Time-dependent matrix product ansatz for interacting reversible dynamics

I will present an explicit time-dependent matrix product ansatz (tMPA), which describes the time-evolution of any local observable in an interacting and deterministic lattice gas, specifically for the "Rule 54" reversible cellular automaton. The construction is based on an explicit solution of real-space real-time inverse scattering problem. After introducing the model, and sketching the idea of the construction, I will touch upon two physical applications of this tMPA. First, it can be used to find an exact and explicit form for the dynamic structure factor. Second, it is used to solve the extremal case of the inhomogeneous quench problem, where a semi-infinite lattice in the maximum entropy state is joined with an empty semi-infinite lattice. Both of these results rigorously demonstrate a coexistence of ballistic and diffusive transport behaviour in the model.

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