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Kharkov Series in Physics and Mathematics

Kharkov Series in Physics and Mathematics


Series Editors: V.V. Eremenko, L. A. Pastur, V. A. Sirenko

Institute of Low Temperature Physics and Engineering,

National Academy of Sciences of Ukraine, Kharkov.


Editorial Board: G. Feldman, I. Galetich, M. Sherbina


Introduction to the series

This new international book series entitled Kharkov Series in Physics and Mathematics provides a unique medium for the publication of high quality original monographs, multiauthor volumes and reference texts in priority research areas of physics and mathematics for graduate, postgraduate and research/professional readership. The Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, Kharkov has had a long and outstanding tradition in research in physics and mathematics, and is particularly associated with the classical studies and publications of L.D.Landau, L.V.Shubnikov, M.Ostrogradskii, A.Lyapunov and V.Steklov and more recently with the achievements of I.M.Lifshitz, A.I.Akhiezer, V.A.Marchenko, A.V.Pogorelov and V.Drinfeld. Continuing this tradition, this book series will publish and highlight research areas including: condensed matter (theory and experiment), superconductivity, low temperature magnetism and interaction of radiation with matter, cryocrystals, point-contact, optical and magnetic resonance spectroscopies, quantum phase transition, geometry and topology, complex analysis, mathematical modeling, statistical methods in mathematical physics.

Random Finite-Valued Dynamical Systems: Additive Markov Approach 
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Hbk        176pp       2009


O. V. Usatenko, S. S. Apostolov, Z. A. Mayzelis and S. S. Melnik, Institute for Radiophysics and Electronics, Kharkov, Ukraine.



This volume reviews one of the topical areas of research on random discrete dynamic systems from the common standpoint of multistep Markov chains. The authors present a new efficient tool for studying the random systems with a long-range memory which enables a number of crucial theoretical and applications issues to be solved. The proposed methods of constructing sequences with prescribed correlation properties make it possible to design real physical systems (antennas, waveguides, diffraction gratings, multilayered systems) with required spectral characteristics. The problem of generating random sequences is closely linked to forecasting. Therefore this book provides a useful reference for graduates, researchers and professionals in the study of prediction issues in meteorology, sociology, economics and financial areas (technical analysis for traders).


Wave Diffraction by Periodic Multilayer Structures 
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Hbk        164pp       2011


L. M. Lytvynenko and S. L. Prosvirnin Institute of Radioastronomy, Kharkov, Ukraine



This volume offers a new approach to constructing the theory of electromagnetic wave interaction (propagation and scattering) with periodic sequences of screens. The crucial point of the method is an embedding of reflection operator of semi-infinite layered complex structure into the theory of wave scattering. This new technique is applied to the solution of electromagnetic wave scattering by different kinds of periodic structures and includes the investigation of the diffractional properties of multilayer sequences of two-dimensional periodic plane screens. The volume provides a useful reference for radiophysicists and radioengineers and for researchers working in areas of applied physics including acoustics, aero- and hydrodynamics.


Regular and Chaotic Classical and Quantum Dynamics in Multi-well Potentials 
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Hbk        160pp       2013


V. P. Berezovoj, Yu. L. Bolotin, V. A. Cherkaskiy, G. I. Ivashkevich, Kharkov Institute of Physics and Technology, Kharkov, Ukraine



This review is based mainly on the results of the authors original research and considers classical chaos and quantum manifestations of classical stochasticity in two-dimensional potentials with non-trivial topology. Non-linear models with complicated multi-well shape of potential energy surface represent the common case situation and they are used in many important processes in real systems, such as chemical reactions, phase transitions, nuclear reactions and decay of superdeformed nuclei. There is increasing world-wide interest in non-linear dynamics, and this volume provides a useful reference and guide to the exciting topic of classical and quantum chaos. The book is intended for a wide audience of readers who are familiar with the basics of classical and quantum mechanics.


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Hbk        330pp       2010


A. A. Zvyagin, Institute for Low Temperature Physics and Engineering, Kharkov, Ukraine


This volume is presented in three parts and it reviews the main features of the theory of one-dimensional quantum insulating magnetic systems.

Part I: provides a general introduction to the theory of quantum magnets .

Part II: introduces the study of one-dimensional spin systems using special theoretical techniques and presents important exact theoretical results devoted to spin chain models.

Part III: discusses applications of exact results for more realistic models of quasi-one-dimensional magnets and introduces main approximations used in modern theory of one-dimensional magnets


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