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Infinite Ergodic Index of the Ehrenfest Wind-Tree Model

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The set of all possible configurations of the Ehrenfest wind-tree model endowed with the Hausdorff topology is a compact metric space. For a typical configuration we show that the wind-tree… Click to show full abstract

The set of all possible configurations of the Ehrenfest wind-tree model endowed with the Hausdorff topology is a compact metric space. For a typical configuration we show that the wind-tree dynamics has infinite ergodic index in almost every direction. In particular some ergodic theorems can be applied to show that if we start with a large number of initially parallel particles their directions decorrelate as the dynamics evolve, answering the question posed by the Ehrenfests.

Keywords: tree model; infinite ergodic; wind tree; ehrenfest wind; ergodic index

Journal Title: Communications in Mathematical Physics
Year Published: 2017

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