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Theoretical and Mathematical Physics

Calculation of correlation functions in totally asymmetric exactly solvable models on a ring

N. M. Bogoliubov

Published Jun 1, 2013• 3 citations
Publisher
DOI
10.1007/s11232-013-0061-x

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A totally asymmetric exclusion process on a ring with ν nonconserved internal degrees of freedom, where particles hop forward with a rate that depends on their internal state, has been studied. We show, using a mapping of the model to a zero range process with ν different kinds of boxes, that steady-state weights can be written in a matrix product form and calculate the spatial correlations exactly. A comparison of the model with an equivalent conserved system reveals that unequal hopping rates of particles belonging to different internal states are responsible for the nontrivial correlations.
We consider the asymmetric simple exclusion process with Langmuir kinetics on a periodic lattice. We analytically obtain the exact time evolution of correlation functions with arbitrary length starting from the initial state with no particle in the system. The exact stationary state of this model has been known for the totally asymmetric case. We propose a basis transformation which simplifies the proof of the stationarity of this state and enables the generalization to the partially asymmetric case. Moreover, we construct low-energy excitations and obtain the exact relaxation time.