Lyapunov Exponents from Kinetic Theory for a Dilute, Field-Driven Lorentz Gas
- Institute for Theoretical Physics, University of Utrecht, Postbus 80006, 3508 TA Utrecht (The Netherlands)
Positive and negative Lyapunov exponents for a dilute, random, two-dimensional Lorentz gas in an applied field, {ital E{searrow}}, in a steady state at constant energy are computed to order {ital E}{sup 2}. The results are {lambda}{sub {plus_minus}}={lambda}{sub {plus_minus}}{sup 0}{minus}{ital a}{sub {plus_minus}}({ital qE}/{ital mv}){sup 2}{ital t}{sub 0} where {lambda}{sub {plus_minus}}{sup 0} are the exponents for the field-free Lorentz gas, {ital a}{sub +}=11/48, {ital a}{sub {minus}}=7/48, {ital t}{sub 0} is the mean free time between collisions, {ital q} is the charge, {ital m} is the mass, and {ital v} is the speed of the particle. The calculation is based on an extended Boltzmann equation in which a radius of curvature, characterizing the separation of two nearby trajectories, is one of the variables in the distribution function. The analytical results are in excellent agreement with computer simulations. {copyright} {ital 1996 The American Physical Society.}
- DOE Contract Number:
- FG02-88ER13847
- OSTI ID:
- 383282
- Journal Information:
- Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 10 Vol. 77; ISSN 0031-9007; ISSN PRLTAO
- Country of Publication:
- United States
- Language:
- English
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