NANOCOMPUTING. Computational Physics for Nanoscience and Nanotechnology

Transcription

1 NANOCOMPUTING Computational Physics for Nanoscience and Nanotechnology

2 NANOCOMPUTING Computational Physics for Nanoscience and Nanotechnology James J Y Hsu National Cheng Kung University, Taiwan National Tsing Hua University, Taiwan

3 Published by Pan Stanford Publishing Pte. Ltd. Penthouse Level, Suntec Tower 3 8 Temasek Boulevard Singapore [email protected] Web: British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. NANOCOMPUTING Computational Physics for Nanoscience and Nanotechnology Copyright 2009 by Pan Stanford Publishing Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN (Hardcover) ISBN (ebook) Printed in Singapore.

4 PREFACE The contents of this book are based on the material of Nano Computing course I taught at National Tsing Hua University since Nanotechnology is catching attention and gaining importance in both academia and industry alike, and students are very much interested in this emerging topic. There is the need to have a coherent presentation on the related disciplines, namely, theoretical physics, computer science, applied mathematics, and engineering study. In considering the importance of the four technologies for the future, Nano Technology (NT), Biomedical Technology (BT), Information Technology (IT), and Ecology Technology (ET), the course is designed to give breadth on related subjects, but keep depth on computation and physics. On the theoretical side, we cover the Mesoscopic Physics and Nonlinear Many Body Physics. On the computer science, Object Oriented Programming and Parallel Computing are incorporated. On the applied mathematics, Asymptology and Algorithm are reviewed. For the engineering training, some applications and MATLAB are presented. Students are introduced to the multiscales and multisciences from this book, and are requested to solve all the problems by either MATLAB or C++. The target audience for the book is students at the senior and graduate level. The emphasis of this book is to teach students to solve problems from the features and characteristics of the problem itself, and not from a presumed methodology or a predefined tool. It tries

5 Preface to avoid the students from falling into the mind frame of what the old saying, If you are a hammer, everything else is a nail. The rightful problem solving mentality is let the problem reveal where the solution might be, and study the clues to find the answers. Therefore, start from the asymptotic analysis once the problem is translated into a mathematical equation, and get all the hints possible even if a numerical solution is inevitable. This book is organized as follows: It introduces the issues in nanoscience, reviews the mathematical tools both numerical and analytical, and then applies the tools to more advanced problems through a repetition of the ideas and an increase in the level of sophistication so as to allow a deeper understanding of the physics and the problem solving techniques. Finally, it applies the scientific knowledge for practical applications. The ultimate goal of this book is to prepare students with enough background to start working on a research dissertation in theoretical nanoscience. James J. Y. Hsu March 2008 viii James J Y Hsu

6 ACKNOWLEDGEMENTS I would like to thank Professor T. L. Lin for suggesting the course title, and ESS faculty and students for giving me the opportunity to teach this course. The interaction with Professor C. H. Tsai s Carbon Nanotube group was most beneficial. Many insightful help from colleagues, post-doctors and students at both NCKU and NTHU are gratefully acknowledged. Some derivations and programs were aided byyee Mou Kao,Young-Chung Hsue, Chun Hung Lin, Eugene Pogorelov, Chieh-Wen Lo, Ying-Chi Chung, Chi-Yeh Chen, Robert Weng, Wellin Yang, Lichung Ko, and Cheng Hao Wu. This book was proofread by Dr. Fay Sheu. I also thank my wife, Dr. Yen-Hwa Hsu, and my daughters, Ingrid and Jessica, for their support to let me concentrate on research in Taiwan for the past few years.

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8 CONTENTS Preface v Acknowledgement vii Chapter One Little Big Science Tools for Measurement To See is to Believe Carbon Tells Us First Mother Nature Knows Best Challenges in the New Millennium Chapter Two Tools for Analysis MATLAB Program Control Asymptology Chapter Three Mesoscopic Systems Review on Quantum Physics Quantum Chemistry Molecular Biology Condensed Matter Physics Chapter Four Analytical Chapter Multiple Time Scales Multiple Space Scales...124

9 Contents Chapter Five Numerical Chapter Recursion and Divide-and-Conquer Probabilistic Algorithm Evaluation and Search Molecular Dynamics Finite Element Method Chapter Six Nonlinear Many Body Physics and Transport Density Functional Theory Correlation and Coherence Green s Function Method Transport Chapter Seven OOP, MPI and Parallel Computing C++ and Object Oriented Programming Message Passing Interface OpenMP Chapter Eight Low Dimensionality and Nanostructures Quantum Dot and Quantum Wire Nanostructure Electronic Properties Chapter Nine Special Topics Plasmon Quantum Hall Effect Chaos and Stochasticity x James J Y Hsu

10 Contents Chapter Ten Applications Carbon Nanotube Water Dynamics Molecular Computer References 333 Function Index 345 Author Index 349 Keyword Index 353 Nano Computing xi

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