We consider the asymmetric simple exclusion process confined to the nonnegative integers with an open boundary at 0. The point 0 is connected to a reservoir where particles are injected and ejected at prescribed rates subject to the exclusion rule. We derive formulas for the transition probability as a function of time from states where initially there are m particles to states where there are n particles.
REFERENCES
1.
B.
Derrida
, M.
Evans
, V.
Hakim
, and V.
Pasquier
, “Exact solution of a 1D asymmetric exclusion model using a matrix formulation
,” J. Phys. A
26
, 1493
–1517
(1993
).2.
B.
Derrida
and A.
Gerschenfeld
, “Current fluctuations of the one dimensional symmetric simple exclusion process with step initial condition
,” J. Stat. Phys.
136
, 1
–15
(2009
).3.
P. L.
Krapivsky
, “Symmetric exclusion process with a localized source
,” Phys. Rev. E
86
, 041103
(2012
).4.
T. M.
Liggett
, Interacting Particle Systems
(Springer-Verlag
, New York
, 2005
).5.
G. M.
Schütz
, “Exact solution of the master equation for the asymmetric exclusion process
,” J. Stat. Phys.
88
, 427
–445
(1997
).6.
T.
Sasamoto
and L.
Williams
, “Combinatorics of the asymmetric exclusion process on a semi-infinite lattice
,” e-print arXiv:1204.1114.7.
H.
Spohn
, “Long range correlations for stochastic lattice gases in a non-equilibrium state
,” J. Phys. A
16
, 4275
–4291
(1983
).8.
C. A.
Tracy
and H.
Widom
, “Integral formulas for the asymmetric simple exclusion process
,” Commun. Math. Phys.
279
, 815
–844
(2008
).9.
C. A.
Tracy
and H.
Widom
, “Erratum to ‘Integral formulas for the asymmetric simple exclusion process’
,” Commun. Math. Phys.
304
, 875
–878
(2011
).10.
C. A.
Tracy
and H.
Widom
, “The Bose gas and asymmetric simple exclusion process on the half-line
,” J. Stat. Phys.
150
, 1
–12
(2013
).© 2013 AIP Publishing LLC.
2013
AIP Publishing LLC
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