Tomaž Prosen – University of Ljubljana
Wednesday, November 19th, 2025
Zoom opens: 10:30AM EST
Seminar begins: 10:45AM EST
(Deformed) Rule 54: Unusual Integrable Model
I will discuss a fascinating example of exactly solvable reversible cellular automaton in 1+1 dimensions, the rule 54, and two of its deformations which turn the model into either quantum or stochastic cellular automaton.
Deterministic reversible rule 54 automaton provides a unique example of interacting particle dynamics with exactly solvable time automorphism of the algebra of local observables and consequently exactly solvable dynamical structure factor.
The (deformed) model can be interpreted as arguably the simplest integrable dynamics with interaction round-a-face. Both deformations, being parametrixed by an arbitrary unitary or stochastic 2x2 matrix, respectively, exhibit some features of integrability. The later (stochastic version) can be interpeted as a lattice discretization of deformed t-PNG (polynuclear growth) model. I will discuss the construction of non-trivial conservation laws of the quantum deformation and the matrix product form of the steady state of the boundary driven stochastic deformation.