Nonequilibrium steady states for certain Hamiltonian models

Kevin K. Lin, Lai-Sang Young

Research output: Contribution to journalArticle

Abstract

We report the results of a numerical study of nonequilibrium steady states for a class of Hamiltonian models. In these models of coupled matter-energy transport, particles exchange energy through collisions with pinned-down rotating disks. In Commun. Math. Phys. 262, 237-267, 2006, Eckmann and Young studied 1D chains and showed that certain simple formulas give excellent approximations of energy and particle density profiles. Keeping the basic mode of interaction in Commun. Math. Phys. 262, 237-267, 2006, we extend their prediction scheme to a number of new settings: 2D systems on different lattices, driven by a variety of boundary (heat bath) conditions including the use of thermostats. Particle-conserving models of the same type are shown to behave similarly. The second half of this paper examines memory and finite-size effects, which appear to impact only minimally the profiles of the models tested in Commun. Math. Phys. 262, 237-267, 2006. We demonstrate that these effects can be significant or insignificant depending on the local geometry. Dynamical mechanisms are proposed, and in the case of directional bias in particle trajectories due to memory, correction schemes are derived and shown to give accurate predictions.

Original languageEnglish (US)
Pages (from-to)630-657
Number of pages28
JournalJournal of Statistical Physics
Volume139
Issue number4
DOIs
StatePublished - May 2010

Fingerprint

Nonequilibrium Steady State
Thermostat
Energy Transport
Rotating Disk
thermostats
Particle Trajectory
2-D Systems
Heat Bath
Finite Size Effects
particle trajectories
Prediction
Density Profile
rotating disks
profiles
predictions
Energy
Model
Numerical Study
baths
Collision

Keywords

  • Energy profiles
  • Finite-size effects
  • Hamiltonian models
  • Memory effects
  • Nonequilibrium steady states
  • Particle densities

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Nonequilibrium steady states for certain Hamiltonian models. / Lin, Kevin K.; Young, Lai-Sang.

In: Journal of Statistical Physics, Vol. 139, No. 4, 05.2010, p. 630-657.

Research output: Contribution to journalArticle

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