Field-dependent conductivity and diffusion in a two-dimensional lorentz gas

Journal Article · Mon Mar 01 04:00:00 EST 1993 · Journal of Statistical Physics; (United States)

DOI:https://doi.org/10.1007/BF01049423· OSTI ID:6730751

Baranyai, A ^[1]; Evans, D J ^[2]; Cohen, E G.D. ^[3]

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1. Australian National Univ., Canberra (Australia) Eoetvos Univ. (Hungary)
2. Australian National Univ., Canberra (Australia)
3. Rockefeller Univ., New York (United States)

The conductivity and diffusion of a color-charged two-dimensional thermostatted Lorentz gas in a color field is studied by a varieyt of methods. In this gas, point particles move through a regular triangular array of soft scatterers, where, in the presence of a field, a nonequilibrium stationary state is reached by coupling to a Gaussian thermostat. The zero-field conductivity and diffusion coefficient are computed with equilibrium molecular dynamics dynamics from the Green-Kubo formula and the Einstein relation. Their values are consistent and approach those obtained by Machta and Zwanzig in the limit of hard (disk) scatterers. The field-dependent conductivity is obtained from its constitutive relation, from the coupling constant to the thermostat, and by using the recently derived conjugate pairing rule of Evans, Cohen, and Morriss, from the two maximal Lyapunov exponents of the Lorentz gas in the stationary state. All these methods give consistent results. Finally, elements of the field-dependent diffusion tensor have been computed. At zero field, they are consistent with the zero-field conductivity, but they vanish beyond a critical field strength, suggesting a dynamical phase transition at the critical field; the conductivity appears to remain finite, approaching a constant value for large field strengths.

• OSTI ID: 6730751
• Journal Information: Journal of Statistical Physics; (United States), Journal Name: Journal of Statistical Physics; (United States) Vol. 70:5-6; ISSN JSTPBS; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COLLISIONS
CRITICAL FIELD
DIFFUSION
DYNAMICS
EQUILIBRIUM
FIELD THEORIES
FLUIDS
FULLY IONIZED GASES
GASES
IONIZED GASES
LAGRANGIAN FIELD THEORY
LORENTZ GAS
MAGNETIC FIELDS
MECHANICS
PHYSICAL PROPERTIES
QUANTUM FIELD THEORY
TENSOR FIELDS
THERMAL CONDUCTIVITY
THERMODYNAMIC PROPERTIES
TWO-DIMENSIONAL CALCULATIONS