Kinetic theory of phonons in weakly anharmonic particle chains

Tutkimustuotos: Artikkeli kirjassa/raportissa/konferenssijulkaisussaKirjan luku tai artikkeliTieteellinenvertaisarvioitu

Kuvaus

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.
Alkuperäiskielienglanti
OtsikkoThermal transport in low dimensions : from statistical physics to nanoscale heat transfer
ToimittajatStefano Lepri
Sivumäärä56
Vuosikerta921
KustantajaSpringer
Julkaisupäivä7 huhtikuuta 2016
Sivut159-214
ISBN (painettu)978-3-319-29259-5
ISBN (elektroninen)978-3-319-29261-8
DOI - pysyväislinkit
TilaJulkaistu - 7 huhtikuuta 2016
OKM-julkaisutyyppiA3 Kirjan tai muun kokoomateoksen osa

Julkaisusarja

NimiLecture Notes in Physics
KustantajaSpringer
Vuosikerta921
ISSN (painettu)0075-8450

Tieteenalat

  • 112 Tilastotiede

Lainaa tätä

Lukkarinen, J. (2016). Kinetic theory of phonons in weakly anharmonic particle chains. teoksessa S. Lepri (Toimittaja), Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer (Vuosikerta 921, Sivut 159-214). (Lecture Notes in Physics; Vuosikerta 921). Springer. https://doi.org/10.1007/978-3-319-29261-8_4
Lukkarinen, Jani. / Kinetic theory of phonons in weakly anharmonic particle chains. Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer. Toimittaja / Stefano Lepri. Vuosikerta 921 Springer, 2016. Sivut 159-214 (Lecture Notes in Physics).
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title = "Kinetic theory of phonons in weakly anharmonic particle chains",
abstract = "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.",
keywords = "112 Statistics and probability",
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Lukkarinen, J 2016, Kinetic theory of phonons in weakly anharmonic particle chains. julkaisussa S Lepri (Toimittaja), Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer. Vuosikerta 921, Lecture Notes in Physics, Vuosikerta 921, Springer, Sivut 159-214. https://doi.org/10.1007/978-3-319-29261-8_4

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

Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer. toim. / Stefano Lepri. Vuosikerta 921 Springer, 2016. s. 159-214 (Lecture Notes in Physics; Vuosikerta 921).

Tutkimustuotos: Artikkeli kirjassa/raportissa/konferenssijulkaisussaKirjan luku tai artikkeliTieteellinenvertaisarvioitu

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PY - 2016/4/7

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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.

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Lukkarinen J. Kinetic theory of phonons in weakly anharmonic particle chains. julkaisussa Lepri S, toimittaja, Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer. Vuosikerta 921. Springer. 2016. s. 159-214. (Lecture Notes in Physics). https://doi.org/10.1007/978-3-319-29261-8_4