We propose a general exact method of calculating dynamical correlation
functions in dual symplectic brick-wall circuits in one dimension. These are
deterministic classical many-body dynamical systems which can be interpreted in
terms of symplectic dynamics in two orthogonal (time and space) directions. In
close analogy with quantum dual-unitary circuits, we prove that two-point
dynamical correlation functions are non-vanishing only along the edges of the
light cones. The dynamical correlations are exactly computable in terms of a
one-site Markov transfer operator, which is generally of infinite
dimensionality. We test our theory in a specific family of dual-symplectic
circuits, describing the dynamics of a classical Floquet spin chain.
Remarkably, for these models, the rotational symmetry leads to a transfer
operator with a block diagonal form on the basis of spherical harmonics. This
allows us to obtain analytical predictions for simple local observables. We
demonstrate the validity of our theory by comparison with Montecarlo
simulations, displaying excellent agreement for different choices of
observables.Comment: 16 pages, 5 figure