### Abstract

Original language | English |
---|---|

Title of host publication | Thermal transport in low dimensions : from statistical physics to nanoscale heat transfer |

Editors | Stefano Lepri |

Number of pages | 56 |

Volume | 921 |

Publisher | Springer |

Publication date | 7 Apr 2016 |

Pages | 159-214 |

ISBN (Print) | 978-3-319-29259-5 |

ISBN (Electronic) | 978-3-319-29261-8 |

DOIs | |

Publication status | Published - 7 Apr 2016 |

MoE publication type | A3 Book chapter |

### Publication series

Name | Lecture Notes in Physics |
---|---|

Publisher | Springer |

Volume | 921 |

ISSN (Print) | 0075-8450 |

### Fields of Science

- 112 Statistics and probability

### Cite this

*Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer*(Vol. 921, pp. 159-214). (Lecture Notes in Physics; Vol. 921). Springer. https://doi.org/10.1007/978-3-319-29261-8_4

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*Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer.*vol. 921, Lecture Notes in Physics, vol. 921, Springer, pp. 159-214. https://doi.org/10.1007/978-3-319-29261-8_4

**Kinetic theory of phonons in weakly anharmonic particle chains.** / Lukkarinen, Jani.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Scientific › peer-review

TY - CHAP

T1 - Kinetic theory of phonons in weakly anharmonic particle chains

AU - Lukkarinen, Jani

PY - 2016/4/7

Y1 - 2016/4/7

N2 - The aim of the chapter is to develop the kinetic theory of phonons in classical particle chains to a point which allows comparing the kinetic theory of normally conducting chains, with an anharmonic pinning potential, to the kinetic theory of the anomalously conducting FPU chains. In addition to reviewing the related literature, the chapter contains a streamlined derivation of the phonon Boltzmann collision operators using Wick polynomials, as well as details about the estimates which are needed to study the effect of the collision operator. This includes explicit solutions of the collisional constraints, both with and without harmonic pinning. We also recall in detail the derivation of the Green–Kubo formula for thermal conductivity in these systems, and the relation between entropy and the Boltzmann H-theorem for the phonon Boltzmann equations. The focus is in systems which are spatially translation invariant perturbations of thermal equilibrium states. We apply the results to obtain detailed predictions from kinetic theory for the Green–Kubo correlation functions, and hence the thermal conductivities, of the chain with a quartic pinning potential as well as the standard FPU-β chain.

AB - The aim of the chapter is to develop the kinetic theory of phonons in classical particle chains to a point which allows comparing the kinetic theory of normally conducting chains, with an anharmonic pinning potential, to the kinetic theory of the anomalously conducting FPU chains. In addition to reviewing the related literature, the chapter contains a streamlined derivation of the phonon Boltzmann collision operators using Wick polynomials, as well as details about the estimates which are needed to study the effect of the collision operator. This includes explicit solutions of the collisional constraints, both with and without harmonic pinning. We also recall in detail the derivation of the Green–Kubo formula for thermal conductivity in these systems, and the relation between entropy and the Boltzmann H-theorem for the phonon Boltzmann equations. The focus is in systems which are spatially translation invariant perturbations of thermal equilibrium states. We apply the results to obtain detailed predictions from kinetic theory for the Green–Kubo correlation functions, and hence the thermal conductivities, of the chain with a quartic pinning potential as well as the standard FPU-β chain.

KW - 112 Statistics and probability

U2 - 10.1007/978-3-319-29261-8_4

DO - 10.1007/978-3-319-29261-8_4

M3 - Chapter

SN - 978-3-319-29259-5

VL - 921

T3 - Lecture Notes in Physics

SP - 159

EP - 214

BT - Thermal transport in low dimensions

A2 - Lepri, Stefano

PB - Springer

ER -