Integrability of a deterministic cellular automaton driven by stochastic boundaries
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| Description: |
Prosen, T (University of Ljubljana)
Wednesday 13th January 2016 - 15:00 to 16:00 |
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| Created: | 2016-01-25 15:08 |
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| Collection: | Mathematical Aspects of Quantum Integrable Models in and out of Equilibrium |
| Publisher: | Isaac Newton Institute |
| Copyright: | Prosen, T |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | We propose an interacting many-body space-time-discrete Markov chain model, which is composed of an integrable deterministic and reversible cellular automaton (the rule 54 of [Bobenko et al, CMP 158, 127 (1993)]) on a finite one-dimensional lattice Z_2^n, and local stochastic Markov chains at the two lattice boundaries which provide chemical baths for absorbing or emitting the solitons. Ergodicity and mixing of this many-body Markov chain is proven for generic values of bath parameters, implying existence of a unique non-equilibrium steady state. The latter is constructed exactly and explicitly in terms of a particularly simple form of matrix product ansatz which is termed a patch ansatz. This gives rise to an explicit computation of observables and k-point correlations in the steady state as well as the construction of a nontrivial set of local conservation laws. Feasibility of an exact solution for the full spectrum and eigenvectors (decay modes) of the Markov matrix is sug gested as well. We conjecture that our ideas can pave the road towards a theory of integrability of boundary driven classical deterministic lattice systems. |
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