On the distribution of free path lengths for the periodic Lorentz gas

Jean Bourgain; François Golse; Bernt Wennberg

doi:10.1007/s002200050249

On the distribution of free path lengths for the periodic Lorentz gas

Jean Bourgain
, François Golse
, Bernt Wennberg

Institute for Advanced Study
Laboratoire de Probabilités et Modèles Aléatoires
Chalmers University of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

Consider the domain Zε = {x ∈ Rⁿ dist(x, εZⁿ) > εγ}, and let the free path length be defined as τε(x, ω) = inf {t > 0 | x - tω ∈ Zε} . The distribution of values of τε is studied in the limit as ε → 0 for all γ ≥ 1. It is shown that the value γ_c = n/n-1 is critical for this problem: in other words, the limiting behavior of τε depends only on whether γ is larger or smaller than γ_c.

Original language	English
Pages (from-to)	491-508
Number of pages	18
Journal	Communications in Mathematical Physics
Volume	190
Issue number	3
DOIs	https://doi.org/10.1007/s002200050249
Publication status	Published - 1 Jan 1998
Externally published	Yes

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title = "On the distribution of free path lengths for the periodic Lorentz gas",

abstract = "Consider the domain Zε = \{x ∈ Rn dist(x, εZn) > εγ\}, and let the free path length be defined as τε(x, ω) = inf \{t > 0 | x - tω ∈ Zε\} . The distribution of values of τε is studied in the limit as ε → 0 for all γ ≥ 1. It is shown that the value γc = n/n-1 is critical for this problem: in other words, the limiting behavior of τε depends only on whether γ is larger or smaller than γc.",

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AU - Golse, François

AU - Wennberg, Bernt

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N2 - Consider the domain Zε = {x ∈ Rn dist(x, εZn) > εγ}, and let the free path length be defined as τε(x, ω) = inf {t > 0 | x - tω ∈ Zε} . The distribution of values of τε is studied in the limit as ε → 0 for all γ ≥ 1. It is shown that the value γc = n/n-1 is critical for this problem: in other words, the limiting behavior of τε depends only on whether γ is larger or smaller than γc.

AB - Consider the domain Zε = {x ∈ Rn dist(x, εZn) > εγ}, and let the free path length be defined as τε(x, ω) = inf {t > 0 | x - tω ∈ Zε} . The distribution of values of τε is studied in the limit as ε → 0 for all γ ≥ 1. It is shown that the value γc = n/n-1 is critical for this problem: in other words, the limiting behavior of τε depends only on whether γ is larger or smaller than γc.

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DO - 10.1007/s002200050249

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JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

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On the distribution of free path lengths for the periodic Lorentz gas

Abstract

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