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1 Heat Transport in Low Dimensions: Introduction and Phenomenology |
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1 | (38) |
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1 | (2) |
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3 | (3) |
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1.3 Signatures of Anomalous Transport |
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6 | (11) |
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1.3.1 Diverging Finite-Size Conductivity |
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7 | (1) |
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8 | (2) |
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1.3.3 Diffusion of Perturbations |
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10 | (2) |
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1.3.4 Relaxation of Spontaneous Fluctuations |
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12 | (1) |
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1.3.5 Temperature Profiles |
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13 | (4) |
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1.4 Universality and Theoretical Approaches |
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17 | (6) |
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17 | (2) |
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1.4.2 Connection with the Interface Problem |
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19 | (1) |
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1.4.3 Other Universality Classes |
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20 | (2) |
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1.4.4 Comparison with Simulations and Experiments |
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22 | (1) |
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1.5 The Coupled Rotors Model |
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23 | (1) |
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1.6 Two-Dimensional Lattices |
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24 | (1) |
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1.7 Integrable Nonlinear Systems |
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25 | (1) |
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26 | (7) |
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26 | (3) |
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1.8.2 The Discrete Nonlinear Schrodinger Equation |
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29 | (4) |
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1.9 Conclusions and Open Problems |
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33 | (6) |
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34 | (5) |
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2 Heat Transport in Harmonic Systems |
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39 | (68) |
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39 | (3) |
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2.2 Steady State Current from Langevin Equations and Green's Function Formalism |
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42 | (8) |
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2.2.1 Derivation of the Langevin Equation and It's Steady-State Solution |
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42 | (4) |
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2.2.2 Steady State Properties |
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46 | (4) |
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2.3 Steady State Current Fluctuations |
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50 | (15) |
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50 | (4) |
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2.3.2 Cumulant Generating Function for Harmonic Lattices |
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54 | (11) |
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2.4 Explicit Results for Steady State Properties in Ordered and Disordered Harmonic Crystal |
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65 | (34) |
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66 | (22) |
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2.4.2 Temperature Profiles |
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88 | (3) |
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91 | (8) |
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99 | (8) |
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100 | (1) |
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101 | (6) |
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3 Fluctuating Hydrodynamics Approach to Equilibrium Time Correlations for Anharmonic Chains |
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107 | (52) |
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3.1 Introduction, Long Time Tails for Simple Fluids |
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107 | (6) |
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113 | (8) |
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3.3 Nonlinear Fluctuating Hydrodynamics |
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121 | (9) |
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130 | (8) |
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3.5 Molecular Dynamics Simulations |
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138 | (7) |
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3.6 Total Current Correlations |
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145 | (3) |
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3.7 Other ID Hamiltonian Systems |
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148 | (11) |
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155 | (4) |
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4 Kinetic Theory of Phonons in Weakly Anharmonic Particle Chains |
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159 | (56) |
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4.1 Kinetic Scaling Limit for Weakly Anharmonic Chains |
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159 | (22) |
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159 | (3) |
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4.1.2 Free Motion of Phonons |
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162 | (3) |
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4.1.3 Particle Chains with Anharmonic Perturbations |
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165 | (5) |
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4.1.4 Choice of Initial Data |
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170 | (5) |
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175 | (6) |
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4.2 Phonon Boltzmann Equation of Spatially Homogeneous Anharmonic Chains |
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181 | (17) |
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4.2.1 Identifying the Collision Operator |
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181 | (7) |
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4.2.2 Solution of the Collisional Constraints |
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188 | (10) |
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4.3 Energy Transport in the Kinetic Theory of Phonons |
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198 | (14) |
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4.3.1 Entropy and H-Theorem of the Phonon Boltzmann Equations |
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198 | (2) |
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200 | (1) |
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4.3.3 Green-Kubo Formula and the Linearized Boltzmann Equation |
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201 | (2) |
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4.3.4 Kinetic Theory Prediction for Thermal Conductivity in Chains with Anharmonic Pinning |
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203 | (5) |
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4.3.5 Anomalous Energy Conduction in the Kinetic Theory of FPU Chains |
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208 | (4) |
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212 | (3) |
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213 | (2) |
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5 Thermal Conductivity in Harmonic Lattices with Random Collisions |
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215 | (24) |
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215 | (4) |
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216 | (1) |
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217 | (1) |
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5.1.3 Dynamics with Stochastic Collisions |
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217 | (1) |
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5.1.4 Equilibrium Stationary Measures |
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218 | (1) |
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5.1.5 Macroscopic Space-Time Scales |
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218 | (1) |
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5.2 Hyperbolic Scaling: The Linear Wave Equation |
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219 | (1) |
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5.3 Superdiffusive Evolution of the Temperature Profile |
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220 | (1) |
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5.4 The Diffusive Behavior of the Phonon-Modes |
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221 | (1) |
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5.5 Equilibrium Fluctuations |
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222 | (1) |
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5.6 The Phonon Boltzmann Equation |
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223 | (4) |
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5.7 Non-acoustic Chains: Beam Dynamics |
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227 | (1) |
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5.8 A Simpler Model with Two Conserved Quantities |
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228 | (2) |
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5.8.1 The Extension Problem for the Skew-Fractional Laplacian |
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229 | (1) |
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5.9 The Dynamics in Higher Dimension |
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230 | (1) |
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5.10 Thermal Boundary Conditions and the Non-equilibrium Stationary States |
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231 | (2) |
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5.11 The Non-linear Chain |
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233 | (1) |
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5.12 The Disordered Chain |
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234 | (5) |
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236 | (3) |
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6 Simulation of Heat Transport in Low-Dimensional Oscillator Lattices |
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239 | (36) |
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6.1 Simulation of Heat Transport with Non-equilibrium Heat Bath Method and Equilibrium Green-Kubo Method |
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240 | (18) |
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6.1.1 Power-Law Divergent Thermal Conductivity in 1D Momentum-Conserving Nonlinear Lattices |
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240 | (8) |
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6.1.2 Logarithmic Divergent Thermal Conductivity in 2D Momentum-Conserving Nonlinear Lattices |
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248 | (5) |
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6.1.3 Normal Heat Conduction in a 3D Momentum-Conserving Nonlinear Lattice |
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253 | (5) |
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6.2 Simulation of Heat Transport with the Diffusion Method |
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258 | (17) |
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260 | (8) |
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268 | (5) |
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273 | (2) |
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7 Simulation of Dimensionality Effects in Thermal Transport |
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275 | (30) |
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275 | (2) |
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277 | (6) |
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7.2.1 Anharmonic Lattice Dynamics |
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277 | (3) |
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7.2.2 Equilibrium Molecular Dynamics |
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280 | (1) |
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7.2.3 Non-equilibrium Molecular Dynamics |
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281 | (1) |
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7.2.4 Empirical Interatomic Potentials |
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282 | (1) |
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7.3 Carbon Based Nanostructures |
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283 | (7) |
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283 | (4) |
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287 | (3) |
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7.4 Nanostructured Silicon |
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290 | (10) |
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291 | (6) |
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7.4.2 Ultra-Thin Silicon Membranes |
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297 | (3) |
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300 | (5) |
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301 | (4) |
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8 Experimental Probing of Non-Fourier Thermal Conductors |
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305 | (34) |
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305 | (2) |
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8.2 Experimental Methods for Probing Non-Fourier Thermal Conduction |
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307 | (5) |
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8.3 Non-Fourier (Ballistic) Thermal Conduction in SiGe Nanowires |
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312 | (7) |
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8.4 Non-Fourier (Ballistic) Thermal Conduction in Si-Ge interfaces |
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319 | (5) |
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8.5 Non-Fourier (Ballistic) Thermal Conduction in Multiwall Nanotubes |
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324 | (5) |
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8.6 Non-Fourier (Anomalous) Thermal Conduction in Ultralong Carbon Nanotubes |
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329 | (5) |
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334 | (5) |
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335 | (4) |
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9 Thermal Transport in Graphene, Few-Layer Graphene and Graphene Nanoribbons |
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339 | (26) |
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339 | (1) |
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9.2 Basics of Phonon Transport and Thermal Conductivity |
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340 | (2) |
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9.3 Experimental Data for Thermal Conductivity of Graphene and Few-Layer Graphene |
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342 | (4) |
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9.4 Theories of Phonon Thermal Conductivity in Graphene, Few-Layer Graphene and Graphene Nanoribbons |
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346 | (12) |
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9.4.1 Specifics of Two-Dimensional Phonon Transport |
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353 | (5) |
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358 | (7) |
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358 | (7) |
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10 From Thermal Rectifiers to Thermoelectric Devices |
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365 | (44) |
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10.1 Dynamical Foundations of Fourier Law |
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365 | (3) |
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10.2 Fourier Law in Quantum Mechanics |
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368 | (7) |
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10.2.1 Fourier Law and the Onset of Quantum Chaos |
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370 | (5) |
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10.3 Controlling the Heat Flow: Thermal Rectifiers |
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375 | (10) |
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10.3.1 The Fourier Law and the Design of a Thermal Rectifier |
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375 | (2) |
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10.3.2 A One-Dimensional Model for a Thermal Rectifier |
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377 | (5) |
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10.3.3 Model in Higher Dimension |
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382 | (2) |
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10.3.4 Building an Actual Thermal Rectifier |
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384 | (1) |
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10.4 Thermoelectric Efficiency |
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385 | (18) |
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10.4.1 The Thermoelectric Figure of Merit ZT |
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386 | (2) |
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10.4.2 The Onsager Matrix |
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388 | (1) |
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10.4.3 Non-interacting Systems |
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389 | (3) |
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10.4.4 Interacting Systems |
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392 | (5) |
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10.4.5 Breaking Time-Reversibility |
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397 | (3) |
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10.4.6 Inelastic Scattering and Probe Terminals |
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400 | (3) |
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403 | (6) |
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404 | (5) |
Index |
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409 | |