scholarly journals Numerical Estimation of the Current Large Deviation Function in the Asymmetric Simple Exclusion Process with Open Boundary Conditions

2011 ◽  
Vol 80 (11) ◽  
pp. 114001 ◽  
Author(s):  
Tetsuya Mitsudo ◽  
Shinji Takesue
Keyword(s):  
Large Deviation ◽  
Exclusion Process ◽  
Open Boundary ◽  
Numerical Estimation ◽  
Open Boundary Conditions ◽  
Deviation Function ◽  
Simple Exclusion Process ◽  
Large Deviation Function ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion

THEORETICAL INVESTIGATION OF SYNCHRONOUS TOTALLY ASYMMETRIC EXCLUSION PROCESSES ON LATTICES WITH A SHORTCUT

2010 ◽  
Vol 24 (28) ◽  
pp. 5539-5546 ◽  
Author(s):  
SONG XIAO ◽  
JIU-JU CAI ◽  
FEI LIU ◽  
MINGZHE LIU
Keyword(s):  
Phase Diagram ◽  
Exclusion Process ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Exclusion Processes ◽  
Density Profiles ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
Asymmetric Exclusion Processes ◽  
Good Agreement

In this paper, a synchronous totally asymmetric simple exclusion process (TASEP) with a shortcut under open boundary conditions is investigated. The shortcut is located in the bulk and characterized by shortcut probability q. The phase diagram and density profiles of the model are obtained. It is found that the phase diagram of the model includes three regions, similar to the normal synchronous TASEP. Interestingly, the phase diagram does not change with q. Monte Carlo simulations are used to obtain the bulk density of different phases and they are in good agreement with the approximate stationary state solutions of the model.

scholarly journals Mapping TASEP back in time

2021 ◽  
Author(s):  
Leonid Petrov ◽  
Axel Saenz
Keyword(s):  
Markov Process ◽  
Continuous Time ◽  
Exclusion Process ◽  
Discrete Space ◽  
Baxter Equation ◽  
Simple Exclusion Process ◽  
Open Questions ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
Hammersley Process

AbstractWe obtain a new relation between the distributions $$\upmu _t$$ μ t at different times $$t\ge 0$$ t ≥ 0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions $$\upmu _t$$ μ t backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving $$\upmu _t$$ μ t which in turn brings new identities for expectations with respect to $$\upmu _t$$ μ t . The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang–Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.

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