Ergodicity and Energy Distributions for Some Boundary Driven Integrable Hamiltonian Chains |
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Authors: | Peter Balint Kevin K Lin Lai-Sang Young |
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Institution: | (1) Department of Math., SUNY at New Paltz, New Paltz, NY 12561, USA;(2) Courant Institute of Math. Science, 251 Mercer St., New York, NY 10012, USA |
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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. |
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Keywords: | |
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