Field-dependent conductivity and diffusion in a two-dimensional Lorentz gas |
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Authors: | András Baranyai Denis J Evans E G D Cohen |
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Institution: | (1) Research School of Chemistry, Australian National University, GPO Box 4, ACT 2601 Canberra, Australia;(2) Present address: Laboratory of Theoretical Chemistry, Eötvos University, Múzeum krt 6-8, 1088 Budapest, Hungary;(3) Rockefeller University, 10021 New York, New York |
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Abstract: | The conductivity and diffusion of a color-charged two-dimensional thermostatted Lorentz gas in a color field is studied by a variety 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. |
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Keywords: | Conductivity diffusion field-dependence Lorentz gas Lyapunov exponents |
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