Nonlinear Dynamics of Nanosystems

Nonlinear Dynamics of Nanosystems......Page 2
List of Contributors......Page 8
Contents......Page 12
Preface......Page 20
Part I Fluctuations......Page 24
1.1 Introduction......Page 26
1.2.1 From Newton's Equations to Stochastic Processes......Page 29
1.2.2 Entropy and the Second Law of Thermodynamics......Page 35
1.2.3 Identifying the Nonequilibrium Constraints and the Currents with Graph Analysis......Page 36
1.2.4 Fluctuation Theorem for the Currents......Page 38
1.2.5 Consequences for Linear and Nonlinear Response Coefficients......Page 40
1.2.6 Temporal Disorder......Page 41
1.2.7 Nanosystems Driven by Time-Dependent Forces......Page 43
1.3.1 Friction in Double-Walled Carbon Nanotubes......Page 46
1.3.2 Electromagnetic Heating of Microplasmas......Page 55
1.4.1 F1-ATPase Motor......Page 57
1.4.2 Continuous-State Description......Page 60
1.4.3 Discrete-State Description......Page 66
1.5 Chemical Nanosystems......Page 70
1.5.1 Chemical Transistor......Page 71
1.5.2 Chemical Multistability......Page 75
1.5.3 Chemical Clocks......Page 78
1.5.4 Chemical Clocks Observed in Field Emission Microscopy......Page 81
1.5.5 Single-Copolymer Processes......Page 85
1.6 Conclusions and Perspectives......Page 90
References......Page 96
2.1 Introduction......Page 100
2.2 Thermostated Dynamical Systems......Page 101
2.3 The Transient Fluctuation Theorem......Page 104
2.4 Thermodynamic Interpretation of the Dissipation Function......Page 107
2.5 The Dissipation Theorem......Page 109
2.6 Nonequilibrium Work Relations......Page 111
2.7 Nonequilibrium Work Relations for Thermal Processes......Page 116
2.8.2 Integrated Fluctuation Theorem......Page 119
2.8.3 Second Law Inequality......Page 120
2.8.4 Nonequilibrium Partition Identity......Page 121
2.8.5 The Steady State Fluctuation Theorem......Page 122
2.9 Experiments......Page 125
2.10 Conclusion......Page 127
References......Page 132
3.1 Introduction to Microscopic Ratchets......Page 136
3.2 The Feynman Ratchet......Page 138
3.3 Tunneling Ratchets: Temperature Driven Current Reversal......Page 139
3.4 Rocked Ratchets in the Deep Quantum Regime......Page 141
3.5 Rocked Shallow Ratchets......Page 143
3.6 Spin Ratchets......Page 144
References......Page 145
Part II Surface Effects......Page 146
4 Dynamics of Nanoscopic Capillary Waves......Page 147
4.1.1 Stochastic Interfaces......Page 148
4.1.2 Acoustic Waves......Page 150
4.1.3 Capillary Waves......Page 151
4.1.4 Linearized Stochastic Hydrodynamics......Page 152
4.2 Surface Tension at Nanometer Length Scales: Effect of Long Range Forces and Bending Energies......Page 155
4.3 Thermal Noise Influences Fluid Flow in Nanoscopic Films......Page 158
4.3.1 Dynamics of the Film Thickness......Page 159
4.3.2 Comparison with Experiments......Page 161
4.3.3 Linearized Stochastic Thin Film Equation......Page 162
References......Page 167
5.2 Electromigration-Driven Islands and Voids......Page 169
5.2.1 Electromigration of Single Layer Islands......Page 170
5.2.2 Continuum vs. Discrete Modeling......Page 173
5.2.3 Nonlocal Shape Evolution: Two-Dimensional Voids......Page 176
5.2.4 Nonlocal Shape Evolution: Vacancy Islands with Terrace Diffusion......Page 177
5.3 Step Bunching on Vicinal Surfaces......Page 178
5.3.1 Stability of Step Trains......Page 179
5.3.2 Strongly and Weakly Conserved Step Dynamics......Page 180
5.3.3 Continuum Limit, Traveling Waves and Scaling Laws......Page 181
5.3.4 A Dynamic Phase Transition......Page 183
5.3.5 Coarsening......Page 185
5.3.6 Nonconserved Dynamics......Page 186
5.3.7 Beyond the Quasistatic Approximation......Page 187
References......Page 188
6 Casimir Forces and Geometry in Nanosystems......Page 191
6.1 Casimir Effect......Page 192
6.2 Dependence on Shape and Geometry......Page 194
6.2.1 Deformed Surfaces......Page 195
6.2.2 Lateral Forces......Page 202
6.2.3 Cylinders......Page 206
6.2.4 Spheres......Page 212
6.3 Dependence on Material Properties......Page 213
6.3.1 Lifshitz Formula......Page 214
6.3.2 Nanoparticles: Quantum Size Effects......Page 215
6.4 Casimir Force Driven Nanosystems......Page 218
References......Page 225
Part III Nanoelectromechanics......Page 229
7.1 Basics of the Duffing Oscillator......Page 230
7.2 NEMS Resonators and Their Nonlinear Properties......Page 232
7.3 Transition Dynamics of the Duffing Resonator......Page 235
7.4 Energy for “Uphill” Type Transitions......Page 237
7.5 Energy Calculation Using a Variational Technique......Page 241
7.6 Frequency Tuning......Page 243
7.7 Bifurcation Amplifier......Page 244
References......Page 245
8.1 Nonlinearities in NEMS and MEMS Resonators......Page 248
8.1.2 Origin of Nonlinearity in NEMS and MEMS Resonators......Page 249
8.1.3 Nonlinearities Arising from External Potentials......Page 250
8.1.4 Nonlinearities Due to Geometry......Page 251
8.2.1 The Scaled Duffing Equation of Motion......Page 254
8.2.2 A Solution Using Secular Perturbation Theory......Page 255
8.2.3 Addition of Other Nonlinear Terms......Page 262
8.3 Parametric Excitation of a Damped Duffing Resonator......Page 263
8.3.1 Driving Below Threshold: Amplification and Noise Squeezing......Page 266
8.3.2 Linear Instability......Page 268
8.3.3 Nonlinear Behavior Near Threshold......Page 269
8.3.4 Nonlinear Saturation above Threshold......Page 272
8.3.5 Parametric Excitation at the Second Instability Tongue......Page 274
8.4.1 Modeling an Array of Coupled Duffing Resonators......Page 277
8.4.2 Calculating the Response of an Array......Page 279
8.4.3 The Response of Very Small Arrays and Comparison of Analytics and Numerics......Page 282
8.4.4 Response of Large Arrays and Numerical Simulation......Page 284
8.5 Amplitude Equation Description for Large Arrays......Page 285
8.5.1 Amplitude Equations for Counter Propagating Waves......Page 286
8.5.2 Reduction to a Single Amplitude Equation......Page 287
8.5.3 Single Mode Oscillations......Page 288
References......Page 290
9.1 Introduction......Page 294
9.2 Operation of Dynamic Mode Atomic Force Microscopy......Page 296
9.3.1 Nonlinear Oscillation and Its Influence on Imaging......Page 297
9.3.2 Model of a Cantilever under Tip--Sample Interaction......Page 299
9.3.3 Application of Time-Delayed Feedback Control......Page 300
9.3.4 Experimental Setup for Control of Nonlinear Cantilever Dynamics......Page 301
9.3.5 Experimental Demonstration of the Stabilization of Cantilever Oscillations......Page 302
9.4.1 Model of Single Atoms and Molecules......Page 304
9.4.2 Analysis Based on an Action-Angle Formulation......Page 306
9.4.3 Dynamics of Single Atoms Induced by Probes......Page 308
9.5 Concluding Remarks......Page 310
References......Page 311
Part IV Nanoelectronics......Page 314
10.1 Introduction: Quantum Transport through Chaotic Conductors......Page 315
10.2 Semiclassical Limit of the Landauer Transport Approach......Page 317
10.3 Quantum Transmission: Configuration Space Approach......Page 319
10.3.1 Diagonal Contribution......Page 320
10.3.2 Nondiagonal Contribution......Page 321
10.3.3 Magnetic Field Dependence of the Nondiagonal Contribution......Page 325
10.3.4 Ehrenfest Time Dependence of the Nondiagonal Contribution......Page 326
10.4.1 Phase Space Approach......Page 327
10.4.2 Calculation of the Full Transmission......Page 329
10.5 Semiclassical Research Paths: Present and Future......Page 331
References......Page 332
11.1 Introduction......Page 335
11.2 Wire-Lead Model and Current Noise......Page 336
11.2.1 Charge, Current, and Current Fluctuations......Page 338
11.2.2 Full Counting Statistics......Page 339
11.3.1 Perturbation Theory and Reduced Density Operator......Page 340
11.3.2 Computation of Moments and Cumulants......Page 341
11.3.3 Floquet Decomposition......Page 343
11.4 Transport under Multi-Photon Emission and Absorption......Page 346
11.4.1 Electron Pumping......Page 347
11.4.2 Coherent Current Suppression......Page 348
11.5 Conclusions......Page 350
References......Page 351
12.1 Introduction......Page 353
12.2 Control of Chaotic Domain and Front Patterns in Superlattices......Page 357
12.3 Control of Noise-Induced Oscillations in Superlattices......Page 361
12.4 Control of Chaotic Spatiotemporal Oscillations in Resonant Tunneling Diodes......Page 369
12.5 Noise-Induced Spatiotemporal Patterns in Resonant Tunneling Diodes......Page 378
12.6 Conclusion......Page 389
References......Page 391
Part V Optic-Electronic Coupling......Page 397
13 Laser-Assisted Electron Transport in Nanoscale Devices......Page 398
13.1 Open Quantum Systems......Page 399
13.1.1 Quantum Master Equation Approach......Page 400
13.1.2 Time-Local and Time-Nonlocal Master Equations......Page 402
13.1.3 Full Counting Statistics......Page 406
13.2 Model System Describing Molecular Wires and Quantum Dots......Page 414
13.3 The Single Resonant Level Model......Page 420
13.4 Influence of Laser Pulses......Page 427
References......Page 432
14.1 Introduction......Page 436
14.2 Experimental......Page 439
14.3.1 Localized Surface Plasmons Probed by TR-2PPE......Page 443
14.3.2 Single Particle Plasmon Spectroscopy by Means of Time-Resolved Photoemission Microscopy......Page 446
14.4 Conclusion......Page 452
References......Page 453
15.1 Introduction......Page 456
15.2 Wave Propagation in Periodic Photonic Structures......Page 457
15.2.1 Linear Propagation......Page 458
15.2.2 Nonlinear Propagation......Page 459
15.3.1 Mathematical Description of Photorefractive Photonic Lattices......Page 460
15.3.2 Experimental Configuration for Photorefractive Lattice Creation......Page 461
15.4 Complex Optically-Induced Lattices in Two Transverse Dimensions......Page 462
15.4.1 Triangular Lattices......Page 463
15.4.2 Multiperiodic Lattices......Page 466
15.5 Vortex Clusters......Page 469
15.5.2 Compensation of Anisotropy in Hexagonal Photonic Lattices......Page 470
15.5.3 Ring-Shaped Vortex Clusters......Page 471
15.5.4 Multivortex Clusters......Page 475
15.6 Summary and Outlook......Page 476
References......Page 477
Index......Page 480