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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	491-508
Nombre de pages	18
journal	Communications in Mathematical Physics
Volume	190
Numéro de publication	3
Les DOIs	https://doi.org/10.1007/s002200050249
état	Publié - 1 janv. 1998
Modification externe	Oui

Accès au document

10.1007/s002200050249

Contient cette citation

@article{843a001f50e34afe9f1c585fb258bfc5,

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.",

author = "Jean Bourgain and Fran{\c c}ois Golse and Bernt Wennberg",

year = "1998",

month = jan,

day = "1",

doi = "10.1007/s002200050249",

language = "English",

volume = "190",

pages = "491--508",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

number = "3",

}

TY - JOUR

T1 - On the distribution of free path lengths for the periodic Lorentz gas

AU - Bourgain, Jean

AU - Golse, François

AU - Wennberg, Bernt

PY - 1998/1/1

Y1 - 1998/1/1

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.

U2 - 10.1007/s002200050249

DO - 10.1007/s002200050249

M3 - Article

AN - SCOPUS:0032326766

SN - 0010-3616

VL - 190

SP - 491

EP - 508

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -

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

Résumé

Accès au document

Empreinte digitale

Contient cette citation