Complex Phenomena in Nanoscale Systems NATO Science for Peace and Security Series This Series presents the results of scientific meetings supported under the NATO Programme: Science for Peace and Security (SPS). The NATO SPS Programme supports meetings in the following Key Priority areas: (1) Defence Against Terrorism; (2) Countering other Threats to Security and (3) NATO, Partner and Mediterranean Dialogue Country Priorities. The types of meeting supported are generally "Advanced Study Institutes" and "Advanced Research Workshops". The NATO SPS Series collects together the results of these meetings. The meetings are co- organized by scientists from NATO countries and scientists from NATO's "Partner" or "Mediterranean Dialogue" countries. The observations and recommendations made at the meetings, as well as the contents of the volumes in the Series, reflect those of parti- cipants and contributors only; they should not necessarily be regarded as reflecting NATO views or policy. Advanced Study Institutes (ASI) are high-level tutorial courses intended to convey the latest developments in a subject to an advanced-level audience Advanced Research Workshops (ARW) are expert meetings where an intense but informal exchange of views at the frontiers of a subject aims at identifying directions for future action Following a transformation of the programme in 2006 the Series has been re-named and re-organised. Recent volumes on topics not related to security, which result from meetings supported under the programme earlier, may be found in the NATO Science Series. The Series is published by IOS Press, Amsterdam, and Springer, Dordrecht, in conjunction with the NATO Public Diplomacy Division. Sub-Series A. Chemistry and Biology Springer B. Physics and Biophysics Springer C. Environmental Security Springer D. Information and Communication Security IOS Press E. Human and Societal Dynamics IOS Press http://www.nato.int/science http://www.springer.com http://www.iospress.nl Series B: Physics and Biophysics Complex Phenomena in Nanoscale Systems edited by Giulio Casati Center for Linear and Complex Systems, Como, Italy and Davron Matrasulov Heat Physics Department, Uzbek Academy of Sciences Tashkent, Uzbekistan Published in cooperation with NATO Public Diplomacy Division Proceedings of the NATO Advanced Research Workshop on Recent Advances in Nonlinear Dynamics and Complex System Physics: From Natural to Social Sciences and Security Tashkent, Uzbekistan 12 – 17 October 2008 Library of Congress Control Number: 2009929397 ISBN 978-90-481-3119-8 (PB) ISBN 978-90-481-3118-1 (HB) ISBN 978-90-481-3120-4 (e-book) Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com Printed on acid-free paper All Rights Reserved © Springer Science + Business Media B.V. 2009 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. PREFACE The objective of this NATO Advanced Research Workshop on “Recent Advances in Nonlinear Dynamics and Complex System Physics” was to bring together researchers working in different areas of nonlinear dynamics and its application to various topics such as nanoscale physics, cold atoms, Bose-Einstein condensates, quantum information, non-equilibrium systems and econophysics. Most of the talks were concentrated on quantum trans- port and nonlinear phenomena in nanostructures and cold atom systems, including quantum dots, graphene and trapped cold atoms. Special attention was brought to possible practical applications in nano-scale physics and engineering. A special feature of the meeting was the fact that most of the speakers and participants were young researchers who presented interesting talks in different areas. Over a total of 55 talks, 28 were 50-min talks by well known scientists while the other talks were half-hour ones, mostly by young researchers. Panel discussions have attracted a broad audience of theoretical and ex- perimental physicists interested in a deeper understanding of various partic- ular aspects and recent progress on the topics of the meeting. A round table discussion has been organized on the final day of the conference in order to comment on the conference talks and to present concluding remarks. The workshop has been wonderfully and efficiently organized by the local committee chaired by P.K. Khabibullaev and with K. Nakamura, A.A. Saidov, Kh.Yu. Rakhimov, U. Salomov, G. Milibaeva as members. A group of PhD students from the Heat Physics Department helped for several and important organizational matters. Our special thanks go to Olga Karpova for her help with the secretarial duties before, during and after the conference. We would like to thanks also Khakim Butanov, Nurmukhammad Iskandarov and Hamid Yusupov for their valuable assistance in the preparation of the proceedings of the conference. Finally, we wish to thank NATO Science for Peace and Security Program for the financial support. Additional support was provided by the Heat Physics Department of the Uzbek Academy of Sciences and Physical Society of Uzbekistan. Como, Italy Giulio Casati Tashkent, Uzbekistan Davron Matrasulov v CONTENTS Preface v List of Contributors ix M.D. Croitoru, A.A. Shanenko, and F.M. Peeters/ Tuning the Superconducting Properties of Nanomaterials 1 M. Hentschel and T.-Y. Kwon/Optical Microcavities of Spiral Shape: From Quantum Chaos to Directed Laser Emission 15 S. Schmidt and Y. Alhassid/ Mesoscopic Interplay of Superconductivity and Ferromagnetism in Ultra-Small Metallic Grains 25 H.L. Calvo, H.M. Pastawski, and R.A. Jalabert/ Time-Reversal Mirrors in Chaotic Cavities 37 O. Giraud, B. Georgeot, and J. Martin/ Entanglement and Localization of Wavefunctions 51 M. Robnik and V.G. Romanovski/ Exact Analysis of Adiabatic Invariants in Time Dependent Harmonic Oscillator 65 P. Schmelcher, F. Lenz, D. Matrasulov, Z.A. Sobirov, and S.K. Avazbaev/ Time-Dependent Quantum Billiards 81 D. Ullmo/ Screening of the Coulomb Interaction in a Generic Ballistic Quantum Dot 97 T.S. Monteiro, A. Rancon, and J. Ruostekoski/ Kicked Bose– Einstein Condensates: In Search of Exponential Instability 109 A.F. Sadreev/ Vortices in the Ground State of Spinor Bose–Einstein Condensates 121 K. Nakamura/ Nonlinear Dynamics of Wave Packets and Vortices in Bose–Einstein Condensates 137 B. Kubala, M. Ludwig, and F. Marquardt/ Optomechanics 153 vii viii CONTENTS A. Rakhimov and Z. Narzikulov/ Hohenberg–Martin Dilemma for Bose Condensed Systems and its Solution 165 B.S. Kandemir/ Phonons and Electron–Phonon Interactions in Single-Walled Achiral Carbon Nanotubes 177 Sh. Masuda and K. Nakamura/ Fast-Forward Problem in Microscopic and Macroscopic Quantum Mechanics 183 F.Kh. Abdullaev, R.M. Galimzyanov, and Kh.N. Ismatul- laev/ Collective Oscillations of a Quasi One Dimensional Bose Condensate Under Damping 189 U.R. Salomov, D. Matrasulov, and N.E. Iskandarov/ Nonlinear Dynamics of the Kicked Square Billiard 197 V.I. Kuvshinov, A.V. Kuzmin, and V.A. Piatrou/ Chaotic Instantons and Exponential Widening of the Ground Quasienergy Doublet in Kicked Double Well Potential 203 F. Lenz, C. Petri, F.N.R. Koch, and P. Schmelcher/ A Fresh View on Fermi Acceleration in Driven Two-Dimensional Billiards 209 Z.A. Sobirov, D. Matrasulov, Sh. Ataev, and H. Yusupov/ Time De- pendent Neutrino Billiards 215 B.L. Oksengendler, N.N. Turaeva, and A. Zakhidov/ Statistic Theory of Multiple Exciton Generation in Quantum Dot Based Solar Cells 223 A.E. Atamuratov/ Modelling of Quantum Wires in the Interface Layer of the Semiconductor-Oxide Structures with Charge Built in Oxide 229 T. Miyaguchi/ Nonlinear Responses in Hard Disk Systems 237 H. Tutu/ Stochastic Landau–Lifshitz–Gilbert Equation with Delayed Feedback Field: Efficiency for Maintaining a UPO 245 K. Kudo and T.S. Monteiro/ Spin Dynamics and Quantum Transport in Quantum Spin Chains Under an Oscillating Field 253 S.K. Avazbaev and D. Delande/ Extraction of Partial Waves and Fluxes of the Hydrogen Atom in a Strong Magnetic Field Using the Complex Rotation Method 259 T. Monnai/Markovian Limit of a Spatio-Temporal Correlated Open Systems 265 Index 273 LIST OF CONTRIBUTORS F.Kh. Abdullaev Physical-Technical Institute of the Academy of Sciences, G. Mavlyanov 2-b, Tashkent 100084, Uzbekistan Y. Alhassid Center for Theoretical Physics, Yale University, New Haven, Connecticut 06520, U.S.A. Sh. Ataev Heat Physics Department of the Uzbek Academy of Sciences, 28 Katartal Street, 100135 Tashkent, Uzbekistan Atabek E. Atamuratov Urganch State University, Urganch, Uzbekistan x LIST OF CONTRIBUTORS Bertrand Georgeot Universite´ de Toulouse; UPS; Laboratoire de Physique The´orique (IRSAMC); CNRS; LPT (IRSAMC), Toulouse, France LIST OF CONTRIBUTORS xi V.I. Kuvshinov Joint Institute for Power and Nuclear Research, Krasina Streeet 99, Minsk 220109, Belarus A.V. Kuzmin Joint Institute for Power and Nuclear Research, Krasina Streeet 99, Minsk 220109, Belarus T.-Y. Kwon Max-Planck Institut fu¨r Physik Komplexer Systeme, No¨thnitzer Street 38, 01187 Dresden, Germany Florian Lenz Physikalisches Institut, Universita¨t Heidelberg, Philosophenweg 12, 69120 Heidelberg, Germany