Ergodicity and energy distributions for some boundary driven integrable Hamiltonian chains

Peter Balint, Kevin K. Lin, Lai Sang Young

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)199-228
Number of pages30
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - Jan 2009

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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