### Abstract

We consider a one-dimensional harmonic crystal with conservative noise, in contact with two stochastic Langevin heat baths at different temperatures. The noise term consists of collisions between neighbouring oscillators that exchange their momenta, with a rate gamma. The stationary equations for the covariance matrix are exactly solved in the thermodynamic limit (N -> infinity). In particular, we derive an analytical expression for the temperature profile, which turns out to be independent of gamma. Moreover, we obtain an exact expression for the leading term of the energy current, which scales as 1/root gamma N. Our theoretical results are finally found to be consistent with the numerical solutions of the covariance matrix for finite N.

Original language | English |
---|---|

Article number | 025001 |

Number of pages | 15 |

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

Volume | 42 |

Issue number | 2 |

DOIs | |

Publication status | Published - 16 Jan 2009 |

### Keywords

- harmonic crystal
- fouriers law
- conduction
- lattices
- reservoirs

### Cite this

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

*42*(2), [025001]. https://doi.org/10.1088/1751-8113/42/2/025001

**A stochastic model of anomalous heat transport : analytical solution of the steady state.** / Lepri, S.; Mejia-Monasterio, C.; Politi, A.

Research output: Contribution to journal › Article

*Journal of Physics. A, Mathematical and theoretical*, vol. 42, no. 2, 025001. https://doi.org/10.1088/1751-8113/42/2/025001

}

TY - JOUR

T1 - A stochastic model of anomalous heat transport

T2 - analytical solution of the steady state

AU - Lepri, S.

AU - Mejia-Monasterio, C.

AU - Politi, A.

PY - 2009/1/16

Y1 - 2009/1/16

N2 - We consider a one-dimensional harmonic crystal with conservative noise, in contact with two stochastic Langevin heat baths at different temperatures. The noise term consists of collisions between neighbouring oscillators that exchange their momenta, with a rate gamma. The stationary equations for the covariance matrix are exactly solved in the thermodynamic limit (N -> infinity). In particular, we derive an analytical expression for the temperature profile, which turns out to be independent of gamma. Moreover, we obtain an exact expression for the leading term of the energy current, which scales as 1/root gamma N. Our theoretical results are finally found to be consistent with the numerical solutions of the covariance matrix for finite N.

AB - We consider a one-dimensional harmonic crystal with conservative noise, in contact with two stochastic Langevin heat baths at different temperatures. The noise term consists of collisions between neighbouring oscillators that exchange their momenta, with a rate gamma. The stationary equations for the covariance matrix are exactly solved in the thermodynamic limit (N -> infinity). In particular, we derive an analytical expression for the temperature profile, which turns out to be independent of gamma. Moreover, we obtain an exact expression for the leading term of the energy current, which scales as 1/root gamma N. Our theoretical results are finally found to be consistent with the numerical solutions of the covariance matrix for finite N.

KW - harmonic crystal

KW - fouriers law

KW - conduction

KW - lattices

KW - reservoirs

U2 - 10.1088/1751-8113/42/2/025001

DO - 10.1088/1751-8113/42/2/025001

M3 - Article

VL - 42

JO - Journal of Physics. A, Mathematical and theoretical

JF - Journal of Physics. A, Mathematical and theoretical

SN - 1751-8113

IS - 2

M1 - 025001

ER -