Solitons in Molecular Systems - A. S. Davydov

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Résumé :
Approach your problems from the It isn't that they can't see the end and begin with the answers. solution. It is that they can't Then one day, perhaps you will see the problem. find the final question. G.K. Chesterton. The Scandal of 'The Hermit Clad in Crane Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono? graphs and textbooks on increasingly topics. However, the tree of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro? gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electric engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as complete integrable systems, chaos, synergetics and large-scale order, which are almost impossible to fit into the existing classifica? tion schemes. The draw upon widely different sections of mathematics.

Sommaire:
I. Collective Excitations in Quasi-Periodical Molecular Structures.- II. Excitations of Solitons in One-Dimensional Molecular Systems.- III. Dynamical Properties of Solitons.- IV. Solitons in Molecular Systems With Nonlinear Intermolecular Interactions.- V. Super-Sound Acoustic Solitons.- VI. Theory of Electron Transfer by Solitons.- VII. Space-Periodic Excitations in Nonlinear Systems.- VIII. Long Waves in Nonlinear Media with Cubic Dispersion.- IX the Nonlinear Sine-Gordon Equation.- X. Some Nonlinear Phenomena in Solids.- XI. Conformal Excitations in One-Dimensional Molecular Systems.- XII. Solitons and Proton Motion in Molecular Systems with Hydrogen Bonds.- XIII. Three-Dimensional Soliton (Polarons) in Ionic Crystal.- Appendix A. Coherent Phonon States in One-Dimensional Systems.- Al. Free Vibrations. Phonons.- A2. Vibrations of Atoms in the Presence of External Force.- A3. Virtual Phonons. Coherent States.- A4. Coherent States: Different Representations.- A5. General Properties of Coherent States.- A6. The Time-Dependent Evolution of Coherent States.- A7. Evaluation of Thermodynamical Averages.- Appendix B. Elementary Information of the Jacobian Elliptic Functions.- Appendix C. Elementary Data on the Jacobi Theta Functions.- C1. Relation of Theta Functions to Elliptic Functions and Integrals.- Appendix D. Solitons and the Molecular Mechanism of the Action of Microwave Radiation on Living Cells.- Appendix E. Subsonic and Supersonic Solitons in Quasi-One-Dimensional Molecular Structures.- E1. Basic Equations.- E2. An Integral Equation for the Case of Dispersion and Anharmonicity.- E3. Subsonic and Supersonic Solutions of the First Kind.- E4. Supersonic Solitons of the Second Kind.- Notes.- Additional Bibliography.