scholarly journals Diffusive Behaviour of the Equilibrium Fluctuations in the Asymmetric Exclusion Processes

2019 ◽  
Author(s):  
Claudio Landim ◽  
Stefano Olla ◽  
Srinivasa R. S. Varadhan
Keyword(s):  
Exclusion Processes ◽  
Equilibrium Fluctuations ◽  
Asymmetric Exclusion ◽  
Asymmetric Exclusion Processes ◽  
Diffusive Behaviour

ASYMMETRIC EXCLUSION PROCESSES ON LATTICES WITH A JUNCTION: THE EFFECT OF UNEQUAL INJECTION RATES

2009 ◽  
Vol 20 (06) ◽  
pp. 967-978 ◽  
Author(s):  
XIONG WANG ◽  
RUI JIANG ◽  
KATSUHIRO NISHINARI ◽  
MAO-BIN HU ◽  
QING-SONG WU
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Exclusion Processes ◽  
Asymmetric Exclusion ◽  
Asymmetric Exclusion Processes ◽  
Injection Rates

Asymmetric exclusion processes (ASEP) on lattices with a junction, in which two or more parallel lattice branches combine into a single one, is important as a model for complex transport phenomena. This paper investigates the effect of unequal injection rates in ASEP with a junction. It is a generalization of the work of Pronina and Kolomeisky [J. Stat. Mech. P07010 (2005)], in which only equal injection rates are considered. It is shown that the unequal rates give rise to new phases and the phase diagram structure is qualitatively changed. The phase diagram and the density profiles are investigated by using Monte Carlo simulations, mean field approximation and domain wall approach. The analytical results are in good agreement with Monte Carlo simulations.

Zoned Inhomogeneity in Asymmetric Exclusion Processes with Random Update and Off-Ramp

2014 ◽  
Vol 1049-1050 ◽  
pp. 1586-1594
Author(s):  
Ya Fei Wang ◽  
Bing Qi Liu ◽  
Gang Yang ◽  
Xu Cao
Keyword(s):  
Theoretical Analysis ◽  
Phase Diagrams ◽  
Ramp Rate ◽  
Exclusion Processes ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
Asymmetric Exclusion ◽  
Asymmetric Exclusion Processes

In this letter, we investigate asymmetric simple exclusion processes (ASEPs) with zoned inhomogeneity and off-ramp by the means of theoretical analysis and simulations. According to the theoretical analysis, we can find that the phase diagrams existing in this one-lane system varies with different hopping rate p and off-ramp rate q and the condition for p<0.5 and p>0.5 is distinctly different . It should be noticed that LD/LD, LD/HD and MC/HD can exist in this system no matter how hopping rate p and off-ramp rate q change.

scholarly journals Integrable Stochastic Dualities and the Deformed Knizhnik–Zamolodchikov Equation

2018 ◽  
Vol 2020 (19) ◽  
pp. 5872-5925 ◽  
Author(s):  
Zeying Chen ◽  
Jan de Gier ◽  
Michael Wheeler
Keyword(s):  
Single Species ◽  
Integer Lattice ◽  
The Self ◽  
New Method ◽  
Exclusion Processes ◽  
Asymmetric Exclusion ◽  
Special Case ◽  
Asymmetric Exclusion Processes ◽  
Zamolodchikov Equation

Abstract We present a new method for obtaining duality functions in multi-species asymmetric exclusion processes (mASEP), from solutions of the deformed Knizhnik–Zamolodchikov (KZ) equations. Our method reproduces, as a special case, duality functions for the self-dual single species ASEP on the integer lattice.

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