### Abstract

We study the dynamics of long-wavelength fluctuations in one-dimensional (1D) many-particle systems as described by self-consistent mode-coupling theory. The corresponding non-linear integro-differential equations for the relevant correlators are solved analytically and checked numerically. In particular, we find that the memory functions exhibit a power-law decay accompanied by relatively fast oscillations. Furthermore, the scaling behaviour and, correspondingly, the universality class depend on the order of the leading non-linear term. In the cubic case, both viscosity and thermal conductivity diverge in the thermodynamic limit. In the quartic case, a faster decay of the memory functions leads to a finite viscosity, while the thermal conductivity exhibits an even faster divergence. Finally, our analysis puts on a firmer basis the previously conjectured connection between anomalous heat conductivity and anomalous diffusion.

Original language | English |
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Article number | P02007 |

Number of pages | 17 |

Journal | Journal of statistical mechanics-Theory and experiment |

Volume | 2007 |

DOIs | |

Publication status | Published - Dec 2007 |

### Keywords

- transport processes
- heat transfer ( theory)
- heat-conduction
- thermal-conductivity
- dimensional lattices
- diffusion
- dynamics
- relaxation
- systems
- chains
- tails

### Cite this

*Journal of statistical mechanics-Theory and experiment*,

*2007*, [P02007]. https://doi.org/10.1088/1742-5468/2007/02/P02007