### Abstract

We study heat transport in a chain of harmonic oscillators with random elastic collisions between nearest-neighbours. The equations of motion of the covariance matrix are numerically solved for free and fixed boundary conditions. In the thermodynamic limit, the shape of the temperature profile and the value of the stationary heat flux depend on the choice of boundary conditions. For free boundary conditions, they also depend on the coupling strength with the heat baths. Moreover, we find a strong violation of local equilibrium at the chain edges that determine two boundary layers of size root N (where N is the chain length) that are characterized by a different scaling behaviour from the bulk. Finally, we investigate the relaxation towards the stationary state, finding two long time scales: the first corresponds to the relaxation of the hydrodynamic modes; the second is a manifestation of the finiteness of the system.

Original language | English |
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Article number | 145001 |

Number of pages | 16 |

Journal | Journal of Physics. A, Mathematical and theoretical |

Volume | 43 |

Issue number | 14 |

DOIs | |

Publication status | Published - 9 Apr 2010 |

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*Journal of Physics. A, Mathematical and theoretical*,

*43*(14), [145001]. https://doi.org/10.1088/1751-8113/43/14/145001

**Nonequilibrium dynamics of a stochastic model of anomalous heat transport : numerical analysis.** / Delfini, L.; Lepri, S.; Livi, R.; Mejia-Monasterio, C.; Politi, A.

Research output: Contribution to journal › Article

*Journal of Physics. A, Mathematical and theoretical*, vol. 43, no. 14, 145001. https://doi.org/10.1088/1751-8113/43/14/145001

}

TY - JOUR

T1 - Nonequilibrium dynamics of a stochastic model of anomalous heat transport

T2 - numerical analysis

AU - Delfini, L.

AU - Lepri, S.

AU - Livi, R.

AU - Mejia-Monasterio, C.

AU - Politi, A.

PY - 2010/4/9

Y1 - 2010/4/9

N2 - We study heat transport in a chain of harmonic oscillators with random elastic collisions between nearest-neighbours. The equations of motion of the covariance matrix are numerically solved for free and fixed boundary conditions. In the thermodynamic limit, the shape of the temperature profile and the value of the stationary heat flux depend on the choice of boundary conditions. For free boundary conditions, they also depend on the coupling strength with the heat baths. Moreover, we find a strong violation of local equilibrium at the chain edges that determine two boundary layers of size root N (where N is the chain length) that are characterized by a different scaling behaviour from the bulk. Finally, we investigate the relaxation towards the stationary state, finding two long time scales: the first corresponds to the relaxation of the hydrodynamic modes; the second is a manifestation of the finiteness of the system.

AB - We study heat transport in a chain of harmonic oscillators with random elastic collisions between nearest-neighbours. The equations of motion of the covariance matrix are numerically solved for free and fixed boundary conditions. In the thermodynamic limit, the shape of the temperature profile and the value of the stationary heat flux depend on the choice of boundary conditions. For free boundary conditions, they also depend on the coupling strength with the heat baths. Moreover, we find a strong violation of local equilibrium at the chain edges that determine two boundary layers of size root N (where N is the chain length) that are characterized by a different scaling behaviour from the bulk. Finally, we investigate the relaxation towards the stationary state, finding two long time scales: the first corresponds to the relaxation of the hydrodynamic modes; the second is a manifestation of the finiteness of the system.

U2 - 10.1088/1751-8113/43/14/145001

DO - 10.1088/1751-8113/43/14/145001

M3 - Article

VL - 43

JO - Journal of Physics. A, Mathematical and theoretical

JF - Journal of Physics. A, Mathematical and theoretical

SN - 1751-8113

IS - 14

M1 - 145001

ER -