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The wind-round-tree model and the two-dimensional Lorentz gas |
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| Authors: | J. Gü mez J. M. Cerver S. Velasco |
| Affiliation: | a Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Cantabria, 37001, Santander, Spain b Departamento de Física Teórica, Facultad de Ciencias, Universidad de Salamanca, 37008, Salamanca, Spain c Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Salamanca, 37008, Salamanca, Spain |
| Abstract: | In this Letter we establish the equivalence of the two-dimensional nonoverlapping Lorentz gas and the Ehrenfests' wind-tree model considering round (instead of square) trees. To obtain the Boltzmann equation for this latter model we use the infinite polygonal limit which turns out to be smooth and continuous. Finally we present the general solution of the Boltzmann equation which provides a simple discussion on the ergodicity of the model. |
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