### Abstract

We consider systems of moving particles in 1-dimensional space interacting through energy storage sites. The ends of the systems are coupled to heat baths, and resulting steady states are studied. When the two heat baths are equal, an explicit formula for the (unique) equilibrium distribution is given. The bulk of the paper concerns nonequilibrium steady states, i.e., when the chain is coupled to two unequal heat baths. Rigorous results including ergodicity are proved. Numerical studies are carried out for two types of bath distributions. For chains driven by exponential baths, our main finding is that the system does not approach local thermodynamic equilibrium as system size tends to infinity. For bath distributions that are sharply peaked Gaussians, in spite of the near-integrable dynamics, transport properties are found to be more normal than expected.

Original language | English (US) |
---|---|

Pages (from-to) | 199-228 |

Number of pages | 30 |

Journal | Communications in Mathematical Physics |

Volume | 294 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2009 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*294*(1), 199-228. https://doi.org/10.1007/s00220-009-0918-x

**Ergodicity and energy distributions for some boundary driven integrable Hamiltonian chains.** / Balint, Peter; Lin, Kevin K.; Young, Lai-Sang.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 294, no. 1, pp. 199-228. https://doi.org/10.1007/s00220-009-0918-x

}

TY - JOUR

T1 - Ergodicity and energy distributions for some boundary driven integrable Hamiltonian chains

AU - Balint, Peter

AU - Lin, Kevin K.

AU - Young, Lai-Sang

PY - 2009/1

Y1 - 2009/1

N2 - We consider systems of moving particles in 1-dimensional space interacting through energy storage sites. The ends of the systems are coupled to heat baths, and resulting steady states are studied. When the two heat baths are equal, an explicit formula for the (unique) equilibrium distribution is given. The bulk of the paper concerns nonequilibrium steady states, i.e., when the chain is coupled to two unequal heat baths. Rigorous results including ergodicity are proved. Numerical studies are carried out for two types of bath distributions. For chains driven by exponential baths, our main finding is that the system does not approach local thermodynamic equilibrium as system size tends to infinity. For bath distributions that are sharply peaked Gaussians, in spite of the near-integrable dynamics, transport properties are found to be more normal than expected.

AB - We consider systems of moving particles in 1-dimensional space interacting through energy storage sites. The ends of the systems are coupled to heat baths, and resulting steady states are studied. When the two heat baths are equal, an explicit formula for the (unique) equilibrium distribution is given. The bulk of the paper concerns nonequilibrium steady states, i.e., when the chain is coupled to two unequal heat baths. Rigorous results including ergodicity are proved. Numerical studies are carried out for two types of bath distributions. For chains driven by exponential baths, our main finding is that the system does not approach local thermodynamic equilibrium as system size tends to infinity. For bath distributions that are sharply peaked Gaussians, in spite of the near-integrable dynamics, transport properties are found to be more normal than expected.

UR - http://www.scopus.com/inward/record.url?scp=72249106501&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=72249106501&partnerID=8YFLogxK

U2 - 10.1007/s00220-009-0918-x

DO - 10.1007/s00220-009-0918-x

M3 - Article

AN - SCOPUS:72249106501

VL - 294

SP - 199

EP - 228

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -