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arXiv · 1702.08096

On the free path length distribution for linear motion in an n-dimensional box

Samuel Holmin·Pär Kurlberg·Daniel Månsson
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Abstract

We consider the distribution of free path lengths, or the distance between consecutive bounces of random particles, in an n-dimensional rectangular box. If each particle travels a distance R, then, as R tends to infinity the free path lengths coincides with the distribution of the length of the intersection of a random line with the box (for a natural ensemble of random lines) and we give an explicit formula (piecewise real analytic) for the probability density function in dimension two and three. In dimension two we also consider a closely related model where each particle is allowed to bounce N times, as N tends to infinity, and give an explicit (again piecewise real analytic) formula for its probability density function. Further, in both models we can recover the side lengths of the box from the location of the discontinuities of the probability density functions.

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Samuel Holmin, Pär Kurlberg, Daniel Månsson. 2017-02-26. On the free path length distribution for linear motion in an n-dimensional box. https://doi.org/10.1088/1751-8121%2Faae5ee

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