Energy Localisation And Transfer

By: Thierry Dauxois (Editor), Anna Litvak-hinenzon (Editor), Anna Spanoudaki (Editor), Robert S Mackay (Editor)

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Hardcover | 12 February 2004

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428 Pages

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This book provides an introduction to localised excitations in spatially discrete systems, from the experimental, numerical and mathematical points of view. Also known as discrete breathers, nonlinear lattice excitations and intrinsic localised modes; these are spatially localised time periodic motions in networks of dynamical units. Examples of such networks are molecular crystals, biomolecules, and arrays of Josephson superconducting junctions. The book also addresses the formation of discrete breathers and their potential role in energy transfer in such systems.

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Non-Fiction Science Physics Classical Mathematics Energy Atomic & Molecular Physics Relativity Physics Applied Physics Biophysics Mathematics Quantum Physics & Quantum Mechanics & Quantum Field Theory Booktopia Publisher Services

World Scientific Publishing

Preface	p. v
Computational Studies of Discrete Breathers	p. 1
Introduction	p. 1
A bit on numerics of solving ODEs	p. 6
Observing and analyzing breathers in numerical runs	p. 10
Targeted initial conditions	p. 10
Breathers in transient processes	p. 17
Breathers in thermal equilibrium	p. 23
Obtaining breathers up to machine precision: Part I	p. 25
Method No.1 - designing a map	p. 26
Method No.2 - saddles on the rim with space-time separation	p. 30
Method No.3 - homoclinic orbits with time-space separation	p. 31
Obtaining breathers up to machine precision: Part II	p. 33
Method No.4 - Newton in phase space	p. 35
Method No.5 - steepest descent in phase space	p. 37
Symmetries	p. 38
Perturbing breathers	p. 39
Linear stability analysis	p. 40
Plane wave scattering	p. 43
Breathers in dissipative systems	p. 47
Obtaining dissipative breathers	p. 48
Perturbing dissipative breathers	p. 49
Computing quantum breathers	p. 51
The dimer	p. 54
The trimer	p. 58
Quantum roto-breathers	p. 65
Some applications instead of conclusions	p. 66
Acknowledgments	p. 68
References	p. 68
Vibrational Spectroscopy and Quantum Localization	p. 73
Introduction	p. 74
Nonlinear dynamics and energy localization	p. 74
Nonlinear dynamics and vibrational spectroscopy	p. 76
Vibrational spectroscopy techniques	p. 78
Some definitions	p. 78
Spatial resolution	p. 80
Coherence length	p. 80
Energy localization	p. 81
The Franck-Condon principle	p. 81
Optical techniques	p. 82
Neutron scattering techniques	p. 84
Nuclear cross-sections	p. 85
Coherent versus incoherent scattering	p. 85
Contrast	p. 86
Penetration depth	p. 86
Wavelength	p. 86
Scattering function	p. 87
A (not so) simple example	p. 89
Molecular vibrations	p. 92
The harmonic approximation: Normal modes	p. 92
Anharmonicity	p. 93
Local modes	p. 93
Diatomic molecules	p. 94
Polyatomic molecules	p. 95
Local versus normal mode separability	p. 96
Zeroth-order descriptions of the nuclear Hamiltonian	p. 98
Breakdown of the zeroth-order descriptions	p. 99
The water molecule	p. 100
The normal mode model	p. 100
The local mode model	p. 101
Vibrational wave functions and spectrum	p. 102
Eigenstates and eigenfunctions	p. 103
The algebraic force-field Hamiltonian	p. 104
Other molecules	p. 107
Local modes and energy localization	p. 109
Crystals	p. 110
The harmonic approximation: Phonons	p. 111
The linear single-particle chain	p. 113
The linear di-atom chain	p. 113
Phonon-phonon interaction	p. 113
Phonon-electron interaction	p. 116
Local modes	p. 119
Nonlinear dynamics	p. 123
Quantum rotational dynamics for infinite chains of coupled rotors	p. 123
Strong vibrational coupling: Hydrogen bonding	p. 131
Davydov's model	p. 139
Conclusion	p. 141
Vibrational spectroscopy and nonlinear dynamics	p. 141
Optical vibrational spectroscopy and energy localization	p. 141
Molecules	p. 142
Crystals	p. 142
Inelastic neutron scattering spectroscopy of solitons	p. 142
Vibrational spectroscopy and dynamical models	p. 143
References	p. 143
Slow Manifolds	p. 149
Introduction	p. 149
Normally Hyperbolic versus General Case	p. 152
Hamiltonian versus General Case	p. 154
Improving a slow manifold	p. 160
Symplectic slow manifolds	p. 162
The Methods of Collective Coordinates	p. 169
Velocity Splitting	p. 171
Poisson slow manifolds	p. 173
Slow manifolds with Internal Oscillation	p. 173
Internal oscillation: U(1)-symmetric Hamiltonians	p. 176
Internal oscillation: General Hamiltonians	p. 181
Bounds on time evolution	p. 185
Weak Damping	p. 187
Acknowledgements	p. 187
References	p. 188
Localized Excitations in Josephson Arrays. Part I: Theory and Modeling	p. 193
Introduction	p. 193
The single Josephson junction	p. 194
Josephson effect	p. 194
Superconducting tunnel junctions	p. 194
Long Josephson junctions	p. 199
Quantum effects in Josephson junctions	p. 200
Modeling Josephson arrays	p. 201
Series arrays	p. 203
rf-SQUID	p. 204
dc-SQUID	p. 204
JJ parallel array	p. 205
JJ ladder array	p. 206
2D arrays	p. 207
Localized excitations in Josephson arrays: Vortices and kinks	p. 209
Vortices in 2D arrays	p. 209
Single vortex properties at zero temperature	p. 210
Array properties at non-zero temperatures	p. 211
2D arrays with small junctions	p. 211
Kinks in parallel arrays	p. 212
Fluxon ratchet potentials	p. 215
Charge solitons in 1D arrays	p. 217
Discrete breathers in Josephson arrays	p. 217
Oscillobreather in an ac biased parallel array	p. 219
Rotobreathers in Josephson arrays	p. 220
The ladder array	p. 220
Rotobreathers in a dc biased ladder	p. 221
Analysis of the breather solutions using a dc model	p. 225
Simulations	p. 226
Breather existence diagrams	p. 229
Different [lambda] regimes	p. 233
Breather-vortex collision in the Josephson ladder	p. 236
Single-plaquette arrays	p. 238
DBs in two-dimensional Josephson junction arrays	p. 238
Acknowledgments	p. 240
References	p. 241
Localized Excitations in Josephson Arrays. Part II: Experiments	p. 247
Introduction	p. 247
Fabrication of Josephson arrays	p. 248
Materials	p. 249
Low-temperature superconducting technology	p. 249
High-temperature superconducting technology	p. 251
Layout	p. 252
Junction parameters	p. 254
Measurement techniques	p. 255
Generation of localized excitations	p. 256
Hot probe imaging techniques	p. 257
Experiments in the classical regime	p. 259
Fluxons in Josephson arrays	p. 259
Parallel 1-D arrays	p. 259
Ladders	p. 261
2-D arrays	p. 261
Rotobreathers in Josephson ladders	p. 262
Meandered states in 2-D Josephson arrays	p. 264
Experiments in the quantum regime	p. 265
Single Josephson junction	p. 265
Coupled Josephson junctions	p. 268
Conclusions and outlook	p. 269
Acknowledgments	p. 269
References	p. 270
Protein Functional Dynamics: Computational Approaches	p. 273
Introduction	p. 273
Protein structure	p. 273
Energetics of protein stabilisation	p. 275
Protein folding	p. 276
On-lattice models	p. 277
Off-lattice models	p. 283
More detailed models	p. 285
Protein conformational changes	p. 285
Functional motions	p. 285
Collective motions	p. 286
Low-frequency normal modes	p. 289
Normal mode analysis	p. 289
The RTB approximation	p. 291
Comparison with crystallographic B-factors	p. 292
Comparison with conformational changes	p. 293
Simplified potentials	p. 296
Dissipation of energy in proteins	p. 297
Conclusion	p. 298
Acknowledgments	p. 299
References	p. 299
Nonlinear Vibrational Spectroscopy: A Method to Study Vibrational Self-Trapping	p. 301
Introduction: The Story of Davidov's Soliton	p. 301
Nonlinear Spectroscopy of Vibrational Modes	p. 303
Harmonic and Anharmonic Potential Energy Surfaces	p. 303
Linear and Nonlinear Spectroscopy	p. 305
Proteins and Vibrational Excitons	p. 307
Theoretical Background	p. 307
Experimental Observation	p. 309
Hydrogen Bonds and Anharmonicity	p. 310
Theoretical Background	p. 310
Experimental Observation	p. 312
Vibrational Self-Trapping	p. 314
Theoretical Background	p. 314
Experimental Observation	p. 315
Conclusion and Outlook	p. 319
Acknowledgments	p. 320
Feynman Diagram Description of Linear and Nonlinear Spectroscopy	p. 321
References	p. 323
Breathers in Biomolecules?	p. 325
Introduction	p. 325
Classical vibrations	p. 326
Local modes in small molecules	p. 326
Local modes in large molecules	p. 327
Local modes in crystals	p. 329
Localisation of vibrations and chemical reaction rates	p. 330
Fluctuational opening in DNA	p. 331
Quantum self-trapping	p. 333
Discussion	p. 337
Acknowledgments	p. 339
References	p. 339
Statistical Physics of Localized Vibrations	p. 341
Introduction/Outlook	p. 341
Thermal DNA denaturation: A domain-wall driven transition?	p. 343
ILMs in DNA dynamics?	p. 345
Helix formation and melting in polypeptides	p. 348
Definitions, Notation	p. 348
Thermodynamics	p. 350
Acknowledgments	p. 351
References	p. 352
Localization and Targeted Transfer of Atomic-Scale Nonlinear Excitations: Perspectives for Applications	p. 355
Introduction	p. 355
Discrete Breathers	p. 359
DBs in periodic lattices	p. 360
DBs in random systems	p. 371
Targeted energy transfer	p. 376
Nonlinear resonance	p. 378
Targeted energy transfer in a nonlinear dimer	p. 380
Targeted energy transfer through discrete breathers	p. 383
Ultrafast Electron Transfer	p. 387
Nonlinear dynamical model for ET	p. 390
ET in the Dimer	p. 394
Catalytic ET in a trimer	p. 395
The example of bacterial photosynthetic reaction center	p. 396
Conclusions and perspectives	p. 400
Acknowledgments	p. 402
References	p. 402
Index	p. 405
Table of Contents provided by Rittenhouse. All Rights Reserved.

Energy Localisation And Transfer

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