Behavior at small distances and low temperatures of the ion-ion distribution function of the two-dimensional Coulomb gas |
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Authors: | Michel Lavaud |
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Institution: | (1) Groupe de Recherche sur l'Énergétique des Milieux Ionisés (GREMI), UA 831, UFR Faculté des Sciences, 45067 Orleans, France |
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Abstract: | We compute upper and lower bounds for the canonical ion-ion distribution functiong
11
(N)
(r) of the two-dimensional Coulomb gas for smallr and 1<<2, where is the plasma parameter. Both bounds are proportional tor
2-/(-1), which proves thatg
11
(N)
(r) behaves asr
2-, as conjectured by Hansen and Viot. We conjecture that, in the thermodynamic limit,g
11(r) ~ 2(-1)-1(r/a)2-, wherea=(n)–1/2 is the mean interionic distance. We also compute the canonical one-body distribution function with one pair (+,–) in a disk, for anyr and any. |
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Keywords: | Two dimensions Coulomb gas point ions point electrons distribution function small distances low temperatures |
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