CONTENTS -- Preface -- CHAPTER 1 COMPUTATIONAL STUDIES OF DISCRETE BREATHERS -- 1 Introduction -- 2 A bit on numerics of solving ODEs -- 3 Observing and analyzing breathers in numerical runs -- 3.1 Targeted initial conditions -- 3.2 Breathers in transient processes -- 3.3 Breathers in thermal equilibrium -- 4 Obtaining breathers up to machine precision: Part I -- 4.1 Method No.1 - designing a map -- 4.2 Method No.2 - saddles on the rim with space-time separation -- 4.3 Method No.3 - homoclinic orbits with time-space separation -- 5 Obtaining breathers up to machine precision: Part II -- 5.1 Method No.4 - Newton in phase space -- 5.2 Method No.5 - steepest descent in phase space -- 5.3 Symmetries -- 6 Perturbing breathers -- 6.1 Linear stability analysis -- 6.2 Plane wave scattering -- 7 Breathers in dissipative systems -- 7.1 Obtaining dissipative breathers -- 7.2 Perturbing dissipative breathers -- 8 Computing quantum breathers -- 8.1 The dimer -- 8.2 The trimer -- 8.3 Quantum roto-breathers -- 9 Some applications instead of conclusions -- Acknowledgments -- References -- CHAPTER 2 VIBRATIONAL SPECTROSCOPY AND QUANTUM LOCALIZATION -- 1 Introduction -- 1.1 Nonlinear dynamics and energy localization -- 1.2 Nonlinear dynamics and vibrational spectroscopy -- 2 Vibrational spectroscopy techniques -- 2.1 Some definitions -- 2.2 Optical techniques -- 2.3 Neutron scattering techniques -- 2.4 A (not so) simple example -- 3 Molecular vibrations -- 3.1 The harmonic approximation: Normal modes -- 3.2 Anharmonicity -- 3.3 Local modes -- 3.4 Local versus normal mode separability -- 3.5 The water molecule -- 3.6 The algebraic force-field Hamiltonian -- 3.7 Other molecules -- 3.8 Local modes and energy localization -- 4 Crystals -- 4.1 The harmonic approximation: Phonons -- 4.2 Phonon-phonon interaction.

4.3 Phonon-electron interaction -- 4.4 Local modes -- 4.5 Nonlinear dynamics -- 5 Conclusion -- 5.1 Vibrational spectroscopy and nonlinear dynamics -- 5.2 Optical vibrational spectroscopy and energy localization -- 5.3 Inelastic neutron scattering spectroscopy of solitons -- 5.4 Vibrational spectroscopy and dynamical models -- References -- CHAPTER 3 SLOW MANIFOLDS -- 1 Introduction -- 2 Normally Hyperbolic versus General Case -- 3 Hamiltonian versus General Case -- 4 Improving a slow manifold -- 5 Symplectic slow manifolds -- 6 The Methods of Collective Coordinates -- 7 Velocity Splitting -- 8 Poisson slow manifolds -- 9 Slow manifolds with Internal Oscillation -- 10 Internal oscillation: U(1)-symmetric Hamiltonians -- 11 Internal oscillation: General Hamiltonians -- 12 Bounds on time evolution -- 13 Weak Damping -- Acknowledgements -- References -- CHAPTER 4 LOCALIZED EXCITATIONS IN JOSEPHSON ARRAYS. PART I: THEORY AND MODELING -- 1 Introduction -- 2 The single Josephson junction -- 2.1 Josephson effect -- 2.2 Superconducting tunnel junctions -- 2.3 Long Josephson junctions -- 2.4 Quantum effects in Josephson junctions -- 3 Modeling Josephson arrays -- 3.1 Series arrays -- 3.2 rf-SQUID -- 3.3 dc-SQUID -- 3.4 JJ parallel array -- 3.5 JJ ladder array -- 3.6 2D arrays -- 4 Localized excitations in Josephson arrays: Vortices and kinks -- 4.1 Vortices in 2D arrays -- 4.2 2D arrays with small junctions -- 4.3 Kinks in parallel arrays -- 4.4 Charge solitons in ID arrays -- 5 Discrete breathers in Josephson arrays -- 5.1 Oscillobreather in an ac biased parallel array -- 5.2 Rotobreathers in Josephson arrays -- 5.3 The ladder array -- 5.4 Rotobreathers in a dc biased ladder -- 5.5 Single-plaquette arrays -- 5.6 DBs in two-dimensional Josephson junction arrays -- Acknowledgments -- References.

CHAPTER 5 LOCALIZED EXCITATIONS IN JOSEPHSON ARRAYS. PART II: EXPERIMENTS -- 1 Introduction -- 2 Fabrication of Josephson arrays -- 2.1 Materials -- 2.2 Layout -- 2.3 Junction parameters -- 3 Measurement techniques -- 3.1 Generation of localized excitations -- 3.2 Hot probe imaging techniques -- 4 Experiments in the classical regime -- 4.1 Fluxons in Josephson arrays -- 4.2 Rotobreathers in Josephson ladders -- 4.3 Meandered states in 2-D Josephson arrays -- 5 Experiments in the quantum regime -- 5.1 Single Josephson junction -- 5.2 Coupled Josephson junctions -- 6 Conclusions and outlook -- Acknowledgments -- References -- CHAPTER 6 PROTEIN FUNCTIONAL DYNAMICS: COMPUTATIONAL APPROACHES -- 1 Introduction -- 2 Protein structure -- 3 Energetics of protein stabilisation -- 4 Protein folding -- 4.1 On-lattice models -- 4.2 Off-lattice models -- 4.3 More detailed models -- 5 Protein conformational changes -- 5.1 Functional motions -- 5.2 Collective motions -- 5.3 Low-frequency normal modes -- 6 Dissipation of energy in proteins -- 7 Conclusion -- Acknowledgments -- References -- CHAPTER 7 NONLINEAR VIBRATIONAL SPECTROSCOPY: A METHOD TO STUDY VIBRATIONAL SELF-TRAPPING -- 1 Introduction: The Story of Davidov's Soliton -- 2 Nonlinear Spectroscopy of Vibrational Modes -- 2.1 Harmonic and Anharmonic Potential Energy Surfaces -- 2.2 Linear and Nonlinear Spectroscopy -- 3 Proteins and Vibrational Excitons -- 3.1 Theoretical Background -- 3.2 Experimental Observation -- 4 Hydrogen Bonds and Anharmonicity -- 4.1 Theoretical Background -- 4.2 Experimental Observation -- 5 Vibrational Self-Trapping -- 5.1 Theoretical Background -- 5.2 Experimental Observation -- 6 Conclusion and Outlook -- Acknowledgments -- Appendix: Feynman Diagram Description of Linear and Nonlinear Spectroscopy -- References.

CHAPTER 8 BREATHERS IN BIOMOLECULES ? -- 1 Introduction -- 2 Classical vibrations -- 2.1 Local modes in small molecules -- 2.2 Local modes in large molecules -- 2.3 Local modes in crystals -- 2.4 Localisation of vibrations and chemical reaction rates -- 2.5 Fluctuational opening in DNA -- 3 Quantum self-trapping -- 4 Discussion -- Acknowledgments -- References -- CHAPTER 9 STATISTICAL PHYSICS OF LOCALIZED VIBRATIONS -- 1 Introduction/Outlook -- 2 Thermal DNA denaturation: A domain-wall driven transition? -- 3 ILMs in DNA dynamics? -- 4 Helix formation and melting in polypeptides -- 4.1 Definitions Notation -- 4.2 Thermodynamics -- Acknowledgments -- References -- CHAPTER 10 LOCALIZATION AND TARGETED TRANSFER OF ATOMIC-SCALE NONLINEAR EXCITATIONS: PERSPECTIVES FOR APPLICATIONS -- 1 Introduction -- 2 Discrete Breathers -- 2.1 DBs in periodic lattices -- 2.2 DBs in random systems -- 3 Targeted energy transfer -- 3.1 Nonlinear resonance -- 3.2 Targeted energy transfer in a nonlinear dimer -- 3.3 Targeted energy transfer through discrete breathers -- 4 Ultrafast Electron Transfer -- 4.1 Nonlinear dynamical model for ET -- 4.2 ET in the Dimer -- 4.3 Catalytic ET in a trimer -- 4.4 The example of bacterial photosynthetic reaction center -- 5 Conclusions and perspectives -- Acknowledgments -- References -- Index.