The Asymmetri Ex lusion Pro ess An Integrable

Description

The Asymmetri Ex lusion Pro ess : An Integrable Model for Non-Equilibrium Statisti al Me hani s Kirone Malli k Institut de Physique Théorique, CEA Sa lay (Fran e)

• intera ting


• pro ess


• asymmetri ex lusion


• markov equation


• ex lusion pro


• brownian motors


• matrix ansatz

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 7
• Langue: English

Extrait

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x L SITES
N PARTICLES
L
Ω =
( )
N
CONFIGURATIONS
x asymmetry parameter
P (x ,...,x ) 1≤x <...<x ≤L t
t 1 N 1 N
X
dP
t
= [P (x ,...,x −1,...,x )−P (x ,...,x ,...x )] =MP
t 1 i N t 1 i N t
dt
i
(x = 0) x <x −1.
i−1 i
tov:EquationtheMarkattimeforoofProb.The.sumisASEP
L
X
1+x 1+x
+ − − + z z
M = S S +xS S + S S −
l l+1
l l+1 l l+1
4 4
l=1
Mψ =Eψ
−1
• E = 0 P = Ω
• ℜ(E)< 0
x=0
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L T ∼L
•
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z ,...z
1 N

x j−x
j j
2 (z +1)
i
ψ(x ,...,x ) = det 1≤i,j≤N
1 N
j
(z −1)
i
P
1
• ψ E = (−N+ z )
j
j
2
• (x =x −1).
k−1 k
•
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Y
z −1
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N L−N L
(1−z ) (1+z ) =−2 i = 1,...N
i i
z +1
j
j=1
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• Y (1−z ) (1+z ) =Y .
i i
• N z ,...z L
c(1) c(N)
c :{c(1),...,c(N)}⊂{1,...,L}.
• A (Y) =Y
c
N
Y
z −1
c(j)
L
A (Y) =−2 .
c
z +1
c(j)
j=1
• Y z
c(j)
c
N
X
2E (Y) =−N + z .
c
c(j)
j=1
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