%0 Book Section %1 statphys23_0356 %A Lukkarinen, J. %A Spohn, H. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K boltzmann chain conductivity equation fpu-beta kinetic phonon statphys23 theory thermal topic-3 %T Anomalous energy transport in the FPU-$\beta$ chain %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=356 %X We employ kinetic theory to study energy transport properties in the Fermi-Pasta-Ulam-$\beta$ (FPU-$\beta$) chain. A definite Boltzmann-Peierls phonon transport equation can be identified with a kinetic scaling limit of the chain. This allows connecting the current correlation function of the Green-Kubo formula for thermal conductivity with the linearized collision operator of the phonon Boltzmann equation. As shown in the joint work with Kenichiro Aoki K. Aoki, J. Lukkarinen, and H. Spohn, J.\ Stat.\ Phys.\ 124 (2006) 1105--1129 (cond-mat/0602082), such an application of the kinetic theory yields a finite thermal conductivity for quartic on-site perturbations, and the actual value agrees reasonably well with molecular dynamics simulations. In contrast, for the FPU-$\beta$ chain the kinetic theory predicts an infinite conductivity: by a rigorous analysis of the linearized collision operator, we show that the energy current correlations decay as $t^-3/5$ on the kinetic time scale, which leads to a divergent time-integral. This joint work with Herbert Spohn is described in detail in J. Lukkarinen and H. Spohn, Anomalous energy transport in the FPU-$\beta$ chain, in preparation.

@incollection{statphys23_0356, abstract = {We employ kinetic theory to study energy transport properties in the Fermi-Pasta-Ulam-$\beta$ (FPU-$\beta$) chain. A definite Boltzmann-Peierls phonon transport equation can be identified with a kinetic scaling limit of the chain. This allows connecting the current correlation function of the Green-Kubo formula for thermal conductivity with the linearized collision operator of the phonon Boltzmann equation. As shown in the joint work with Kenichiro Aoki [K. Aoki, J. Lukkarinen, and H. Spohn, J.\ Stat.\ Phys.\ {\bf 124} (2006) 1105--1129 (cond-mat/0602082)], such an application of the kinetic theory yields a finite thermal conductivity for quartic on-site perturbations, and the actual value agrees reasonably well with molecular dynamics simulations. In contrast, for the FPU-$\beta$ chain the kinetic theory predicts an infinite conductivity: by a rigorous analysis of the linearized collision operator, we show that the energy current correlations decay as $t^{-3/5}$ on the kinetic time scale, which leads to a divergent time-integral. This joint work with Herbert Spohn is described in detail in [J. Lukkarinen and H. Spohn, Anomalous energy transport in the FPU-$\beta$ chain, in preparation].}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Lukkarinen, J. and Spohn, H.}, biburl = {https://www.bibsonomy.org/bibtex/217889ef79a9e9e8fa288826b69b9a736/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {a4cb665ca527e9497335d5c7eadef8bb}, intrahash = {17889ef79a9e9e8fa288826b69b9a736}, keywords = {boltzmann chain conductivity equation fpu-beta kinetic phonon statphys23 theory thermal topic-3}, month = {9-13 July}, timestamp = {2007-06-20T10:16:18.000+0200}, title = {Anomalous energy transport in the FPU-$\beta$ chain}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=356}, year = 2007 }