Part I Fluctuations
1 Nonequilibrium Nanosystems ................................... 1
Pierre Gaspard
1.1 Introduction ............................................ 1
1.2 Statistical Thermodynamics of Nonequilibrium
Nanosystems ............................................. 4
1.2.1 From Newton's Equations to Stochastic
Processes ........................................ 4
1.2.2 Entropy and the Second Law of Thermodynamics .... 10
1.2.3 Identifying the Nonequilibrium Constraints and
the Currents with Graph Analysis ................ 11
1.2.4 Fluctuation Theorem for the Currents ............ 13
1.2.5 Consequences for Linear and Nonlinear Response
Coefficients .................................... 15
1.2.6 Temporal Disorder ............................... 16
1.2.7 Nanosystems Driven by Time-Dependent Forces ..... 18
1.3 Mechanical Nanosystems ................................. 21
1.3.1 Friction in Double-Walled Carbon Nanotubes ...... 21
1.3.1.1 Translational Friction ................. 23
1.3.1.2 Rotational Friction .................... 28
1.3.2 Electromagnetic Heating of Microplasmas ......... 30
1.3.2.1 The Undriven System and Its
Hamiltonian ............................ 30
1.3.2.2 The Driven System and the Fluctuation
Theorem ................................ 31
1.4 Mechanochemical Nanosystems ............................ 32
1.4.1 F1-ATPase Motor ................................. 32
1.4.2 Continuous-State Description .................... 35
1.4.3 Discrete-State Description ...................... 41
1.5 Chemical Nanosystems ................................... 45
1.5.1 Chemical Transistor ............................. 46
1.5.2 Chemical Multistability ......................... 50
1.5.3 Chemical Clocks ................................. 53
1.5.4 Chemical Clocks Observed in Field Emission
Microscopy ...................................... 56
1.5.5 Single-Copolymer Processes ...................... 60
1.5.5.1 Copolymerization without a Template .... 61
1.5.5.2 Copolymerization with a Template ....... 63
1.5.5.3 DNA Replication ........................ 64
1.6 Conclusions and Perspectives ........................... 65
References ............................................. 71
2 Thermodynamics of Small Systems ............................. 75
Denis J. Evans, Stephen R. Williams, and Debra J. Searles
2.1 Introduction ........................................... 75
2.2 Thermostated Dynamical Systems ......................... 76
2.3 The Transient Fluctuation Theorem ...................... 79
2.4 Thermodynamic Interpretation of the Dissipation
Function ............................................... 82
2.5 The Dissipation Theorem ................................ 84
2.6 Nonequilibrium Work Relations .......................... 86
2.7 Nonequilibrium Work Relations for Thermal Processes .... 91
2.8 Corollaries of the Fluctuation Theorem and
Nonequilibrium Work Relations .......................... 94
2.8.1 Generalized Fluctuation Theorem ................. 94
2.8.2 Integrated Fluctuation Theorem .................. 94
2.8.3 Second Law Inequality ........................... 95
2.8.4 Nonequilibrium Partition Identity ............... 96
2.8.5 The Steady State Fluctuation Theorem ............ 97
2.8.6 Minimum Average Work Principle ................. 100
2.9 Experiments ........................................... 100
2.10 Conclusion ............................................ 102
References ................................................. 107
3 Quantum Dissipative Ratchets ............................... 111
Milena Grifoni
3.1 Introduction to Microscopic Ratchets .................. 111
3.2 The Feynman Ratchet ................................... 113
3.3 Tunneling Ratchets: Temperature Driven Current
Reversal .............................................. 114
3.4 Rocked Ratchets in the Deep Quantum Regime ............ 116
3.5 Rocked Shallow Ratchets ............................... 118
3.6 Spin Ratchets ......................................... 119
References ............................................ 120
Part II Surface Effects
4 Dynamics of Nanoscopic Capillary Waves ..................... 121
Klaus Mecke, Kerstin Falk, and Markus Rauscher
4.1 Stochastic Hydrodynamics .............................. 122
4.1.1 Stochastic Interfaces .......................... 122
4.1.2 Acoustic Waves ................................. 124
4.1.1 Capillary Waves ................................ 125
4.1.4 Linearized Stochastic Hydrodynamics ............ 126
4.2 Surface Tension at Nanometer Length Scales: Effect
of Long Range Forces and Bending Energies ............. 129
4.3 Thermal Noise Influences Fluid Flow in Nanoscopic
Films ................................................. 132
4.3.1 Dynamics of the Film Thickness ................. 133
4.3.2 Comparison with Experiments .................... 135
4.3.3 Linearized Stochastic Thin Film Equation ....... 136
References ................................................. 141
5 Nonlinear Dynamics of Surface Steps ........................ 143
Joachim Krug
5.1 I ntroduction ......................................... 143
5.2 Electromigration-Driven Islands and Voids ............. 143
5.2.1 Electromigration of Single Layer Islands ....... 144
5.2.2 Continuum vs. Discrete Modeling ................ 147
5.2.3 Nonlocal Shape Evolution: Two-Dimensional
Voids .......................................... 150
5.2.4 Nonlocal Shape Evolution: Vacancy Islands
with Terrace Diffusion ......................... 151
5.3 Step Bunching on Vicinal Surfaces ..................... 152
5.3.1 Stability of Step Trains ....................... 153
5.3.2 Strongly and Weakly Conserved Step Dynamics .... 154
5.3.3 Continuum Limit, Traveling Waves and Scaling
Laws ........................................... 155
5.3.4 A Dynamic Phase Transition ..................... 157
5.3.5 Coarsening ..................................... 159
5.3.6 Nonconserved Dynamics .......................... 160
5.3.7 Beyond the Quasistatic Approximation ........... 161
5.4 Conclusions ........................................... 162
References ............................................ 162
6 Casimir Forces and Geometry in Nanosystems ................. 165
Thorsten Emig
6.1 Casimir Effect ........................................ 166
6.2 Dependence on Shape and Geometry ...................... 168
6.2.1 Deformed Surfaces .............................. 169
6.2.2 Lateral Forces ................................. 176
6.2.3 Cylinders ...................................... 180
6.2.4 Spheres ........................................ 186
6.3 Dependence on Material Properties ..................... 187
6.3.1 Lifshitz Formula ............................... 188
6.3.2 Nanoparticles: Quantum Size Effects ............ 189
6.4 Casimir Force Driven Nanosystems ...................... 192
6.5 Conclusion ............................................ 199
References ................................................. 199
Part III Nanoelectromechanics
7 The Duffing Oscillator for Nanoelectromechanical Systems ... 203
Sequoyah Aldridge
7.1 Basics of the Duffing Oscillator ...................... 203
7.2 NEMS Resonators and Their Nonlinear Properties ........ 205
7.3 Transition Dynamics of the Duffing Resonator .......... 208
7.4 Energy for "Uphill" Type Transitions .................. 210
7.5 Energy Calculation Using a Variational Technique ...... 214
7.6 Frequency Tuning ...................................... 216
7.7 Bifurcation Amplifier ................................. 217
7.8 Conclusion ............................................ 218
References ................................................. 218
8 Nonlinear Dynamics of Nanomechanical Resonators ............ 221
Ron Lifshitz and M.C. Cross
8.1 Nonlinearities in NEMS and MEMS Resonators ............ 221
8.1.1 Why Study Nonlinear NEMS and MEMS? ............. 222
8.1.2 Origin of Nonlinearity in NEMS and MEMS
Resonators ..................................... 222
8.1.3 Nonlinearities Arising from External
Potentials ..................................... 223
8.1.4 Nonlinearities Due to Geometry ................. 224
8.2 The Directly-Driven Damped Duffing Resonator .......... 227
8.2.1 The Scaled Duffing Equation of Motion .......... 227
8.2.2 A Solution Using Secular Perturbation Theory ... 228
8.2.3 Addition of Other Nonlinear Terms .............. 235
8.3 Parametric Excitation of a Damped Duffing Resonator ... 236
8.3.1 Driving Below Threshold: Amplification and
Noise Squeezing ................................ 239
8.3.2 Linear Instability ............................. 241
8.3.3 Nonlinear Behavior Near Threshold .............. 242
8.3.4 Nonlinear Saturation above Threshold ........... 245
8.3.5 Parametric Excitation at the Second
Instability Tongue ............................. 247
8.4 Parametric Excitation of Arrays of Coupled Duffing
Resonators ............................................ 250
8.4.1 Modeling an Array of Coupled Duffing
Resonators ..................................... 250
8.4.2 Calculating the Response of an Array ........... 252
8.4.3 The Response of Very Small Arrays and
Comparison of Analytics and Numerics ........... 255
8.4.4 Response of Large Arrays and Numerical
Simulation ..................................... 257
8.5 Amplitude Equation Description for Large Arrays ....... 258
8.5.1 Amplitude Equations for Counter Propagating
Waves .......................................... 259
8.5.2 Reduction to a Single Amplitude Equation ....... 260
8.5.3 Single Mode Oscillations ....................... 261
References ................................................. 263
9 Nonlinear Dynamics in Atomic Force Microscopy and Its
Control for Nanoparticle Manipulation ...................... 267
Kohei Yamasue and Takashi Hikihara
9.1 Introduction .......................................... 267
9.2 Operation of Dynamic Mode Atomic Force Microscopy ..... 269
9.3 Nonlinear Dynamics and Control of Cantilevers ......... 270
9.3.1 Nonlinear Oscillation and Its Influence on
Imaging ........................................ 270
9.3.2 Model of a Cantilever under Tip-Sample
Interaction .................................... 272
9.3.3 Application of Time-Delayed Feedback Control ... 273
9.3.4 Experimental Setup for Control of Nonlinear
Cantilever Dynamics ............................ 274
9.3.4.1 Circuit Implement of Time-Delayed
Feedback Control ...................... 274
9.3.4.2 Frequency Response of Magnetic
Actuators and Deflection Sensors ...... 275
9.3.5 Experimental Demonstration of the
Stabilization of Cantilever Oscillations ....... 275
9.4 Manipulation of Single Atoms at Material Surfaces ..... 277
9.4.1 Model of Single Atoms and Molecules ............ 277
9.4.2 Analysis Based on an Action-Angle
Formulation .................................... 279
9.4.3 Dynamics of Single Atoms Induced by Probes ..... 281
9.4.4 Control of Manipulation ........................ 283
9.5 Concluding Remarks .................................... 283
References ............................................ 284
Part IV Nanoelectronics
10 Classical Correlations and Quantum Interference in
Ballistic Conductors ....................................... 287
Daniel Waltner and Klaus Richter
10.1 Introduction: Quantum Transport through Chaotic
Conductors ............................................ 287
10.2 Semiclassical Limit of the Landauer Transport
Approach .............................................. 289
10.3 Quantum Transmission: Configuration Space Approach .... 291
10.3.1 Diagonal Contribution .......................... 292
10.3.2 Nondiagonal Contribution ....................... 293
10.3.3 Magnetic Field Dependence of the Nondiagonal
Contribution ................................... 297
10.3.4 Ehrenfest Time Dependence of the Nondiagonal
Contribution ................................... 298
10.4 Quantum Transmission: Phase Space Approach ............ 299
10.4.1 Phase Space Approach ........................... 299
10.4.2 Calculation of the Full Transmission ........... 301
10.5 Semiclassical Research Paths: Present and Future ...... 303
References ............................................ 304
11 Nonlinear Response of Driven Mesoscopic Conductors ......... 307
Franz J. Kaiser and Sigmund Kohler
11.1 Introduction .......................................... 307
11.2 Wire-Lead Model and Current Noise ..................... 308
11.2.1 Charge, Current, and Current Fluctuations ...... 310
11.2.2 Full Counting Statistics ....................... 311
11.3 Master Equation Approach .............................. 312
11.3.1 Perturbation Theory and Reduced Density
Operator ....................................... 312
11.3.2 Computation of Moments and Cumulants ........... 313
11.3.3 Floquet Decomposition .......................... 315
11.3.3.1 Fermionic Floquet Operators .......... 315
11.3.3.2 Master Equation and Current
Formula .............................. 316
11.3.4 Spinless Electrons ............................ 318
11.4 Transport under Multi-Photon Emission and
Absorption ............................................ 318
11.4.1 Electron Pumping ............................... 319
11.4.2 Coherent Current Suppression ................... 320
11.5 Conclusions ........................................... 322
References ............................................ 323
12 Pattern Formation and Time Delayed Feedback Control
at the Nanoscale ........................................... 325
Eckehard Schöll
12.1 Introduction .......................................... 325
12.2 Control of Chaotic Domain and Front Patterns in
Superlattices ......................................... 329
12.3 Control of Noise-Induced Oscillations in
Superlattices ......................................... 333
12.4 Control of Chaotic Spatiotemporal Oscillations in
Resonant Tunneling Diodes ............................. 341
12.5 Noise-Induced Spatiotemporal Patterns in Resonant
Tunneling Diodes ...................................... 350
12.6 Conclusion ............................................ 361
References ................................................. 363
Part V Optic-Electronic Coupling
13 Laser-Assisted Electron Transport in Nanoscale Devices ..... 369
Ciprian Padurariu, Atef Fadl Amin, and Ulrich
Kleinckathöfer
13.1 Open Quantum Systems .................................. 370
13.1.1 Quantum Master Equation Approach .............. 371
13.1.2 Time-Local and Time-Nonlocal Master
Equations ..................................... 373
13.1.3 Full Counting Statistics ...................... 377
13.2 Model System Describing Molecular Wires and Quantum
Dots .................................................. 385
13.3 The Single Resonant Level Model ....................... 391
13.4 Influence of Laser Pulses ............................. 398
13.5 Summary and Outlook ................................... 403
References ................................................. 403
14 Two-Photon Photoemission of Plasmonic Nanostructures
with High Temporal and Lateral Resolution .................. 407
Michael Bauer, Daniela Bayer, Carsten Wiemann, and Martin
Aeschlimann
14.1 Introduction .......................................... 407
14.2 Experimental .......................................... 410
14.3 Results and Discussion ................................ 414
14.3.1 Localized Surface Plasmons Probed by TR-2PPE ... 414
14.3.2 Single Particle Plasmon Spectroscopy by Means
of Time-Resolved Photoemission Microscopy ...... 417
14.4 Conclusion ............................................ 423
References ............................................ 424
15 Dynamics and Nonlinear Light Propagation in Complex
Photonic Lattices .......................................... 427
Bernd Terhalle, Patrick Rose, Dennis Göries, Jörg
Imbrock, and Cornelia Denz
15.1 Introduction .......................................... 427
15.2 Wave Propagation in Periodic Photonic Structures ...... 428
15.2.1 Linear Propagation ............................. 429
15.2.2 Nonlinear Propagation .......................... 430
15.3 Optically-Induced Photonic Lattices in
Photorefractive Media ................................. 431
15.3.1 Mathematical Description of Photorefractive
Photonic Lattices .............................. 431
15.3.2 Experimental Configuration for
Photorefractive Lattice Creation ............... 432
15.4 Complex Optically-Induced Lattices in Two Transverse
Dimensions ............................................ 433
15.4.1 Triangular Lattices ............................ 434
15.4.2 Multiperiodic Lattices ......................... 437
15.5 Vortex Clusters ....................................... 440
15.5.1 Necessary Stability Criterion .................. 441
15.5.2 Compensation of Anisotropy in Hexagonal
Photonic Lattices .............................. 441
15.5.3 Ring-Shaped Vortex Clusters .................... 442
15.5.4 Multivortex Clusters ........................... 446
15.6 Summary and Outlook ................................... 447
References ............................................ 448
Index ......................................................... 451
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