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SUMMARY:Integrability of a deterministic cellular automaton driven by stoc
 hastic boundaries - Tomaz Prosen (University of Ljubljana  )
DTSTART:20160113T150000Z
DTEND:20160113T160000Z
UID:TALK64628@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We propose an interacting many-body space-time-discrete Markov
  chain model\,  which is composed of an integrable deterministic and rever
 sible 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 man
 y-body Markov chain is proven for  generic values of bath parameters\, imp
 lying existence of a unique  non-equilibrium steady state. The latter is c
 onstructed 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 co
 nservation laws. Feasibility of an exact solution for  the full spectrum a
 nd 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 integ
 rability of boundary driven classical deterministic lattice systems.
LOCATION:Seminar Room 1\, Newton Institute
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