DSpace Repository :: Browsing Articles by Subject "Bethe ansatz"

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Open Access
INTEGRABILITY OF THE MULTI-SPECIES TASEP WITH SPECIES-DEPENDENT RATES
(MDPI, 2021-08-27) Lee, Eunghyun
Assume that each species l has its own jump rate bl in the multi-species totally asymmetric simple exclusion process. We show that this model is integrable in the sense that the Bethe ansatz method is applicable to obtain the transition probabilities for all possible N-particle systems with up to N different species.
Open Access
On the TASEP with Second Class Particles
(National Academy of Science of Ukraine, 2018-01-18) Lee, Eunghyun
In this paper we study some conditional probabilities for the totally asymmetric simple exclusion processes (TASEP) with second class particles. To be more specific, we consider a finite system with one first class particle and N−1 second class particles, and we assume that the first class particle is initially at the leftmost position. In this case, we find the probability that the first class particle is at x and it is still the leftmost particle at time t. In particular, we show that this probability is expressed by the determinant of an N×N matrix of contour integrals if the initial positions of particles satisfy the step initial condition. The resulting formula is very similar to a known formula in the (usual) TASEP with the step initial condition which was used for asymptotics by Nagao and Sasamoto [Nuclear Phys. B 699 (2004), 487-502].