’an, China
Li-Bin Fu China Academy of Engineering Physics Beijing, China Di-Fa Ye Institute of Applied Physics and Computational Mathematics Beijing, China
ISBN 978-981-13-2642-4 ISBN 978-981-13-2643-1 https://doi.org/10.1007/978-981-13-2643-1
(eBook)
Library of Congress Control Number: 2018955156 © Springer Nature Singapore Pte Ltd. 2018 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, express 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 Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Preface
Adiabatic theory of both classical and quantum systems plays an important role in addressing various problems with multi-time-scale characteristics, ranging from atomic and molecular processes to the evolution of the universe. In the classical case, the well-known adiabatic theorem states, in terms of action-angle variables, that the action is the adiabatic invariant and that if the Hamiltonian is taken around a given cycle in parameter space, then the angle variable conjugate to the action acquires a purely geometrical quantity, which is termed the Hannay angle. The adiabatic theorem of quantum systems, however, becomes much more intricate due to the involvement of the complex-valued wave function/probability amplitude. A complete theory for the adiabatic evolution of quantum systems rests on three pillars. First, Born and Fock proved the quantum adiabatic th
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