Exponential growth of OTOC Sample Clauses

Exponential growth of OTOC. The defining feature of classically chaotic dynamics is the exponential sensitivity of the system on the initial conditions. Namely, an infinitesimal change in δqj(0) can result in exponentially diverging trajectories (1.12), known as the butterfly effect. For a Hamiltonian systems, where dynamics is encoded in Poisson brackets, this is defined by: i j ∂qi(t) δqi(t) λt ∂q δq |{q (t), p (0)}c| = j (0) ≈ j (0) ∼ e