### 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 |
---|---|

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

**Anomalous kinetics and transport from 1D self-consistent mode-coupling theory.** / Delfini, Luca; Lepri, Stefano; Livi, Roberto; Politi, Antonio.

Research output: Contribution to journal › Article

*Journal of statistical mechanics-Theory and experiment*, vol. 2007, P02007. https://doi.org/10.1088/1742-5468/2007/02/P02007

}

TY - JOUR

T1 - Anomalous kinetics and transport from 1D self-consistent mode-coupling theory

AU - Delfini, Luca

AU - Lepri, Stefano

AU - Livi, Roberto

AU - Politi, Antonio

PY - 2007/12

Y1 - 2007/12

N2 - 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.

AB - 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.

KW - transport processes

KW - heat transfer ( theory)

KW - heat-conduction

KW - thermal-conductivity

KW - dimensional lattices

KW - diffusion

KW - dynamics

KW - relaxation

KW - systems

KW - chains

KW - tails

U2 - 10.1088/1742-5468/2007/02/P02007

DO - 10.1088/1742-5468/2007/02/P02007

M3 - Article

VL - 2007

JO - Journal of statistical mechanics-Theory and experiment

JF - Journal of statistical mechanics-Theory and experiment

SN - 1742-5468

M1 - P02007

ER -