Arvind Ayyer and Kirone Mallick 2010 J. Phys. A: Math. Theor. 43 045003 doi:10.1088/1751-8113/43/4/045003
Exact results for an asymmetric annihilation process with open boundaries
FREE ARTICLEArvind Ayyer and Kirone Mallick
Show affiliationsWe consider a nonequilibrium reaction–diffusion model on a finite one-dimensional lattice with bulk and boundary dynamics inspired by the Glauber dynamics of the Ising model. We show that the model has a rich algebraic structure that we use to calculate its properties. In particular, we show that the Markov dynamics for a system of a given size can be embedded into the dynamics of systems of higher sizes. This remark leads us to devise a technique which we call the transfer matrix Ansatz that allows us to determine the steady-state distribution and correlation functions. Furthermore, we show that the disorder variables satisfy very simple properties and we give a conjecture for the characteristic polynomial of Markov matrices. Finally, we compare the transfer matrix Ansatz used here with the matrix product representation of the steady state of one-dimensional stochastic models.
- PACS
- MSC
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11C20 Matrices, determinants (See also 15A36)
60J05 Markov processes with discrete parameter
82C26 Dynamic and nonequilibrium phase transitions (general)
82C44 Dynamics of disordered systems (random Ising systems, etc.)
- Subjects
- Dates
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Issue 4 (29 January 2010)
Received 6 October 2009, in final form 3 December 2009
Published 4 January 2010
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Exact results for an asymmetric annihilation process with open boundaries
Arvind Ayyer and Kirone Mallick 2010 J. Phys. A: Math. Theor. 43 045003
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